Can we take a little moment to appreciate the fact that they numbered their chapters beginning with zero (which is common in computer science, but not in every day life) and numbered the chapters in binary, just so they could better show off zero?
"0 is the absence of a value" how then could a chapter be represented as 0? Its great intention but it needs to beigin at 1 . Zero should only be used if there are no chapters. 0 chapters, chapter 1 cant just be called chapter 0. Its not cute lol
A huge thankyou to the person who translated this video into Spanish! We like to think that mathematics is something of a universal language, but English is certainly not. If you can speak another language and want to help share this video with a wider audience, you can contribute subtitles here: ua-cam.com/users/timedtext_video?ref=share&v=9Y7gAzTMdMA
*Zero was actually invented in china later copied by others, Chinese kept secret of silk, number system, paper, printing stamp, and gun powder so it didn't come out* *Persian and arab traders spread it to others through silk route*
Emptiness, void, nothingness and Shunya are deeply philosophical concepts that ancient Hindus gave considerable thought and importance. In Hinduism everything seems to have originated from a void or a point which eventually took the shape of a number 0. So in many ways Zero is also a concept and an idea even before it is a number.
Brilliant! Absolutely mind blowing video! Shoutouts to the creators who made this! I was absolutely blown away! I had the same problem of deviding by zero in a world where zero literally can be more that a negative and less than 1. Zero is fascinating and this video absolutely peaked my interest! I'll keep my crazy words here but you nailed it on this video and it's been a pleasure! Truly has! I might hit subscribe if you have more about this?
Thank you Dr. Fry. This has been a great video to share with Year 5 as we have been looking at mathematics though history and its contribution to modern life. After looking at calculating with earlier number systems, I know that they appreciate zero much more now.
@@elliotgale470 numbers are defined while infinity is not defined. In real life anything that has a specific measurement is a number, while infinity has no specific measurement, therefore it's not a number.
That quote within itself also pretty much means 0 is a concept. Which this video I think was trying not to do. Seems pretty contradictory. Can’t divide by 0 because infinite is just a concept and we can’t comprehend. But for some reason people have no issue comprehending nothing.
NOTE FOR AMERICAN VIEWERS: 2:33 By "Roman Empire", she means Byzantium, the eastern empire that survived for centuries after the fall of Rome. Although Byzantium had once belonged to Rome, it was Greek-speaking and had a somewhat different culture, and was influenced at first by Persia and later the Islamic empires.
"Byzantine" is a late term coined by historians. Nobody used the term "byzantine" as a selfdesignation back then. But Romanoi ("roman citizen"), but still hold onto their non-roman ethnicity. Roman Empire was, like every empire, multi-ethnical. So no; the eastern Roman Empire was not _only_ "greek speaking". But inhabited by many different folks that spoke different languages/dielects. Greek was the lingua franca, the language of the elite, ruling class. That means: Church + royalty. Byzantine is just used by historians to divide the Roman Empire to East (konstantinople)/West (milano, rome). The lingua francas of the Roman Empire were not only latin but also greek. Which a lot ppl clearly forget (or don't know). Latin f.e. vocabulary is full of loanwords from ancient greek. Latin also borrowed from etruscan, celtic, semitic and other (still spoken and extinct) languages - so did also greeks. They were always in contact with other folks. But since the roman empire, that lasted a *very* long time and caused a lot extinctions of languages - we'll never know from where many words actually really came from. Also: there was no "islamic empire" in Greece. You mean probably the Ottoman "Empire" (the invading turkic tribe). But Ottoman "Empire" was actually not an _empire._
Thanks for this beautiful upload, but I require a bit of enlightenment, if you please! I trust this video is primarily based on Charles Seife's 'Zero: The Biography of a Dangerous Idea'. Was a little flummoxed to find many a people attribute its invention to Aryabhata, when his book indeed says what you said, Professor Fry: many civilisations have invented a vague concept of zero on their own volition, but it was the Indian mathematician who popularised the same. On the other facet, the book emphatically affirms, which obviously sounds quite a logical claim, that it's none but Babylonians-people who hail from a place often regarded as the 'cradle of civilisation'-who invented the idea of zero. Is there a veracity in this claim, Professor Fry?
If you have one chicken and you divide it among nothing, you have everything that is there of it - the things you are aware of and can count, as also the things you are not aware of and so can not count. Everything is a concept, not a number.
@@gauravmshr No. All numbers are concepts, but not all concepts are numbers. This “not all concepts are numbers” rule allows infinity to be a number. Because after all, what do numbers do? Count things. We need infinity to count things too such as: How many numbers there are The length of an endless line How many decimal numbers exist between 2 and 3 How many digits there are in the decimal expansion of 1/3.
I was going to comment that Hannah's voiceover work is fantastic, but I see that many other people have already mentioned it....I guess I've just commented it again anyway. Seriously RI, get her to do more stuff for you guys.
The best explanation for something divided by zero, think of it as putting that number into nothing, or no groups. It doesn't work, right? This is the best explanation of zero I believe.
Excellent video. Philochrony is the theory that describes the nature of time and demonstrates its existence. Philochrony establishes an analogy between zero and time thus arising the linear zero.
I am amazed by ancient civilizations that did ease computations even without yet use of zero numerals - for e.g. Mesopotamian use sexagesimal numbers without zero place holders and Chinese use blank or no bead setting in counting rods and abacus. However, the later use of zero undeniably enhanced the number systems and math.
This video on ZERO is really commendable . May I please know the software that you have used to create this video as we are also planning to ceate one ? Thanks for this video. Please do revert back as early as possible .
Whenever people ask why isn’t 1/0 infinity the answer always seems to be ‘infinity isn’t a number it’s a concept’. Well, isn’t maths as a whole a concept in itself? It just seems that people are bent on not getting infinity as an answer?
The problem is that 1/0 could just as easily be negative infinity as well. When something can simultaneously be equal to multiple different things that aren't equal to one another, we've got a contradiction. That's kinda the point: 1/0 gives contradictory answers if we think about it in different ways. So 1/0 can't be infinity. It's undefined. (Within every day maths. Funky stuff happens when you go into funky maths.) What we can say is that if we divided 1 by ever smaller positive numbers (i.e. positive numbers that get closer and closer to 0 each repetition), the answers would tend towards positive infinity. And if we divided 1 by ever smaller negative numbers (i.e. negative numbers that get closer and closer to 0 each repetition), the answers would tend towards negative infinity. Also, when people say infinity isn't a number, it's a concept, that's a meaningful statement. All numbers are also concepts, but not all concepts are numbers. Infinity is one of the latter. If you really wanted to call it a number, it doesn't behave like any other number. If you add 1 to any number it just gets 1 bigger. If you take 1 away from any number, it gets one smaller. If you multiply any number by 2, it doubles, and dividing by 2 halves it. Multiplying a number by itself squares it. And so on. But if you add 1 to infinity, it's still just infinity. And ditto for subtracting, multiplication, and so on. (And some of the operations make even less sense.) And all this is before we even talk about the various different kinds of infinities, and different kinds of funky maths. So regardless of what anyone believes, 1/0 ain't infinity.
1 chicken / 0 chickens = remainder 1 chicken. Long division still works with 0 when you use remainders. Is there any mathematical value to that? Probably not... but it still isn't undefined. It becomes an issue when you try to apply it to other equations though because 1/0 != (3/2)-1 != (5/4)-1 etc... since remainder 1 can have completely different values given a different context. Remainder really equals the dividend to be used over the same divisor. I.E. 3/2 = 1+(r1/2) so in the case of 1/0 the remainder of 1 = 1/0 which obviously loops infinitely. Perhaps there is some math there with convergent series using other /0 remainders or something, I don't know.
+vipero07 Yes, that is true. But lets look at it from another perspective: how would you characterize a division where the reminder is equal to the dividend?
really enjoyed this. it's also uncanny as last night I had a thought about zero and just today I earlier posted about it on fb saying ... zero. what is it good for? absolutely nothing.
Numberphile deja-vu. Zero is a more special case in general terms. My dog for example knows that no other dogs means no competition (absence of males), however, another dog means competition and more dogs than him means a tight competition. From survival point of view it looks like simple abstraction in terms of quantity appreciation is built-in to us. It only took for a brain like ours to really put it out there :-) which is fantastic.
Wait, if 1*0=0, shouldn't 1/0=1? I mean you take 1, and divide by nothing, so you're not doing anything to that 1, so shouldn't it just be a 1? What's with the divide by zero error?
+cidshroom You should check out the concept of limits! One of the major problems with trying to give x/0 a value is that it doesn't have a single limit. For example, if you graph 1/x, and start on the positive side of the x axis, (eg 1/10, or some other positive number) and you start picking denominators closer and closer to 0, the value of the function gets very big - it actually does approach infinity! but this is only from the right side - if you did the same thing, but started on the negative side of the x axis, the values race off to negative infinity! Thus, the function 1/x has no limit at 0 - dividing by 0 doesn't yield one specific value!
In simple words, the remainder would be 1 not the quotient. Quotient can be anything because 0* any number is 0. So the quotient of 1/0 can be any number. Hence infinity.
It's true that zero was initially a placeholder, but that's no longer the case. Today it's just a number and nothing more. Each digit in a number contributes a quantity defined as: DIGIT × 10 ^ POS. Where POS is the ordinal position of the digit from right to left starting by zero. For example, the value of the sequence of digits "300" is defined as: 0 × 10^0 + 0 × 10^1 + 3 × 10^2. There are no placeholders, just numbers.
There are no words to describe what Zero is, and we can only describe what "Zero is nothing." Zero (ṣifr in Arabic and צפר in Hebrew) to indicate an empty position. With the help of the natural history of "zero," and the use of "zero" as a starting point, one may consider two types of metaphysics. On the one hand, the epistemological metaphysics, based on the perceptual/rational dichotomy, is related to the zero as a vacancy between numbers. On the other hand, the genetic metaphysics, based on the dichotomy of source-evolution (or origin and derivative), has much to do with the zero as a number between negative and positive numbers. In this respect, zero represents the horizon of metaphysics: we can forever approach it, but we cannot ultimately arrive at it. Though serving as the point of convergence and divergence for all relationships, zero has no definable content of its own. Such is the essence of zero, and of metaphysics as well. For example, there are as many numbers in between 0 and 1 as there are from 1 to the mathematical infinite ∞. This is due to the fact that each number n with n going from 1 to ∞ has an invert number 1/n which tends towards 0 a n tends towards ∞. The limit of 1/x with x tending towards ∞ is 0, and vice versa, 1/x with x tending towards 0 has ∞ as its limit. It can be asked whether space extends infinitely in every direction, and it can be asked whether time extends infinitely in either of the two temporal “directions”. Just as one can ask whether, if space is finite, it has an “end” (whether it is bounded or unbounded), one may ask of time whether, if it is finite, it had a beginning or will have an end or whether it might have neither, but rather be “circular” (be finite but unbounded). As one can ask whether there could be two extended objects that were not spatially related to each other, one can ask whether there could be two events that were not temporally related to each other. One can ask whether space is (a) a real thing-a substance-a thing that exists independently of its inhabitants, or (b) a mere system of relations among those inhabitants. And one can ask the same question about time. It may also be that there is no internal unity to metaphysics. More strongly, perhaps there is no such thing as metaphysics-or at least nothing that deserves to be called a science or a study or a discipline. Perhaps, as some philosophers have proposed, no metaphysical statement or theory is either true or false. Or perhaps, as others have proposed, metaphysical theories have truth-values, but it is impossible to find out what they are. There is no GOD except A-L-L-H (Aleph-Lamed-Lamed-Hah) the last prophet Mohammad. Aleph is infinity - Lamed-Lamed is the Almighty One - Hah all good and love (associated with 99 Names). Mohammad is the space time messenger and not a Robot. Epistemology, put simply, is the study of knowledge. In particular, epistemology focuses on how we come to acquire knowledge and what types of limits there are to our knowledge. In other words, how do we know what is true? I want you to convince me that you are not a robot. What will you say to help me know you're human? Can you ever know for sure that you're not a robot? A different branch of philosophy deals with a related question: What is real? The study of reality is known as metaphysics. It focuses on determining what, if anything, can be said to be real.
X/0 only approaches infinity for positive values of x, for negative values it approaches negative infinity. that is why x/0 is not infinity. the simplest analogy i can think of is the gaps in the graph of tan(x) where it curves up to infinity then suddenly appears coming up from negative infinity
+krabcat Almost right. You mean 1/x approaches ∞ as x approaches 0 from positive values, and -∞ from negative values. When x=0, 1/x is nothing meaningful. At best you can make it an abstract kind of number that becomes 1 when you multiply it by x. Note that allowing for this kills all the usual assumptions you can make that make math useful. That's why we don't normally do this. As for graphings things, why not just 1/x?
According to our college professor the decimal number system was based in Hindu-Arabic number system where basic digits of counting use 1, 2, 3, 4, 5, 6, 7, 8, 9 that were adapted by Arabs from Indians, but the Arabs also added the 0 to the number system. I don't know how accurate such information, we may investigate. Zero may have just been a concept used by the Indians in philosophy during ancient times, but perhaps the Arabs may have been the ones that used it early as numeral. On the other hand the ancient Mayan civilization in South America separately developed vigesimal number system which included zero numeral.
Nope,arabs didn't add zero. Zero was added by aryabhatta The father of algebra i.e Muhammad ibn Musa Al-Khwarizmi mentioned or cited some of his discovery including function of zero. If it was arabs who discovered zero in mathmatics then he wouldn't mention him. Aryabhatta was the first person to use zero in mathmatics to do sum, subtraction and multiplication.
All numbers are just concepts when they are not bound to the rules of physical existence by units of measurement. If you choose to bind it to reality, then there is no addition or subtraction of zero units, and zero units also can not be divided into smaller units, nor can you have any multiples of zero units. You can use logic systems to understand what would happen if the rules of reality were different. Mathematics when attached to units of measurement is one such logic system. There is apparently another one philosophers use, but I have never grasped it's use of symbols.
You can argue that zero is also invented since mathematics can be thought of as a man made tool. There are a few philosphies for how people think of mathematics and you seem to take the other most popular one that being the "discovery" approach. Love your video btw :)
+theDuffChimp Zero is an even number. A number which quantifies a count or an amount of a null size. If you have zero siblings, then you have no siblings, if something has zero weight, then the thing in question has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have equal amount of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings them to one. Non-mathematicians argue that you cannot have zero of something. Mathematicians accept zero as a number, since you could have zero of something. It is mathematicians, and most others, which accept zero as a number ;)
It was difficult for my math students to respect a mathematical concept of zero. To the average person, it means empty, nada in our pockets, in a room, or in our poor love life. But these examples apply to counting what we see: it's our visual bias. Putting 0 on a number line does not indicate no--thing (empty space) as in our lives, but a location on a number line. It's a median between negative numbers & positive numbers. When we cross a two-way traffic street, we hope to reach the median: the middle of the two way traffic before us and behind us. So zero on a number line is just a location. We could define any number on the number line as the middle number that splits two sets of numbers. Blame it on nada, zero, zilch! On teaching algebra, it's hard to divest the popular quantitative approach to zero versus a zipcode called zero: location on a number line Don't tell the negative & positive numbers about this!
@@gamerkits9697 Just sit all day like a fool doing 'nothing' and you will get 'something' - A BAD RESULT whether in sports or academics. By the way deep down,mathematics is real life.
@@thebatman2084 what you said is one of the most idiotic things I've ever heard. Let me define what is " nothingness " : Nothingness is the absence of any existence, infinity concept is the opposite of nothingness. Non existence can never bring something into existence .
But is there anything _outside_ the number system that can confirm that the distance between 1 and -1 is 2? (To me, it seems infinite.) Numbers are representatives of relative quantity. They all represent some quantity more or less than the quantities represented by other numbers. But just as 'infinity' is not a number, but, rather the absolute, non-relative concept of infinite quantity; so too, is 'zero' not a number, but, rather, the absolute, non-relative concept of infinite non-quantity. The absolute absence of quantity, in other words, and thus not a proper number. We use Zero for place holders to represent empty orders of magnitude. It's very useful and convenient, because our minds are finite capacity, so that we can not work with infinite digits. But that is a quality of our minds' abilities, not of external reality itself. An omniscient mind would have no need of a zero place holder, but, rather, would do math with infinite single digits. To me, both of our uses of zero are convenient, but ultimately misleading. And I think this has potentially extremely far reaching consequences for both math and physics. For example, in our number system, we understand that infinity is not a number, so that infinity - 1 is still infinity, basically, because you simply can't subtract a number from a non-number. But when it comes to zero we don't recognize that. So we allow that 0+1 = 1, and so on. But does that correspond to reality? I would say that in reality, if there is true, absolute nothing, there's nothing to add or subtract. It is an immutable absolute conceptual state. So that 0+/- anything still = zero, just as infinity +/- anything still equals infinity. Because you can't add or subtract anything from absolutes, because absolutes are immutable and timeless. They're not measurements of quantity. And measurements of quantity, btw, are divisions of everything. It's probably best, imo. to think of zero and infinity as the opening and closing brackets of the set [All] . Ultimately, they are the same, the duel expressions of the boundary of [All]. Note that this doesn't work _within_ our number system. But consider that she said in the video that Calculus works so well because it avoids having to divide by zero. It's not that our system for numerical notation and the math we do with it works so well _because_ of using zero as a digit. Rather, we manage to make it work very well specifically by _avoiding_ the paradoxes caused by using an immutable absolute concept as the lowest number in the number system(a system of relative quantities.)
There are only to numbers in existence... Zero and one... Zero indicating an absence and one represents presence... On vs off and so on... The accumulation of numbers then represents sequence... So 7 is not a number in itself but rather a sequence of ones that re occur until it represents "7" occurrences... We need to reevaluate our understanding of numbers...
When defining something as having nothing in it such as a hollow ball, would it be correct to say that within that nothingness, is a quantity of 1 cavity within it? I'm not trying to just use words to twist things up, I'm referring to how math always seems to have an exception to the rule and how things change when we get down to molecular states or quantum states. Because of how our dimension potentially interacts with other dimensions, could this be one method of getting something out of nothing?
fine video, but I love it win "science" plunges into illogic... multiplying AND dividing by 0 is identical to doing those things by 1. dividing by 1 is like multiplying by 1, you remain with original number you started with... you aren't added or subtracting anything from the original number. since 0 has no value, when multiplying and dividing by it, you are in fact not multiplying or dividing at all and you arrive at the original number. that sounds logical to me. good vid!
I was thinking this I was like if zero isn’t a positive number so it’s a negative but there’s no such thing as -0 if there was zero would be a positive
then please why you are not able to count 0 As natural number rules saying ,could anyone teach me if the zero is not using in counting then why it is zero? or what is before 1?why we cannot call nothing as a zero? or what could we call to Space? everything that exist in world might be has a space before it or after it then what will call them?
The answer is infinity. You could say that 1 + 1 is not actually 2 because numbers are just concepts if you wanted, but that's not a very good argument.
+Lucid Moses Yeah, but infinity can't be used in calculations. you don't add to infinity, nor subtract from it, because it will always result in infinity. So, it has no practical use, only conceptual use.
Leopoldo Aranha I see. So X / 0 is not infinity because infinity is not a number infinity is not a number because it has no piratical use. X / 0 equals infinity is a piratical use. But X / 0 is not infinity because infinity is not a number infinity is not a number because it has no piratical use. X / 0 equals infinity is a piratical use. But X / 0 is not infinity because infinity is not a number infinity is not a number because it has no piratical use. X / 0 equals infinity is a piratical use. Etc.. etc..
Lucid Moses I like your spell of practical. It is a typo, but it also says something about pirating a logic. Mathematical concepts set does contain the concepts of numbers, but numbers set _only_ contain the concept of numbers. Infinity isn't a concept for a number, as it has no defined quantity. Such as that, infinity, while as much of a mathematical concept as a number, isn't a number.
Lucid Moses Nope. Zero does have a defined quantity, or, better saying, it has no quantity at all. Infinity, on the other hand, has a quantity that is not defined and can't be defined in any way whatsoever. See the difference?
Is it just me, or are the chapters in binary? Also, the positinal number system always met resistance when it came up against established systems. We forget about earlier instances because they happened before the most-recent example and thus the most resent one is the one people focus on.
Nothing is something. At least under the POV of Directed Intelligence. What does that mean? How does meaning mean? Meaningful conversations appreciated.
I think that 'Something' is an unspecified 'Thing', where as, 'Nothing' is specifically 'No Thing', a 'Void'. In the same way, to classify 'Front' we need to recognise 'No Front' (Back) and for 'In' we need 'No In' (Out), etc. These must all be from the POV of a subjective intelligence because these intrinsic pairs of class are meaningless when divided or unrecognised. For there to be 'Things', we need to recognise an absence of 'Things' to classify them - as being not 'No Thing'. A 'Thing' only moves into a 'No Thing' (void) because a 'Thing' cannot move into another 'Thing'. If it moves, it will have to move other 'Things' into 'No Thing' (void). If 'Nothing' is recognised as a 'Something', then how is it classified? What is it paired with? What is 'No Something'? What would I mean if I asked you to: - Imagine nothing? Draw nothing? Do nothing? etc - Imagine no thing? Draw no thing? Do no thing? etc I think as an abstraction 'Nothing' (a void) is 'Something', as with any subject of class, but in context 'Nothing' is 'No Thing', objectively implied as not a thing, and void of all things. I think it must be the same for Zero, so I would subjectively classify it as a 'No Number'.
Nice video but incorrect. The Mayans/Olmec civilizations had a place holder value a shell. As it has been proven the Mayans performed astronomical calculations. These civilizations had this system down thousands of year BC. The evidence is in their pyramids, codices, etc. Recently, many scholars have agreed only the Mayans had the zero as a place holder and they had the concept down. What is general taught today is from an European/Asian point of view.
The zero as a NUMBER was first put forward by Indians 1500 years ago. And the modern number system we use today worldwide negatives and positives emerging from a null point in opposite directions is developed in India.
@@akhilals5471 The impressive thing about the Maya is that people in Europe, Asia and Africa have always been in contact with each other, influencing each other. People in America where isolated from the rest of the world for thousands of years and still they figured it out and came up with the concept of zero.
@@zacharywhite7547 Eventually 0 reveals himself to all his children Don't fear... I AM the alpha and the 0mega I AM the beginning and the End of everything. Quick question.... How come when you multiply 0 and 5 it equals 0?.....shouldn't it give you 5? Even when he makes himself nothing he is still more powerful than infinity....proving that even when left out he still the omnipresent omnipotent king God Jeh0va ......at the end of the day we are nothing without Him... When 0 reveals 1 (Jesus) and then takes him into him.....We are forgiven and saved from death by his promise. His love is the only real thing. Amen Jesus
@@zacharywhite7547 the thing is you don't need anyone influence to develop a concept. Like you don't need an influence to think. And indian invented it way before then the mayas.
Ancient Indians did not just invent the Number system, If you are someone who loves Math, Look up - "Vedic Mathematics". They came up with ways to calculate Square roots of 10 Digit numbers in just 3 seconds, Transforming you into a Human calculator. Ancient Indians used these "Simple Tricks" to calculate Insanely large numbers, Like the ones mentioned in Buddhism. Buddha was once asked - What is the largest number in existence in the Universe ? He replied 10 to the power of 540. That's 10 followed by 540 Zeroes. Whether the Buddha was simple making it up, It doesn't matter and is a whole different topic. What matters is there was a Culture of recognizing and using such crazy large numbers in Ancient India !!!
dividing any number by zero means that that number will never come in the multiplication table of 0, so the table will go on till infinity to get to that number. The answer is infinity for sure, concept or not.
مع الأسف سيدتي المحترمة لم تذكري الخوارزمي مبتكر رقم 0 الحالي كذلك لم تذكري ابن الياسمين(ibn al yassamin) مبتكر الارقام الغبارية او أرقام فاس they call it also the Morroccan numbers. كل هذا موجود في كتب التاريخ الأكاديمية. 😊
In some sense, saying "Infinity is not a number is a concept" is like saying " 1 is not a number is a concept" ( are you saying 1 is not a concept?). Infinity is still a concept don't get me wrong. The opposite of infinity is infinitesimal and that's what you get when you divide by 0. Infinitesimal is not a number, it's a concept.
Infinity is not something you can measure, that's why it's a concept not a number, the number 1 is a specific quantity, while infinity cannot be specified into a defined quantity. I think this video is nonsense, it doesn't explain how you can get something from nothing. You cannot get something from nothing because nothingness is absence of everything, if we talk about infinity concept, nothingness is the exact opposite of infinty, because it's the absence of everything . Infinity is not bounded, it doesn't have a beginning or an end, therefore it encompasses everything .
+grant kohler Another indicator that zero should not be treated as a number is the flaw where multiplying both sides of an equation by zero would prove every equation to be true.
This video tells us how the number came to be. It does not tells us what it is... the title should be “history of number zero” not “what is zero”... you still did not mention the answer to that question. What is zero?
Here are some interesting facts about the number zero. We like to think of it as an empty quantity, but if we pay attention, there are positive numbers and a mirror negative for each positive number, which when combined, give us zero... (+5)+(-5)=0 both mirrors of the number 5 can be represented at the same time by zero. So, zero actually represents an empty quantity (-5) AND a full quantity (+5), *at the same time, in the same space* What? In reality, it represents the existence AND absence of all numbers of a thing *in the same time/space.* Example: A zero quantity apples in a box. Actually means, all possible apple numbers exist in this box as well as the absence of them exists at the same time in this box. That is very confusing to think of. I know. That’s why I like it. If we say there are zero apples in a box. Mathematically, it means there are (let’s say) 5 apples exist, and the same 5 apples don’t exist *at the same time* Therefor, an empty space should not be represented by a zero. It should be represented by a negative number of what you are looking for. Example: This box has a -5 apples. Since I’m looking for +5 apples and cannot find it. If I’m not looking for a specific number of a specific thing... let’s say I’m looking for *anything at all* in that box. It should be calculated as: *Box contains a negative infinite quantity of anything* So, what is zero?? My brain will explode. My theory is: Zero is everything and nothing at the same time. If that is correct, then we cannot experience zero in reality. Which I think is sad 😨
Every number can have a corresponding relationship in the material world except for zero. It is impossible to have zero of anything. Even in binary computing systems it only implies a length of time between 1s.
There is a philosophy called "Saankhya Darshan." Darshan in sanskrit means 'to see' or philosophy. Saankhya gave rise to 'Sankhyaa' the numbers in sanskrit. 0 in Vedas is not nothingness. It is exactly opposite. It is 'complete'. Read the shanti mantra that defines this. "om poornamada poornamidam poornaat purnam udachyate. Poornasya poornamadaya poornam ewa awashishyate" It means if you add completeness to complete, you get complete. If you completely remove completeness, completeness still remains. After 9, that location is NOT nothing. It is complete.... That's 0 and then you move to next place.... I don't know if West knows this.... If anyone can take credit of zero then it is only "Saankhya philosophy" and vedic sukta....
Интересная история... Деление не всегда идет именно от умножения... или сложения... или даже вычитания... Иногда оно выражает относительное значение между зависимыми величинами... Такое выражение когда 0×0 большинство безоговорочно посчитают равным 0... но на самом деле это поверхностный взгляд... Ведь относительный ответ X/0=0 означает что X=0×0... без учета безотносительного остатка... Хотя о чем это я... делить на ноль многим запрещено почти на законодательном уровне... Многие думают что на ноль можно умножать а делить "почти" совсем ни как нельзя... Типа X×0 = 0 это нормально лишь потому что 0/X = 0...? Но из этого же следует что сам X = 0/0...? Х=0⁰...? ну и где логика... Давайте рассмотрим один из вариантов как обычно происходит действие деления... 6:2=6/2=(2+4)/2=2/2+4/2=1+(2+2)/2= =1+2/2+2/2=1+1+2/2=3 (без остатка...) 7:2=7/2=(2+5)/2=2/2+5/2= =1+(2+3)/2=1+2/2+3/2= =1+1+(2+1)/2=1+1+2/2+1/2= =1+1+1+1/2=3+1/2=3 с остатком 1... И это также можно с помощью принятых форм математических записей выразить как 3½ или 3.5... А что же происходит когда якобы производят деление на ноль... многие говорят что это будет равно какой то бесконечности... 15:0=15/0=(0+15)/0=0/0+(0+15)/0= =0/0+0/0+(0+15)/0=0/0+...+0/0+15/0... и при дальнейших действиях всегда такое деление будет c постоянным остатком в виде того что "делилось" изначально... в данном случае остаток 15... и почему то вот об этом остатке или забывают или неосознанно замалчивают считая только бесполезные бесконечные действия не приводящие ни к какому результату деления... Если быть немного логичным то видно что даже при бесконечном количестве таких действий деления (а точнее бездействий) вся сумма таких действий равна нулю с постоянным остатком того что было изначально делимым... То есть само такое деление не происходит... сколько было изначально столько и остаётся в остатке неделимо... X:0=X/0=(0/0)×N+X/0=N×(0/0) с неразделённым остатком X где N×(0/0)=0 и N число мнимых манипуляций не производящих деления... поэтому N=0... а не бесконечность... отсюда и получается два ответа при делении на ноль... относительный ответ равен 0... но именно ноль бессмысленных манипуляций... а безотносительный ответ равен самому значению делимого X... В примере 15/0 = 0 целых 15 нулевых... или же 0 целых и 15 в остатке... именно умножая это число на ноль можно получить первоначальное данное значение... Но об этом как правило неумышленно умалчивают... ведь этому не научили... Общепринятая математическая терминология до сих пор никак не может внятно объяснить даже продвинутым математикам (что уж там говорить о простых людях) что же это за такие математические "действия" с нулевыми значаниями и почему "мультипликашка" multiplicatio (умножение) с "отсутствующим" множителем ноль возможно (при всей своей абсурдности)... а вот "дивизионка" division (деление) на ноль ответ неопределен от полного категорического запрета до "игр разума"... "положительной и отрицательной бесконечности вселенной"... или же "совершенно не имеет смысла"... А если всё же хоть немного подумать... Любое значение X не равное нулю деленное на ноль всегда имеет два значения... Относительный ответ ВСЕГДА = 0... Безотносительный ответ равен самому неделенному Х
Полное непонимание современной математики темы умножения на ноль и тем более деления на ноль... При записи умножения числового значения X на ноль получаем ----- X×0=0 X /\ 0/0 Перенос ноля через знак равно превращает равенство в качельное неравенство типа ---- 100% /\ 0% Сам знак процентов кстати пишется как 0/0... То же самое и с делением на ноль... ---- X/0=0 Х /\ 0×0 Перенос ноля через знак равно превращает равенство в качельное неравенство... Я называю это нулёвыми значениями (не нулевыми а именно нулёвыми... "ни разу взятыми" или "ни разу трачеными" то есть "нерастрачеными" если это об умножении на ноль... "ни разу делёнными" или "неразделёнными" если это о делении на ноль)... И непонимание до сих пор этого простого меня очень удивляет... 220 вольт делить на ток 0 Ампер это сопротивление = 0 Ом... но это просто не потраченое напряжение... 1 торт не взятый кусками ни разу (деленный на ноль) 1/0 это 0 кусков взятых но это все тот же 1 неразделённый торт... 5 монет ни разу не взятых 5×0 это 0 взятых монет но вопрос как правило звучит "сколько будет" а не сколько взято... так вот будет все те же 5 невзятых "нулёвых" монет... И это всего лишь маленькая вершина айсберга действий с нолем... Сложение и вычитание нуля не меняет первоначального значения... а почему? да потому что на самом деле не происходит самого математического действия как такового... ничего не прибавляется и не убавляется при этом... С умножением и делением на ноль происходит примерно тоже самое... Ничего не происходит при этих действиях... всего лишь описывается что первоначальные значения не изменяются... хотя ответов получается два относительный = 0 безотносительный = 100% = 1×Х(нулёвое) в зависимости от поставленного вопроса... И безотносительный ответ имеет гораздо больше смысла... 5 метров × 5 метров × 0 метров = 25 метров² × 0 метров = ? Относительно нуля ответ 0 метров³ Безотносительно нуля = 25 метров² ---- 25м²(=100%) /\ 0м³ : 0м (= 0м²) Перенос нуля (при умножении на ноль или делении на ноль) через знак равно превращает равенство в качельное неравенство ----- 1×X(нулёвое)(=100%) /\ 0(=0%) Безотносительный ответ при действиях умножения и деления с нулем не учитывает как само действие с нулем так и его измерение... 5 яблок : 0 корзин = ? Относительный ответ 0 яблок на корзину... Безотносительный ответ 5 неразделенных яблок (без корзин)... Убираем ноль и его измерение из вычисления и получаем нетронутые первоначальные данные и можем дальше с ними что то вычислять... ---- 5 яблок нулёвых (= 100%) /\ 0 корзин × 0 яблок/на корзину (= 0) Чисто качельное 100% неравенство... Откуда здесь могут взяться какие то бесконечности? Или черные дыры? Кстати 0(нулёвый) / 0(нулёвый) = 1 Впрочем как и любое другое число раз делённое на само себя... Это всего лишь малая часть моего личного взгляда на действия с нулем и он не ограничивается только этими действиями...
Ноль не имеет численного значения... он лишь описывает отсутствие чего либо... Практически все действия с нолем на самом деле не происходят... Многие пытаются ноль "всунуть" в основные математические действия... при этом абсолютно не понимая смысла самой записи таких действий... но с нулем есть только математические "бездействия" и чаще всего действия "умножения" и "деления" связанные с нулем говорят что есть что то безотносительное до той поры пока вместо нуля в таких выражениях не появится числовое значение... Лишь после этого выражение становится относительным... Если напряжение = 0 и сила тока = 0 то это не значит что при этом всегда нет сопротивления... Если скорость = 0 и время = 0 то расстояние при этом может быть каким угодно (в том числе и отсутствовать)... Поймите главное перенос нуля через знак равно изменяет смысл равенства на качельное неравенство 100% того что было изначально и есть до сих пор и с другой стороны 0% того что якобы "взято"... И никаких бесконечностей и всяких "черных дыр" при явном нуле в таких действиях никогда не будет... Чисто математически ЛЮБОЕ "действие" когда Х не равное нулю "умножается" на ноль или "делится" будет равно ВСЕГДА нулю... то есть отсутствию таких отношений... Но смысл совершенно не в этом... любое такое "действие" описывает лишь неизменность самого стопроцентно имеющегося значения X при этих нулевых "операциях" с ним...
Что касается "деления" 0/0... (или по другому выражения типа 0⁰...) Если вы делите два различных нуля один на другой (с различными мерами измерения) то "относительный" математический ответ этого будет 0 = 0% того что использовано... Но безотносительный ответ будет равен 100% того что было дано изначально и не было использовано в ходе бездейственного "деления" отсутствия одной величины на отсутствие другой... Если делить один ноль сам на себя (с одной и той же мерой измерения) то ответ равен 1 раз... И никаких 2 раза... 3 раза... и т.п. у отсутствия величины в виде ноля не будет... Интересно как можно объяснить 0/0 = 0⁰ с точки зрения "практических" равенств... Многие считают что 0⁰ = 1... Напряжение U = 0 вольт... Сила тока I = 0 ампер... Сопротивление R = U/I = 0/0 = 0⁰ = 1...? Ом...? Весело... Дистанция S = 0 километров... Время t = 0 часов... Cкорость V = S/t = 0/0 = 0⁰ = 1...? километров/час...? Смешно... Объем V = 0 метров³... Ширина W = 0 метров... Высота H = 0 метров... Длина L = V/(W×H) = 0/(0×0) = 0/0² = 0‐¹ = 1/0...? = ...? Сколько будет...? метров? Интересно сможет хоть кто то это объяснить хоть как то математически... Нужно знать историю происхождения таких нулей...
Многие математики почему то считают что у нуля нет обратной величины... Другие свято верят что величина обратная нулю это "бесконечность"... К сожалению (ну или к счастью) у "бесконечности" есть обратная величина равная 1/бесконечность... И как бы она ни была мала она НИКОГДА не будет равна нулю... И уж точно она не имеет безотносительного значения... К тому же она имеет знак плюс или минус в зависимости от того с каким знаком берется сама "бесконечность"... (если конечно она хоть как то вообще может быть "взята"...) У полного отсутствия в виде нуля есть обратная величина... это полное присутствие... и для нуля это равно единице... то есть 100% присутствие чего либо... 1/0 "относительный" ответ математически равен нулю... но именно он не имеет смысла а вот безотносительный ответ как раз равен "ни разу делённой" то есть нераздельной (нулёвой) единице... Никакой бесконечности при делении на ноль не бывает... если только сама бесконечность не делится на ноль... 1/0 равна 0 целых и 1 в остатке... полностью неделённая единица... Умножьте обратно 0×0 целых и прибавьте остаток 1... получите изначальное имеющееся число якобы "делённое" на ноль... Деление на целые части заканчивается когда вы не можете больше "отсоединить" от делимого количества записанного в делитель... При нуле находящимся в делителе вы не сможете "отсоединить" вообще ничего от делимого числа пытаясь вычесть ноль... даже при "бесконечных" таких попытках... поэтому для действия деления на ноль это равно всегда ноль целых... а остальное неделимый остаток...
Много есть искусственных точек нулевого отсчета в различных измерениях различных величин... Но в большинстве своем они не имеют никакого отношения к делению на ноль... Я лишь изложил некоторые видения своей теории математических "действий" с нулевыми значениями... На сегодняшний день никто не смог переубедить меня в этом... и даже наоборот после дискуссий на эту тему мое личное убеждение в моей правоте возрастает все больше... Вам же желаю всех благ в деле поиска знаний...
+Jack Drewitt In the editing process we'd accidentally ended up with a misplaced chapter title, meaning our oh-so-clever binary chapter system didn't work any more! We're okay with the 59 symbols ;)
If you divide anything by no-thing then there is no division. I don't get why it is so hard for many mathematicians to acknowledge that the issues and requirement for special considerations with zero are of their own creation. Algebra being the main culprit causing confusion. It seems simple and intuitive. 1+0=1. 1-0=1. 1*0=0. Yet divide by zero and suddenly the definition of 0 changes? 0 is none, no-thing, absence within the context of whatever things you are discussing (As in: Using a numeral describe how many chicken emojis exist in this sentence). So if we divide 1 chicken by no chickens (bad example) or 1 centimetre by 0 centimetres we are making no change as the function is negated and there is 0 division. We could try to carry out the function as a subtraction and find ourselves in infinite iterations because as someone else commented 0 goes into any number infinite times...but this is simply not true because 0*x=0. Zero provides context, an interdependent opposite to denotations of value or magnitude. If you have a box of zero and you divide it with a zero width division, x times, there is no division. 0 is the argument at which the value of a function is negated and disappears. It is not positive or negative or even or odd, it is a denotation representing the concept "no-thing" and hence is clearly defined. Not undefined or infinite. Zero as a numeral is confusing because in contradiction to its core meaning it also has a value in mathematics in terms of indicating magnitude in multiples of ten. With the right axioms maths can "prove" anything but that doesn't make it true. See Gödel's work. It is a miracle that maths is as useful as it is to science when it is an incomplete, often misunderstood and contradictory theory.
Can we take a little moment to appreciate the fact that they numbered their chapters beginning with zero (which is common in computer science, but not in every day life) and numbered the chapters in binary, just so they could better show off zero?
"0 is the absence of a value" how then could a chapter be represented as 0? Its great intention but it needs to beigin at 1 . Zero should only be used if there are no chapters. 0 chapters, chapter 1 cant just be called chapter 0. Its not cute lol
@@davidvaldes3456you are correct.
As an Indian its proud to score 0 in exams.
Or rather two 00s after 1 as if u score a single zero with no 1 in front of it then ur Indian parents would come with their chappals
For u not for india
@@yashikakalsiyana9528yes
l😊😅
Today india is zero value
I could listen to Hannah Fry all day. Her accent is so charming and soothing.
I recognised that voice right away
Who is she?
Absolutely
Hannah Fry ❤️
Are units only relevant in the created place?....... Is zero relevant everywhere?.. ..
0110: ok I'm nothing without you.
@@thileepkumars 9
Bravo!! This video is a work of art.
Hinduism 'The birth place of current number system and number zero'.
Ancient indians were so smart. And here we are, modern indians wasting our time running behind jobs instead of creating new jobs.
Running behind money materials
And also polluting there own land. 😂
How clever! The chapter numbers not only start at 0, but are in Binary!
Dr. Fry is so good at explaining :)
So your saying she's not good
Well she is better than you
A huge thankyou to the person who translated this video into Spanish! We like to think that mathematics is something of a universal language, but English is certainly not. If you can speak another language and want to help share this video with a wider audience, you can contribute subtitles here: ua-cam.com/users/timedtext_video?ref=share&v=9Y7gAzTMdMA
+The Royal Institution Merci, gracias and Спасибо to everyone who has submitted translations so far! We really, really appreciate it!
Our very first set of Hindi subtitles are here! धन्यवाद
Romanian subtitles now available too, many thanks!
*Zero was actually invented in china later copied by others, Chinese kept secret of silk, number system, paper, printing stamp, and gun powder so it didn't come out*
*Persian and arab traders spread it to others through silk route*
Never seen a better video than this one!
Emptiness, void, nothingness and Shunya are deeply philosophical concepts that ancient Hindus gave considerable thought and importance. In Hinduism everything seems to have originated from a void or a point which eventually took the shape of a number 0. So in many ways Zero is also a concept and an idea even before it is a number.
Brilliant! Absolutely mind blowing video! Shoutouts to the creators who made this! I was absolutely blown away! I had the same problem of deviding by zero in a world where zero literally can be more that a negative and less than 1. Zero is fascinating and this video absolutely peaked my interest! I'll keep my crazy words here but you nailed it on this video and it's been a pleasure! Truly has! I might hit subscribe if you have more about this?
Thank you Dr. Fry. This has been a great video to share with Year 5 as we have been looking at mathematics though history and its contribution to modern life. After looking at calculating with earlier number systems, I know that they appreciate zero much more now.
"Infinity isn't a number, it's a concept." FUCKING FINALLY! I SEE SO MANY PEOPLE USING IT LIKE IT'S A GODDAMN NUMBER AND IT BUGS THE SHIT OUT OF ME!
All numbers are concepts u boob, quit getting ur panties in a bunch
Sorry, let me rephrase that. Infinity isn't a variable. You cannot use it as a variable.
No I'm sorry, I don't know why I flipped out like that. I hate my job.
@@elliotgale470 numbers are defined while infinity is not defined.
In real life anything that has a specific measurement is a number, while infinity has no specific measurement, therefore it's not a number.
That quote within itself also pretty much means 0 is a concept. Which this video I think was trying not to do. Seems pretty contradictory. Can’t divide by 0 because infinite is just a concept and we can’t comprehend. But for some reason people have no issue comprehending nothing.
NOTE FOR AMERICAN VIEWERS: 2:33 By "Roman Empire", she means Byzantium, the eastern empire that survived for centuries after the fall of Rome. Although Byzantium had once belonged to Rome, it was Greek-speaking and had a somewhat different culture, and was influenced at first by Persia and later the Islamic empires.
"Byzantine" is a late term coined by historians. Nobody used the term "byzantine" as a selfdesignation back then. But Romanoi ("roman citizen"), but still hold onto their non-roman ethnicity.
Roman Empire was, like every empire, multi-ethnical. So no; the eastern Roman Empire was not _only_ "greek speaking". But inhabited by many different folks that spoke different languages/dielects.
Greek was the lingua franca, the language of the elite, ruling class. That means: Church + royalty.
Byzantine is just used by historians to divide the Roman Empire to East (konstantinople)/West (milano, rome).
The lingua francas of the Roman Empire were not only latin but also greek. Which a lot ppl clearly forget (or don't know). Latin f.e. vocabulary is full of loanwords from ancient greek. Latin also borrowed from etruscan, celtic, semitic and other (still spoken and extinct) languages - so did also greeks. They were always in contact with other folks. But since the roman empire, that lasted a *very* long time and caused a lot extinctions of languages - we'll never know from where many words actually really came from.
Also: there was no "islamic empire" in Greece. You mean probably the Ottoman "Empire" (the invading turkic tribe). But Ottoman "Empire" was actually not an _empire._
@@dorakemba2899 what was the ottoman ‘empire’ then
Thanks for this beautiful upload, but I require a bit of enlightenment, if you please! I trust this video is primarily based on Charles Seife's 'Zero: The Biography of a Dangerous Idea'. Was a little flummoxed to find many a people attribute its invention to Aryabhata, when his book indeed says what you said, Professor Fry: many civilisations have invented a vague concept of zero on their own volition, but it was the Indian mathematician who popularised the same. On the other facet, the book emphatically affirms, which obviously sounds quite a logical claim, that it's none but Babylonians-people who hail from a place often regarded as the 'cradle of civilisation'-who invented the idea of zero. Is there a veracity in this claim, Professor Fry?
If you have one chicken and you divide it among nothing, you have everything that is there of it - the things you are aware of and can count, as also the things you are not aware of and so can not count. Everything is a concept, not a number.
Really? All numbers are concepts. That's why they're called "numbers".
@@DepressedJester13 so number is a synonym for concepts? it's not.
@@gauravmshr No. All numbers are concepts, but not all concepts are numbers. This “not all concepts are numbers” rule allows infinity to be a number. Because after all, what do numbers do? Count things. We need infinity to count things too such as:
How many numbers there are
The length of an endless line
How many decimal numbers exist between 2 and 3
How many digits there are in the decimal expansion of 1/3.
@@DepressedJester13 verbosity won't help. you said 'that's why they are called numbers'. and haven't explained that.
@@gauravmshr Well, I just gave a very solid and undebunkable explanation of why infinity SHOULD be a number. That's all the proof most people need.
I was going to comment that Hannah's voiceover work is fantastic, but I see that many other people have already mentioned it....I guess I've just commented it again anyway. Seriously RI, get her to do more stuff for you guys.
verdatum - I recognized her voice, instantly. Brady's fault!
That's so nice
The best explanation for something divided by zero, think of it as putting that number into nothing, or no groups. It doesn't work, right? This is the best explanation of zero I believe.
Excellent video. Philochrony is the theory that describes the nature of time and demonstrates its existence. Philochrony establishes an analogy between zero and time thus arising the linear zero.
It's very hard to find Westerners acknowledging the contributions of ancient Indians in Mathematics and Science.
Thank you, Dr. Fry.
Brilliant and very aesthetically pleasing...my compliments.
Binary chapter numbers, yay!
I Know!! It's so cool!
Looks like you love maths
Love the video love the host 10/10
She's the best!
I am amazed by ancient civilizations that did ease computations even without yet use of zero numerals - for e.g. Mesopotamian use sexagesimal numbers without zero place holders and Chinese use blank or no bead setting in counting rods and abacus. However, the later use of zero undeniably enhanced the number systems and math.
This video on ZERO is really commendable . May I please know the software that you have used to create this video as we are also planning to ceate one ? Thanks for this video. Please do revert back as early as possible .
Beautiful animation!!
I agree
Whenever people ask why isn’t 1/0 infinity the answer always seems to be ‘infinity isn’t a number it’s a concept’. Well, isn’t maths as a whole a concept in itself? It just seems that people are bent on not getting infinity as an answer?
I believe 1/0 is infinity
The problem is that 1/0 could just as easily be negative infinity as well. When something can simultaneously be equal to multiple different things that aren't equal to one another, we've got a contradiction. That's kinda the point: 1/0 gives contradictory answers if we think about it in different ways. So 1/0 can't be infinity. It's undefined. (Within every day maths. Funky stuff happens when you go into funky maths.)
What we can say is that if we divided 1 by ever smaller positive numbers (i.e. positive numbers that get closer and closer to 0 each repetition), the answers would tend towards positive infinity. And if we divided 1 by ever smaller negative numbers (i.e. negative numbers that get closer and closer to 0 each repetition), the answers would tend towards negative infinity.
Also, when people say infinity isn't a number, it's a concept, that's a meaningful statement. All numbers are also concepts, but not all concepts are numbers. Infinity is one of the latter. If you really wanted to call it a number, it doesn't behave like any other number. If you add 1 to any number it just gets 1 bigger. If you take 1 away from any number, it gets one smaller. If you multiply any number by 2, it doubles, and dividing by 2 halves it. Multiplying a number by itself squares it. And so on. But if you add 1 to infinity, it's still just infinity. And ditto for subtracting, multiplication, and so on. (And some of the operations make even less sense.)
And all this is before we even talk about the various different kinds of infinities, and different kinds of funky maths.
So regardless of what anyone believes, 1/0 ain't infinity.
The answer to this question is that you cannot divide by nothing. Simply.
Wonderful balanced insight into a complicated concept... Very helpful for helping to explain to my curious kid ❤
1 chicken / 0 chickens = remainder 1 chicken. Long division still works with 0 when you use remainders. Is there any mathematical value to that? Probably not... but it still isn't undefined. It becomes an issue when you try to apply it to other equations though because 1/0 != (3/2)-1 != (5/4)-1 etc... since remainder 1 can have completely different values given a different context. Remainder really equals the dividend to be used over the same divisor. I.E. 3/2 = 1+(r1/2) so in the case of 1/0 the remainder of 1 = 1/0 which obviously loops infinitely. Perhaps there is some math there with convergent series using other /0 remainders or something, I don't know.
+vipero07 Yes, that is true. But lets look at it from another perspective: how would you characterize a division where the reminder is equal to the dividend?
Such a beautifully-made video!
really enjoyed this.
it's also uncanny as last night I had a thought about zero and just today I earlier posted about it on fb saying ...
zero. what is it good for? absolutely nothing.
Take my like
Zero was invented by Bhaskaracharya in Bihar, India in the 2nd century. Aryabhatta was in the 4th century.
Do you have evidence. Science works on evidence.
You helped my class some how but you did thanks.
Ok
thanks for all the information
Numberphile deja-vu. Zero is a more special case in general terms. My dog for example knows that no other dogs means no competition (absence of males), however, another dog means competition and more dogs than him means a tight competition. From survival point of view it looks like simple abstraction in terms of quantity appreciation is built-in to us. It only took for a brain like ours to really put it out there :-) which is fantastic.
Wait, if 1*0=0, shouldn't 1/0=1?
I mean you take 1, and divide by nothing, so you're not doing anything to that 1, so shouldn't it just be a 1? What's with the divide by zero error?
+cidshroom You should check out the concept of limits! One of the major problems with trying to give x/0 a value is that it doesn't have a single limit. For example, if you graph 1/x, and start on the positive side of the x axis, (eg 1/10, or some other positive number) and you start picking denominators closer and closer to 0, the value of the function gets very big - it actually does approach infinity! but this is only from the right side - if you did the same thing, but started on the negative side of the x axis, the values race off to negative infinity! Thus, the function 1/x has no limit at 0 - dividing by 0 doesn't yield one specific value!
Luke Steeves Ah, that makes far more sense, I didn't even think to try it with variables.
I'll look into this, seems very interesting. Thank you!
+cidshroom 2*0 = 0 = 3*0.
If 1/0 has an answer then multiply both sides by it.
2*0/0 = 2 = 3 = 3*0/0
But 2 is not 3. So 1/0 can't have an answer.
In simple words, the remainder would be 1 not the quotient. Quotient can be anything because 0* any number is 0. So the quotient of 1/0 can be any number. Hence infinity.
yay! this is all-round a lovely thing.
thx for the form im liking this vid but no thx cuz idint help me in my project but i appreciate ur hardworking in this vid
Some of video shows that the arayabhata discovered zero...im confuse
it's Art !! thank you so much for this Amazing video.
It's true that zero was initially a placeholder, but that's no longer the case. Today it's just a number and nothing more.
Each digit in a number contributes a quantity defined as: DIGIT × 10 ^ POS.
Where POS is the ordinal position of the digit from right to left starting by zero.
For example, the value of the sequence of digits "300" is defined as: 0 × 10^0 + 0 × 10^1 + 3 × 10^2.
There are no placeholders, just numbers.
There are no words to describe what Zero is, and we can only describe what "Zero is nothing." Zero (ṣifr in Arabic and צפר in Hebrew) to indicate an empty position. With the help of the natural history of "zero," and the use of "zero" as a starting point, one may consider two types of metaphysics. On the one hand, the epistemological metaphysics, based on the perceptual/rational dichotomy, is related to the zero as a vacancy between numbers. On the other hand, the genetic metaphysics, based on the dichotomy of source-evolution (or origin and derivative), has much to do with the zero as a number between negative and positive numbers. In this respect, zero represents the horizon of metaphysics: we can forever approach it, but we cannot ultimately arrive at it. Though serving as the point of convergence and divergence for all relationships, zero has no definable content of its own. Such is the essence of zero, and of metaphysics as well. For example, there are as many numbers in between 0 and 1 as there are from 1 to the mathematical infinite ∞. This is due to the fact that each number n with n going from 1 to ∞ has an invert number 1/n which tends towards 0 a n tends towards ∞. The limit of 1/x with x tending towards ∞ is 0, and vice versa, 1/x with x tending towards 0 has ∞ as its limit. It can be asked whether space extends infinitely in every direction, and it can be asked whether time extends infinitely in either of the two temporal “directions”. Just as one can ask whether, if space is finite, it has an “end” (whether it is bounded or unbounded), one may ask of time whether, if it is finite, it had a beginning or will have an end or whether it might have neither, but rather be “circular” (be finite but unbounded). As one can ask whether there could be two extended objects that were not spatially related to each other, one can ask whether there could be two events that were not temporally related to each other. One can ask whether space is (a) a real thing-a substance-a thing that exists independently of its inhabitants, or (b) a mere system of relations among those inhabitants. And one can ask the same question about time. It may also be that there is no internal unity to metaphysics. More strongly, perhaps there is no such thing as metaphysics-or at least nothing that deserves to be called a science or a study or a discipline. Perhaps, as some philosophers have proposed, no metaphysical statement or theory is either true or false. Or perhaps, as others have proposed, metaphysical theories have truth-values, but it is impossible to find out what they are. There is no GOD except A-L-L-H (Aleph-Lamed-Lamed-Hah) the last prophet Mohammad. Aleph is infinity - Lamed-Lamed is the Almighty One - Hah all good and love (associated with 99 Names). Mohammad is the space time messenger and not a Robot. Epistemology, put simply, is the study of knowledge. In particular, epistemology focuses on how we come to acquire knowledge and what types of limits there are to our knowledge. In other words, how do we know what is true? I want you to convince me that you are not a robot. What will you say to help me know you're human? Can you ever know for sure that you're not a robot? A different branch of philosophy deals with a related question: What is real? The study of reality is known as metaphysics. It focuses on determining what, if anything, can be said to be real.
3:34 best line
So good!
The video concludes something can come from nothing. Can someone explain to me how this explains the beginning of everything/existence.
No no one can
Awesome .... For me it's just like listening to a bedtime story.
X/0 only approaches infinity for positive values of x, for negative values it approaches negative infinity. that is why x/0 is not infinity. the simplest analogy i can think of is the gaps in the graph of tan(x) where it curves up to infinity then suddenly appears coming up from negative infinity
+krabcat Almost right. You mean 1/x approaches ∞ as x approaches 0 from positive values, and -∞ from negative values. When x=0, 1/x is nothing meaningful. At best you can make it an abstract kind of number that becomes 1 when you multiply it by x. Note that allowing for this kills all the usual assumptions you can make that make math useful. That's why we don't normally do this.
As for graphings things, why not just 1/x?
+krabcat How would you prove +infinity and -infinity are different numbers?
Look up the Riemann sphere.
Ok. But I have a question about the zero, what is the zero?? I found it difficult to know if it has value or not
According to our college professor the decimal number system was based in Hindu-Arabic number system where basic digits of counting use 1, 2, 3, 4, 5, 6, 7, 8, 9 that were adapted by Arabs from Indians, but the Arabs also added the 0 to the number system. I don't know how accurate such information, we may investigate. Zero may have just been a concept used by the Indians in philosophy during ancient times, but perhaps the Arabs may have been the ones that used it early as numeral.
On the other hand the ancient Mayan civilization in South America separately developed vigesimal number system which included zero numeral.
No
Nope,arabs didn't add zero. Zero was added by aryabhatta
The father of algebra i.e Muhammad ibn Musa Al-Khwarizmi mentioned or cited some of his discovery including function of zero. If it was arabs who discovered zero in mathmatics then he wouldn't mention him.
Aryabhatta was the first person to use zero in mathmatics to do sum, subtraction and multiplication.
All numbers are just concepts when they are not bound to the rules of physical existence by units of measurement. If you choose to bind it to reality, then there is no addition or subtraction of zero units, and zero units also can not be divided into smaller units, nor can you have any multiples of zero units. You can use logic systems to understand what would happen if the rules of reality were different. Mathematics when attached to units of measurement is one such logic system. There is apparently another one philosophers use, but I have never grasped it's use of symbols.
The number zero existed long before we "invented" it.
+Physics Videos by Eugene Khutoryansky
Define 'existed'. Numbers don't exist, only what they represent.
+theDuffChimp Actually, zero is a number and a placeholder ;)
You can argue that zero is also invented since mathematics can be thought of as a man made tool. There are a few philosphies for how people think of mathematics and you seem to take the other most popular one that being the "discovery" approach. Love your video btw :)
Tibor Roussou
But doesn't exist in the classical sense. As what it represents also doesn't exist, ergo nothing.
+theDuffChimp Zero is an even number. A number which quantifies a count or an amount of a null size. If you have zero siblings, then you have no siblings, if something has zero weight, then the thing in question has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have equal amount of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings them to one. Non-mathematicians argue that you cannot have zero of something. Mathematicians accept zero as a number, since you could have zero of something. It is mathematicians, and most others, which accept zero as a number ;)
It was difficult for my math students to respect a mathematical concept of zero. To the average person, it means empty, nada in our pockets, in a room, or in our poor love life. But these examples apply to counting what we see: it's our visual bias. Putting 0 on a number line does not indicate no--thing (empty space) as in our lives, but a location on a number line. It's a median between negative numbers & positive numbers. When we cross a two-way traffic street, we hope to reach the median: the middle of the two way traffic before us and behind us. So zero on a number line is just a location. We could define any number on the number line as the middle number that splits two sets of numbers. Blame it on nada, zero, zilch! On teaching algebra, it's hard to divest the popular quantitative approach to zero versus a zipcode called zero: location on a number line
Don't tell the negative & positive numbers about this!
Very well and interestingly presented, good work !
- Can you get something from nothing ?
- No
You're welcome
Mehdi Armachi nothing is something
Explain how nothing is something using examples from real life
@@gamerkits9697 Just sit all day like a fool doing 'nothing' and you will get 'something' - A BAD RESULT whether in sports or academics.
By the way deep down,mathematics is real life.
@@thebatman2084 what you said is one of the most idiotic things I've ever heard.
Let me define what is " nothingness " :
Nothingness is the absence of any existence, infinity concept is the opposite of nothingness.
Non existence can never bring something into existence .
But is there anything _outside_ the number system that can confirm that the distance between 1 and -1 is 2? (To me, it seems infinite.)
Numbers are representatives of relative quantity. They all represent some quantity more or less than the quantities represented by other numbers. But just as 'infinity' is not a number, but, rather the absolute, non-relative concept of infinite quantity; so too, is 'zero' not a number, but, rather, the absolute, non-relative concept of infinite non-quantity. The absolute absence of quantity, in other words, and thus not a proper number.
We use Zero for place holders to represent empty orders of magnitude. It's very useful and convenient, because our minds are finite capacity, so that we can not work with infinite digits. But that is a quality of our minds' abilities, not of external reality itself. An omniscient mind would have no need of a zero place holder, but, rather, would do math with infinite single digits.
To me, both of our uses of zero are convenient, but ultimately misleading. And I think this has potentially extremely far reaching consequences for both math and physics.
For example, in our number system, we understand that infinity is not a number, so that infinity - 1 is still infinity, basically, because you simply can't subtract a number from a non-number.
But when it comes to zero we don't recognize that. So we allow that 0+1 = 1, and so on. But does that correspond to reality? I would say that in reality, if there is true, absolute nothing, there's nothing to add or subtract. It is an immutable absolute conceptual state. So that 0+/- anything still = zero, just as infinity +/- anything still equals infinity. Because you can't add or subtract anything from absolutes, because absolutes are immutable and timeless. They're not measurements of quantity.
And measurements of quantity, btw, are divisions of everything. It's probably best, imo. to think of zero and infinity as the opening and closing brackets of the set [All] . Ultimately, they are the same, the duel expressions of the boundary of [All].
Note that this doesn't work _within_ our number system. But consider that she said in the video that Calculus works so well because it avoids having to divide by zero. It's not that our system for numerical notation and the math we do with it works so well _because_ of using zero as a digit. Rather, we manage to make it work very well specifically by _avoiding_ the paradoxes caused by using an immutable absolute concept as the lowest number in the number system(a system of relative quantities.)
There are only to numbers in existence... Zero and one... Zero indicating an absence and one represents presence... On vs off and so on... The accumulation of numbers then represents sequence... So 7 is not a number in itself but rather a sequence of ones that re occur until it represents "7" occurrences... We need to reevaluate our understanding of numbers...
When defining something as having nothing in it such as a hollow ball, would it be correct to say that within that nothingness, is a quantity of 1 cavity within it?
I'm not trying to just use words to twist things up, I'm referring to how math always seems to have an exception to the rule and how things change when we get down to molecular states or quantum states.
Because of how our dimension potentially interacts with other dimensions, could this be one method of getting something out of nothing?
X divided by zero IS infinity (assuming X>0 or X
X divided by Y is Z only if Y times Z is X.
So... X divided by infinity is undefined, because there is no number Z that multiplied by infinity is X.
Undefined and infinity....are kinda the same thing
Galactic Galaxle Far from it. Infinity is a concept, whereas undefined means "no result".
fine video, but I love it win "science" plunges into illogic... multiplying AND dividing by 0 is identical to doing those things by 1. dividing by 1 is like multiplying by 1, you remain with original number you started with... you aren't added or subtracting anything from the original number. since 0 has no value, when multiplying and dividing by it, you are in fact not multiplying or dividing at all and you arrive at the original number. that sounds logical to me. good vid!
I was thinking this I was like if zero isn’t a positive number so it’s a negative but there’s no such thing as -0 if there was zero would be a positive
then please why you are not able to count 0 As natural number rules saying ,could anyone teach me if the zero is not using in counting then why it is zero? or what is before 1?why we cannot call nothing as a zero? or what could we call to Space? everything that exist in world might be has a space before it or after it then what will call them?
The answer is infinity. You could say that 1 + 1 is not actually 2 because numbers are just concepts if you wanted, but that's not a very good argument.
Hang on a minute. You can't say infinity is just a concept. All numbers are just conceptual.
+Lucid Moses Yeah, but infinity can't be used in calculations. you don't add to infinity, nor subtract from it, because it will always result in infinity. So, it has no practical use, only conceptual use.
Leopoldo Aranha I see. So
X / 0 is not infinity because infinity is not a number
infinity is not a number because it has no piratical use.
X / 0 equals infinity is a piratical use.
But
X / 0 is not infinity because infinity is not a number
infinity is not a number because it has no piratical use.
X / 0 equals infinity is a piratical use.
But
X / 0 is not infinity because infinity is not a number
infinity is not a number because it has no piratical use.
X / 0 equals infinity is a piratical use.
Etc.. etc..
Lucid Moses I like your spell of practical. It is a typo, but it also says something about pirating a logic.
Mathematical concepts set does contain the concepts of numbers, but numbers set _only_ contain the concept of numbers. Infinity isn't a concept for a number, as it has no defined quantity. Such as that, infinity, while as much of a mathematical concept as a number, isn't a number.
Leopoldo Aranha yea, but the same reasoning is true for zero. You can't count zero any more then you can count infinity.
Lucid Moses Nope. Zero does have a defined quantity, or, better saying, it has no quantity at all.
Infinity, on the other hand, has a quantity that is not defined and can't be defined in any way whatsoever. See the difference?
Is it just me, or are the chapters in binary?
Also, the positinal number system always met resistance when it came up against established systems. We forget about earlier instances because they happened before the most-recent example and thus the most resent one is the one people focus on.
Nothing is something. At least under the POV of Directed Intelligence. What does that mean? How does meaning mean? Meaningful conversations appreciated.
I think that 'Something' is an unspecified 'Thing', where as, 'Nothing' is specifically 'No Thing', a 'Void'. In the same way, to classify 'Front' we need to recognise 'No Front' (Back) and for 'In' we need 'No In' (Out), etc. These must all be from the POV of a subjective intelligence because these intrinsic pairs of class are meaningless when divided or unrecognised. For there to be 'Things', we need to recognise an absence of 'Things' to classify them - as being not 'No Thing'.
A 'Thing' only moves into a 'No Thing' (void) because a 'Thing' cannot move into another 'Thing'. If it moves, it will have to move other 'Things' into 'No Thing' (void). If 'Nothing' is recognised as a 'Something', then how is it classified? What is it paired with? What is 'No Something'?
What would I mean if I asked you to:
- Imagine nothing? Draw nothing? Do nothing? etc
- Imagine no thing? Draw no thing? Do no thing? etc
I think as an abstraction 'Nothing' (a void) is 'Something', as with any subject of class, but in context 'Nothing' is 'No Thing', objectively implied as not a thing, and void of all things. I think it must be the same for Zero, so I would subjectively classify it as a 'No Number'.
Nice video but incorrect. The Mayans/Olmec civilizations had a place holder value a shell. As it has been proven the Mayans performed astronomical calculations. These civilizations had this system down thousands of year BC. The evidence is in their pyramids, codices, etc. Recently, many scholars have agreed only the Mayans had the zero as a place holder and they had the concept down.
What is general taught today is from an European/Asian point of view.
The zero as a NUMBER was first put forward by Indians 1500 years ago. And the modern number system we use today worldwide negatives and positives emerging from a null point in opposite directions is developed in India.
@@akhilals5471 The impressive thing about the Maya is that people in Europe, Asia and Africa have always been in contact with each other, influencing each other. People in America where isolated from the rest of the world for thousands of years and still they figured it out and came up with the concept of zero.
@@zacharywhite7547 Eventually 0 reveals himself to all his children
Don't fear... I AM the alpha and the 0mega
I AM the beginning and the End of everything.
Quick question.... How come when you multiply 0 and 5 it equals 0?.....shouldn't it give you 5?
Even when he makes himself nothing he is still more powerful than infinity....proving that even when left out he still the omnipresent omnipotent king God Jeh0va ......at the end of the day we are nothing without Him... When 0 reveals 1 (Jesus) and then takes him into him.....We are forgiven and saved from death by his promise.
His love is the only real thing. Amen Jesus
@@zacharywhite7547 the thing is you don't need anyone influence to develop a concept. Like you don't need an influence to think. And indian invented it way before then the mayas.
Ancient Indians did not just invent the Number system, If you are someone who loves Math, Look up - "Vedic Mathematics". They came up with ways to calculate Square roots of 10 Digit numbers in just 3 seconds, Transforming you into a Human calculator. Ancient Indians used these "Simple Tricks" to calculate Insanely large numbers, Like the ones mentioned in Buddhism.
Buddha was once asked - What is the largest number in existence in the Universe ? He replied 10 to the power of 540. That's 10 followed by 540 Zeroes. Whether the Buddha was simple making it up, It doesn't matter and is a whole different topic. What matters is there was a Culture of recognizing and using such crazy large numbers in Ancient India !!!
And here I thought this video would be about the hypothesis of the Zero-Energy Universe.
God Energy universe you say... That would be interesting
Can you explain why anything to the power of zero is one? I believe it's related to the concept that zero actually means nothing rather than a number.
x^1 = x,, dividing both side by x, x^0 = x/x = 1
How do you add by zero?
You just do
dividing any number by zero means that that number will never come in the multiplication table of 0, so the table will go on till infinity to get to that number. The answer is infinity for sure, concept or not.
very nice video!
Where did the word zero come from?
مع الأسف سيدتي المحترمة لم تذكري الخوارزمي مبتكر رقم 0 الحالي كذلك لم تذكري ابن الياسمين(ibn al yassamin) مبتكر الارقام الغبارية او أرقام فاس they call it also the Morroccan numbers. كل هذا موجود في كتب التاريخ الأكاديمية. 😊
Fuck- how do I know Hannah Fry? Rings a bell...
You'll find zero voices sexier than hers.
yookayman Creepy comments abound!!!!! Damn
Yeah creepy comments weird
Lol. abound.
0 is balancing between positions... positive and negative
Whatever you said this nothing gone inside of my brain but I like the video...
In some sense, saying "Infinity is not a number is a concept" is like saying " 1 is not a number is a concept" ( are you saying 1 is not a concept?). Infinity is still a concept don't get me wrong. The opposite of infinity is infinitesimal and that's what you get when you divide by 0. Infinitesimal is not a number, it's a concept.
Infinity is not something you can measure, that's why it's a concept not a number, the number 1 is a specific quantity, while infinity cannot be specified into a defined quantity.
I think this video is nonsense, it doesn't explain how you can get something from nothing.
You cannot get something from nothing because nothingness is absence of everything, if we talk about infinity concept, nothingness is the exact opposite of infinty, because it's the absence of everything .
Infinity is not bounded, it doesn't have a beginning or an end, therefore it encompasses everything .
It would seem the divide by zero error is an indicator that zero should not be treated as a number.
+grant kohler Another indicator that zero should not be treated as a number is the flaw where multiplying both sides of an equation by zero would prove every equation to be true.
+grant kohler Yet another flaw to consider as to why zero should not be treated as a number is the rule that any number divided by itself equals one.
I'll have what he's having^^^^^^^
there's something called group theory. which requires zero to have a "number" tag. Also, dividing is not a matematical operation, only multiplication
Can anyone please tell me with which programm this video was made?
The animation was done using After Effects, sound and music were done using Final Cut Pro X.
This video tells us how the number came to be. It does not tells us what it is... the title should be “history of number zero” not “what is zero”... you still did not mention the answer to that question. What is zero?
Here are some interesting facts about the number zero.
We like to think of it as an empty quantity, but if we pay attention, there are positive numbers and a mirror negative for each positive number, which when combined, give us zero... (+5)+(-5)=0
both mirrors of the number 5 can be represented at the same time by zero.
So, zero actually represents an empty quantity (-5) AND a full quantity (+5), *at the same time, in the same space*
What?
In reality, it represents the existence AND absence of all numbers of a thing *in the same time/space.*
Example: A zero quantity apples in a box.
Actually means, all possible apple numbers exist in this box as well as the absence of them exists at the same time in this box.
That is very confusing to think of. I know. That’s why I like it.
If we say there are zero apples in a box.
Mathematically, it means there are (let’s say) 5 apples exist, and the same 5 apples don’t exist *at the same time*
Therefor, an empty space should not be represented by a zero. It should be represented by a negative number of what you are looking for.
Example: This box has a -5 apples. Since I’m looking for +5 apples and cannot find it.
If I’m not looking for a specific number of a specific thing... let’s say I’m looking for *anything at all* in that box. It should be calculated as: *Box contains a negative infinite quantity of anything*
So, what is zero?? My brain will explode.
My theory is:
Zero is everything and nothing at the same time. If that is correct, then we cannot experience zero in reality. Which I think is sad 😨
aryabhatta was the fist one to bring the rough concept and complex concepts of ZERO
0 was devloped in india🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳and I also indian🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳😊
Every number can have a corresponding relationship in the material world except for zero. It is impossible to have zero of anything. Even in binary computing systems it only implies a length of time between 1s.
You can't have zero of anything but you can have at least zero of everything
soo nice.......
keep text toooooooo........
it is gives more explanation
There is a philosophy called "Saankhya Darshan." Darshan in sanskrit means 'to see' or philosophy. Saankhya gave rise to 'Sankhyaa' the numbers in sanskrit.
0 in Vedas is not nothingness. It is exactly opposite. It is 'complete'. Read the shanti mantra that defines this.
"om poornamada poornamidam poornaat purnam udachyate.
Poornasya poornamadaya poornam ewa awashishyate"
It means if you add completeness to complete, you get complete.
If you completely remove completeness, completeness still remains.
After 9, that location is NOT nothing. It is complete.... That's 0 and then you move to next place....
I don't know if West knows this.... If anyone can take credit of zero then it is only "Saankhya philosophy" and vedic sukta....
that voice!
What do you mean
Yup. That's she
What a voice
Интересная история...
Деление не всегда идет именно от умножения... или сложения... или даже вычитания...
Иногда оно выражает относительное значение между зависимыми величинами...
Такое выражение когда 0×0 большинство безоговорочно посчитают равным 0...
но на самом деле это поверхностный взгляд...
Ведь относительный ответ X/0=0 означает что X=0×0... без учета безотносительного остатка...
Хотя о чем это я... делить на ноль многим запрещено почти на законодательном уровне...
Многие думают что на ноль можно умножать а делить "почти" совсем ни как нельзя...
Типа X×0 = 0
это нормально лишь потому что 0/X = 0...?
Но из этого же следует что
сам X = 0/0...? Х=0⁰...? ну и где логика...
Давайте рассмотрим один из вариантов как обычно происходит действие деления...
6:2=6/2=(2+4)/2=2/2+4/2=1+(2+2)/2=
=1+2/2+2/2=1+1+2/2=3 (без остатка...)
7:2=7/2=(2+5)/2=2/2+5/2=
=1+(2+3)/2=1+2/2+3/2=
=1+1+(2+1)/2=1+1+2/2+1/2=
=1+1+1+1/2=3+1/2=3 с остатком 1...
И это также можно с помощью принятых форм математических записей выразить как 3½ или 3.5...
А что же происходит когда якобы производят деление на ноль...
многие говорят что это будет равно какой то бесконечности...
15:0=15/0=(0+15)/0=0/0+(0+15)/0=
=0/0+0/0+(0+15)/0=0/0+...+0/0+15/0...
и при дальнейших действиях всегда такое деление будет c постоянным остатком в виде того что "делилось" изначально...
в данном случае остаток 15...
и почему то вот об этом остатке или забывают или неосознанно замалчивают считая только бесполезные бесконечные действия не приводящие ни к какому результату деления...
Если быть немного логичным то видно что даже при бесконечном количестве таких действий деления (а точнее бездействий) вся сумма таких действий равна нулю с постоянным остатком того что было изначально делимым...
То есть само такое деление не происходит...
сколько было изначально столько и остаётся в остатке неделимо...
X:0=X/0=(0/0)×N+X/0=N×(0/0) с неразделённым остатком X
где N×(0/0)=0 и N число мнимых манипуляций не производящих деления...
поэтому N=0... а не бесконечность...
отсюда и получается два ответа при делении на ноль...
относительный ответ равен 0...
но именно ноль бессмысленных манипуляций...
а безотносительный ответ равен самому значению делимого X...
В примере 15/0 = 0 целых 15 нулевых...
или же 0 целых и 15 в остатке... именно умножая это число на ноль можно получить первоначальное данное значение...
Но об этом как правило неумышленно умалчивают... ведь этому не научили...
Общепринятая математическая терминология до сих пор никак не может внятно объяснить даже продвинутым математикам (что уж там говорить о простых людях) что же это за такие математические "действия" с нулевыми значаниями и почему "мультипликашка" multiplicatio (умножение) с "отсутствующим" множителем ноль возможно (при всей своей абсурдности)... а вот "дивизионка" division (деление) на ноль ответ неопределен от полного категорического запрета до "игр разума"... "положительной и отрицательной бесконечности вселенной"...
или же "совершенно не имеет смысла"...
А если всё же хоть немного подумать...
Любое значение X не равное нулю деленное на ноль всегда имеет два значения...
Относительный ответ ВСЕГДА = 0...
Безотносительный ответ равен самому неделенному Х
Полное непонимание современной математики темы умножения на ноль и тем более деления на ноль...
При записи умножения числового значения X на ноль получаем
-----
X×0=0 X /\ 0/0
Перенос ноля через знак равно превращает равенство в качельное неравенство типа
----
100% /\ 0%
Сам знак процентов кстати пишется как 0/0...
То же самое и с делением на ноль...
----
X/0=0 Х /\ 0×0
Перенос ноля через знак равно превращает равенство в качельное неравенство...
Я называю это нулёвыми значениями (не нулевыми а именно нулёвыми...
"ни разу взятыми" или "ни разу трачеными" то есть "нерастрачеными" если это об умножении на ноль...
"ни разу делёнными" или "неразделёнными" если это о делении на ноль)...
И непонимание до сих пор этого простого меня очень удивляет...
220 вольт делить на ток 0 Ампер это сопротивление = 0 Ом... но это просто не потраченое напряжение...
1 торт не взятый кусками ни разу (деленный на ноль) 1/0 это 0 кусков взятых но это все тот же 1 неразделённый торт...
5 монет ни разу не взятых 5×0 это 0 взятых монет но вопрос как правило звучит "сколько будет" а не сколько взято... так вот будет все те же 5 невзятых "нулёвых" монет...
И это всего лишь маленькая вершина айсберга действий с нолем...
Сложение и вычитание нуля не меняет первоначального значения... а почему?
да потому что на самом деле не происходит самого математического действия как такового... ничего не прибавляется и не убавляется при этом...
С умножением и делением на ноль происходит примерно тоже самое...
Ничего не происходит при этих действиях... всего лишь описывается что первоначальные значения не изменяются...
хотя ответов получается два
относительный = 0
безотносительный = 100% = 1×Х(нулёвое)
в зависимости от поставленного вопроса...
И безотносительный ответ имеет гораздо больше смысла...
5 метров × 5 метров × 0 метров =
25 метров² × 0 метров = ?
Относительно нуля ответ 0 метров³
Безотносительно нуля = 25 метров²
----
25м²(=100%) /\ 0м³ : 0м (= 0м²)
Перенос нуля (при умножении на ноль или делении на ноль) через знак равно превращает равенство в качельное неравенство
-----
1×X(нулёвое)(=100%) /\ 0(=0%)
Безотносительный ответ при действиях умножения и деления с нулем не учитывает как само действие с нулем так и его измерение...
5 яблок : 0 корзин = ?
Относительный ответ 0 яблок на корзину...
Безотносительный ответ 5 неразделенных яблок (без корзин)...
Убираем ноль и его измерение из вычисления и получаем нетронутые первоначальные данные и можем дальше с ними что то вычислять...
----
5 яблок нулёвых (= 100%) /\ 0 корзин × 0 яблок/на корзину (= 0)
Чисто качельное 100% неравенство...
Откуда здесь могут взяться какие то бесконечности? Или черные дыры?
Кстати 0(нулёвый) / 0(нулёвый) = 1
Впрочем как и любое другое число раз делённое на само себя...
Это всего лишь малая часть моего личного взгляда на действия с нулем и он не ограничивается только этими действиями...
Ноль не имеет численного значения...
он лишь описывает отсутствие чего либо...
Практически все действия с нолем на самом деле не происходят...
Многие пытаются ноль "всунуть" в основные математические действия... при этом абсолютно не понимая смысла самой записи таких действий...
но с нулем есть только математические "бездействия" и чаще всего действия "умножения" и "деления" связанные с нулем говорят что есть что то безотносительное до той поры пока вместо нуля в таких выражениях не появится числовое значение...
Лишь после этого выражение становится относительным...
Если напряжение = 0 и сила тока = 0 то это не значит что при этом всегда нет сопротивления...
Если скорость = 0 и время = 0 то расстояние при этом может быть каким угодно (в том числе и отсутствовать)...
Поймите главное перенос нуля через знак равно изменяет смысл равенства на качельное неравенство 100% того что было изначально и есть до сих пор и с другой стороны 0% того что якобы "взято"...
И никаких бесконечностей и всяких "черных дыр" при явном нуле в таких действиях никогда не будет...
Чисто математически ЛЮБОЕ "действие" когда Х не равное нулю "умножается" на ноль или "делится" будет равно ВСЕГДА нулю...
то есть отсутствию таких отношений...
Но смысл совершенно не в этом...
любое такое "действие" описывает лишь неизменность самого стопроцентно имеющегося значения X при этих нулевых "операциях" с ним...
Что касается "деления" 0/0...
(или по другому выражения типа 0⁰...)
Если вы делите два различных нуля один на другой (с различными мерами измерения) то "относительный" математический ответ этого будет 0 = 0% того что использовано...
Но безотносительный ответ будет равен 100% того что было дано изначально и не было использовано в ходе бездейственного "деления" отсутствия одной величины на отсутствие другой...
Если делить один ноль сам на себя (с одной и той же мерой измерения) то ответ равен 1 раз...
И никаких 2 раза... 3 раза... и т.п. у отсутствия величины в виде ноля не будет...
Интересно как можно объяснить 0/0 = 0⁰ с точки зрения "практических" равенств...
Многие считают что 0⁰ = 1...
Напряжение U = 0 вольт...
Сила тока I = 0 ампер...
Сопротивление R = U/I = 0/0 = 0⁰ = 1...? Ом...?
Весело...
Дистанция S = 0 километров...
Время t = 0 часов...
Cкорость V = S/t = 0/0 = 0⁰ = 1...? километров/час...?
Смешно...
Объем V = 0 метров³...
Ширина W = 0 метров...
Высота H = 0 метров...
Длина L = V/(W×H) = 0/(0×0) = 0/0² = 0‐¹ = 1/0...? = ...?
Сколько будет...? метров?
Интересно сможет хоть кто то это объяснить хоть как то математически...
Нужно знать историю происхождения таких нулей...
Многие математики почему то считают что у нуля нет обратной величины...
Другие свято верят что величина обратная нулю это "бесконечность"...
К сожалению (ну или к счастью) у "бесконечности" есть обратная величина равная 1/бесконечность...
И как бы она ни была мала она НИКОГДА не будет равна нулю...
И уж точно она не имеет безотносительного значения...
К тому же она имеет знак плюс или минус в зависимости от того с каким знаком берется сама "бесконечность"... (если конечно она хоть как то вообще может быть "взята"...)
У полного отсутствия в виде нуля есть обратная величина... это полное присутствие... и для нуля это равно единице... то есть 100% присутствие чего либо...
1/0 "относительный" ответ математически равен нулю... но именно он не имеет смысла а вот безотносительный ответ как раз равен "ни разу делённой" то есть нераздельной (нулёвой) единице...
Никакой бесконечности при делении на ноль не бывает... если только сама бесконечность не делится на ноль...
1/0 равна 0 целых и 1 в остатке... полностью неделённая единица...
Умножьте обратно 0×0 целых и прибавьте остаток 1...
получите изначальное имеющееся число якобы "делённое" на ноль...
Деление на целые части заканчивается когда вы не можете больше "отсоединить" от делимого количества записанного в делитель...
При нуле находящимся в делителе вы не сможете "отсоединить" вообще ничего от делимого числа пытаясь вычесть ноль...
даже при "бесконечных" таких попытках...
поэтому для действия деления на ноль это равно всегда ноль целых...
а остальное неделимый остаток...
Много есть искусственных точек нулевого отсчета в различных измерениях различных величин...
Но в большинстве своем они не имеют никакого отношения к делению на ноль...
Я лишь изложил некоторые видения своей теории математических "действий" с нулевыми значениями...
На сегодняшний день никто не смог переубедить меня в этом... и даже наоборот после дискуссий на эту тему мое личное убеждение в моей правоте возрастает все больше...
Вам же желаю всех благ в деле поиска знаний...
India is the land where 0 was discovered
Shashank K R I think they made zero mean nothing and gave it more meaning. But I thought that it was Mayans who used zero first as a place holder?
I also like to add a pendulum theory, like high and low tides. Everyone is so linear
What are the chapters counting up in binary?
dope animation
why the re-upload?
+Jack Drewitt We spotted a small error in the original version and couldn't live with ourselves, so reuploaded :)
+The Royal Institution you really shouldn't get so worked up over ... nothing ;)
The Royal Institution theres still not the 60th symbol, what was the error?
+Jack Drewitt In the editing process we'd accidentally ended up with a misplaced chapter title, meaning our oh-so-clever binary chapter system didn't work any more! We're okay with the 59 symbols ;)
The Royal Institution thats rude, i happen to like Sixty Symbols
If you divide anything by no-thing then there is no division. I don't get why it is so hard for many mathematicians to acknowledge that the issues and requirement for special considerations with zero are of their own creation. Algebra being the main culprit causing confusion. It seems simple and intuitive. 1+0=1. 1-0=1. 1*0=0. Yet divide by zero and suddenly the definition of 0 changes?
0 is none, no-thing, absence within the context of whatever things you are discussing (As in: Using a numeral describe how many chicken emojis exist in this sentence). So if we divide 1 chicken by no chickens (bad example) or 1 centimetre by 0 centimetres we are making no change as the function is negated and there is 0 division. We could try to carry out the function as a subtraction and find ourselves in infinite iterations because as someone else commented 0 goes into any number infinite times...but this is simply not true because 0*x=0. Zero provides context, an interdependent opposite to denotations of value or magnitude. If you have a box of zero and you divide it with a zero width division, x times, there is no division. 0 is the argument at which the value of a function is negated and disappears. It is not positive or negative or even or odd, it is a denotation representing the concept "no-thing" and hence is clearly defined. Not undefined or infinite. Zero as a numeral is confusing because in contradiction to its core meaning it also has a value in mathematics in terms of indicating magnitude in multiples of ten. With the right axioms maths can "prove" anything but that doesn't make it true. See Gödel's work. It is a miracle that maths is as useful as it is to science when it is an incomplete, often misunderstood and contradictory theory.
Hello there, can I get myself a chance to contribute my translation to you guys? I would like to translate this video into Vietnamese .
Thank you.