It's a concept which intrigues mathematicians, but scientists aren't so keen on it. More at www.sixtysymbols.com/ With Professor Laurence Eaves and Mike Merrfield
Once when he was still quite small my son asked me what the largest number was. I of course replied that there wasn't one. Upon his insistence that there must be I told to imagine that he take the largest number, whatever it was, and then add one to it. His eyes went wide and his jaw literally dropped. The look of someone who has just seen over the edge. Priceless.
I think the concept of 0 is even more profound than that of infinity. It's hard to imagine something going on forever, but even harder for me to imagine nothingness. No matter, no energy, no space, no anything. Profound.
To work out the answer to an integer divided by zero, you need to first define the number set that you are talking about. For natural numbers (N), whole numbers (W), integers (Z), rational numbers (Q), real numbers (R) and complex numbers (C), the answer is undefined, because there is no element of the set which satisfies the problem. However, when you start using limits and extended real and complex number systems, infinity is defined and can be a solution to the problem. (also see alephs!).
A great example of the math/physics divide is when you're making a Taylor series approximation. Once you write out a few terms, a physicist would say that the remainder is negligible, while a mathematician would worry very much about whether those remainder terms do in fact vanish.
I spent some time learning catastrophe theory at University because it helped removed irritating singularities from my calculations in theoretical Chemistry. It used to be the hip theory in the 1970s but by the time I was at University it was a great tool for dealing with infinities.
When he was about three years old my child started talking about "the end of the number". I soon realised that he was talking about the concept of infinity. And I was surprised because I was planning to introduce this concept to him a bit later. He didn't have the right word then, so he made up his own.
@9hello123 A graph of a non-continous function approaches infinity near the asymptote, the asymptote itself is a point sized hole in the graph, which is why 3/0 is an undefined constant.
@Haiguise1 Take the example of 1/f noise (i.e, signal). It exist in the physiological data such as heart rate, EEG, eye movements. At what scale you take measurements you still see self similarity.
@immrgrunty1363: there is no such thing as dividing a number endless times. You can define infinity as the limit of 3/x as x approaches 0 from the right, but then you are dealing with limits and not regular division. Also, you must explicitly state whether you are coming from the left or right, as in the two cases you end up with + or - infinity (in this case those are different things). If you define 3/0 in regular division, then regular algebra breaks and you cannot solve anything.
@itsmanofpopsicle Yes it does, If we're talking about f(Y) = 3/X, then the asymptote is still 0, it would take an infinite value of Y to reach X. Even if Y is a negative number. In fact if you go to Wikipedia and go to the asymptote article, there's a graph of such a function drawn out.
tavi921 Mathematically, no, 3/0 does not equal infinity because, as you say, it leads to various paradoxes which break maths. That, however, is a problem with algebraic maths, rather than 3/0 not actually being equal to infinity. The problem is that algebraic maths cannot describe infinity adequately. Its like saying 3/0 = banana, and 7/0 = banana so 3 = 7. Thats just what happens when you use a term in algebraic maths that has no mathematical value. Obviously, you can divide 3 by 0 an infinite number of times. This is all that statement means. It has no mathematical value, so you don't do it, but fundamentally its demonstrably true. Mathematically, 3/0 = undefined. And the reason it is undefined is because no one knows how to define it.
***** What I meant is that infinity is a term that describes a concept, not a number. There is no number infinity. So "=" is understood in a logical sense instead of a mathematical sense. Actually I think you were making the same point.
@kristijanadrian No, undefined is a synonym for unknown. ie: either there is no known answer or the question is illogical. Zero and infinity are opposite mathematical concepts, the only thing they have in common is that neither fits neatly into the human mind because of our lack of physical experience with them.
@madadane123 i think its actually undefined if you want to get technical, because if you plot it on a graph the gradient shoots off towards infinity and infinitesimal
The limit as x approaches 0+ of 3/x is infinity, but the limit as it approaches 0- is negative infinity, therefore you cannot associate a value to a number divided by zero, hence the term "undefined".
@THERaikami1 The natural numbers are infinite, but countable - 1, 2, 3, etc. But there are an infinite number of numbers in between 1 and 2, which are uncountable. This is because there are a finite number of natural numbers between any two natural numbers (if x and y are natural numbers and x < y, then there are (y-x)-1 natural numbers in between them), but an infinite number of numbers between any two numbers in general.
for instantaneous velocity it is valid to say that it is the velocity an object will have if from the moment we are interested in it performs uniform linear motion (ΣF=0). the same for acceleration (obviously in this case ΣF=constant)
@Lunarsight Graph f(x)=1/x. The reason a constant divided by 0 is undefined is entirely dependent upon which side the number is coming from--either the positive or the negative. For example, the limit as x approaches 0 from the positive side is +infinity, but the limit as x approaches 0 from the negative side is -infinity. The reason it's undefined is because the two points do not meet.
A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined. Thus, it is sometimes useful to think of a/0, where a ≠ 0, as being Infinity. This infinity can be either positive, negative, or unsigned, depending on context.
@MarkArandjus The problem with that theory is that it doesn't take into account negative numbers- which are smaller than 0.0001. Rather than being a slope down, it actually is a parabola that stops at infinity and goes to -3 and slopes upward.
Iv reciently just watched your video on the speed of light, and it was saying that the speed of light does not stack if you shine a torch from a moving train. But in that sence the speed of light is also infinate? because c + 100m/s is also c. but it has a set value (3x10*8), and infinity has infinate value. ...so does that mean c is a countable infinity?
@TriMiro8107 3/0 is undefined because the in that circumstance, infinity is treated as '0' dividing '3' an endless number of times. so yes, 'infinity,' in a sense, works in that circumstance.
@pigrogromitus Xeno's paradox is hella crazy, but very interesting. Do you know if that has been resolved? It seems to me that if one makes time discrete (i.e, a "Planck time," or what have you), then the paradox is solved--past the Planck time, divisions are either theoretically impossible, or just plain meaningless.
@123Fusselbirne the range is how far the effect is able to reach. and as no matter how far away you get from an object, gravity still interacts. that means it's range is infinite
@MrSuednym Other way around. Mathematicians are applied Physicists. That is a little unfair because both are independent or can be, but they both need each other to get anywhere.
@bohngat But they are mathematical constructions, If you take a snowflake for example there still is a minimum 'resolution' for the fractal which is at the size of the water molecules.
There are cardinal numbers, ordinal numbers, hyper-real numbers, numbers from smooth analysis, and surreal numbers. Those are structures that can be used to discuss infinities within mathematics.
As soon as we use numbers in association with Geometry we soon come up against the problem of Infinity. The Natural Numbers 1, 2, 3, 4,., are used to count discrete objects. In the two-dimensional plane we assume that any point can be represented by a pair of numbers (a, b). Considering a straight line of length one unit, we assume that it consists of points. However, a point has zero width. One then has the problem of how many points you need to form the line. Dedekind and Cantor considered this problem, and the different types of Infinity. However does this Cartesian System of Geometry correctly model the space in which we live? (The Cartesian System assumes that space is continuous). Leibniz considered this problem, and felt that space was NOT continuous; he developed the concept of Infinitesmals and his Differential Calculus from this different concept of space. Perhaps Leibniz had stumbled upon a vague sense of the Planck length.
There's just one room cleaner, despite the size of the hotel. You'd think that would be a problem, and that the hotel is ridiculously understaffed, but the room cleaner has a clever way of getting around this issue. He cleans each room in half the time as he cleaned the last. He spends one hour on the first room, half an hour on the second, one quarter of an hour on the third, ect. Eventually, he gets all rooms cleaned within 2 hours.
the definition of the base unit, ampere "the constant current that will produce an attractive force of 2 × 10-7 newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum" which contains infinity and can we can think of negligible cross section as an infinitecimal?
@LamaPaj That's correct. ∞ is actually the limit of y=3/x when x approaches 0 (if x approaches from the left, if it is negative, then the limit is - ∞). He just wrote it that way to make it more easily understandable. I'm pretty sure he knows that ;)
Me: Oh hey I've seen a Numberphile video on this already 0:25 - "You shouldn't really be talking to a scientist you should be talking to a mathematician" Me: ...I knew it
well thanks for the help, cleared it up a bit! ...ill have to go read up on special relativity. Sorry im still a bit of a newbie when it comes to physics - im only at my A levels at the moment! Thanks again.
Indeterminate is undefined, just that it is possible to assign it any value, though it isn't very helpful. When it comes to something that is undefined, there just isn't a value that can be used to represent it yet. For a time SQRT(-1) was undefined, but now we use i or j. Same thing applies to 1/0, which you can prove a value for if anyone ever payed attention to factorials.
@kristijanadrian Actually an infinte pound bill would have the interesting property that no matter what you bought with it you would always get an infinite pound note as change. The problem with issuing infinite pound notes is social, not mathematical.
@OhhSoulz Is a constant an infinity? Well you could see a constant as an infinite sum of infinitesimals. But there's no need to look at them that way. Let a constant just be a finite constant and everything works out fine.
@ray123ification I don't know. Could be, but I'm fairly certain that whatever can be imagined, can be expressed one way or another. Doesn't mean it's going to be easy, or that anyone will understand what it is you're actually expressing, but it is doable. :>
Infinity, more or less (un)countability is often used in computation theory (the mathematical part of computer science) and used to describe problems and their computable complexity (won't go into details). It's not useless and not just something of the mind as it helps us in many ways (like knowing what to put effort into in algorithmics) and can be shown to be there for instance in the proof of the halting problem with use of diagonalisaton (look it up).
very comforting video. i still dont get that infinite hotel, it is said that every room is full at arrival. where/how/why would you find an empty room then to move someone into?
Always think about infinity as a concept rather than a number so obviously 2+1 isn't 2 but infinity +1 is still infinity, so they don't use the same rules
it is said that every room is occupied. doesnt matter how many there are. if you make up another room, it will be occupied as well. at least that is what "every" means to me. if, for whatever reason, you can make up an empty room, why would you move all people already there one room further? just give it to the person arriving last.
It's inifnity. You don't have to finish the task of "move all people to the n*2 room" because there is no finish. If you check on the people at any point in time, you will see a whole bunch of people walking around at one part of the hotel, and this traffic is moving along the room numbers. In a normal hotel, there would be an end where half the guests are now stuck and have no idea what they are supposed to do. But in an infinitly large hotel there can be no end and therefore nobody is ever complaining about "not having a new room". Here's another little thing showing that thinking about the "end" is somewhat pointless when dealing with infinity: Imagine you have a lamp that can be turned on and off in an instant. Now you turn the lamp on and wait a minute. Turn it off and wait half a minute. Turn it on and wait a quarter of a minute. After 2 minutes, you will have turned the lamp on and off an infinite amount of times. Now here's the question: Is the lamp now on or off?
I was about to post the same comment (7 years later though). Indeed, 3 divided by 0 is not INFINITY !!!!!!!!!!!!!!!! It may have been wiser to ask the question to mathematicians.
@123Fusselbirne exactly. it's kinda funny because you don't really use the symbol for infinity in physics because if you did then F=0 and then the range wouldn't be truly infinite. but like you mention you can have an unimaginably large number for the distance and no matter how much larger you make it there will still be a force. mathematicaly you just can't use the symbol infinite ^^
@ 2:11 please note the Egyptian symbol he shows for infinity is partially the same as the glyph/symbol for KA or the body double, your shadow that follows you around for an eternity. The ka as a spiritual double was born with every man and lived on after he died as long as it had a place to live. After death the ka became supreme. Kings thus claimed to have multiple kas. Rameses II announced that he had over 20. science is a religion >> U do know that?
By definition a countably infinite set is a set that can be put into one-to-one correspondence with the set of natural numbers. For example, you can put the natural numbers and the odd naturals into such a correspondence.
So, the distinction between Mathematicians and Physicists is wether you are concerned with axial-tangential sync-duration limits or compound relative-timing duration wave-particle type measurements, and philosophically, of course it's the same indeterminate qa principle of the perceived meaning of Actuality.., the degree/proportions of Cultural Relativism inherent in "truth in labeling, lawful-ness".
I've written this also as a comment to another Brady's video: Physical world can be described with rational complex numbers. There's no need for irrational numbers as using Plank's measurements all measurements are quantified. But you still need complex numbers to easily describe for example elecro-magnetic fields. On the other hand as a mathematician I'm fascinated by the worlds that are created by imagining infinities that are between aleph0 and aleph1 or lager than aleph1 but not part of the power series of alephs. And that there is such thing as Banch-Tarski paradox which is impossible in nature as one never can cut anything the way the paradox cuts things up.
@megaelliott That's not quite true either. lim 3/x, x-> 0+ = ∞, yes, but lim 3/x, x->0- = -∞. Technically the limit doesn't actually exist because the left- and right-hand limits are disjoint.
@conneelyb You're probably right :P I'll admit right away that the explanation i got is very simplistic, and as you say, its most likley not correct for every aspect of math.
i think you're talking about the limit of 1/x, which is undefined as x approaches 0 for the reasons you stated - the left and right sides of the limit aren't equal to each other. you could say 1/x^2 is defined as infinity as x approaches 0 because both sides of the limit equal each other, but you must remember we are talking about a limiting function and not simple division such as 1/0 (with limits we are talking about 1/a number really really really really close to 0) 1/0 is undefined
6:18 I'm as far to a mathematician as you can think (I'm a sociologist) but I too hate when physicists and astronomers misuse the term infinity. It's one of the few complains I have anyway. Otherwise I love them and admire them deeply :-)
@l0rdoflol I can see the logic in your teacher's explanation: taking 0 people out each time allows for infinite iteration. However, translate to an algorithm & u have a conditional expression & recursive function i.e. for each iteration, if X != 0, take X people out then return to calling function, Else do nothing and return to calling function. So you would have infinite iterations of that recursive function but the amount of people taken out is a running total i.e. countable.
I thought the gravitational force that acts between two masses has a range from 0 to infinity 1/r^2 law, it is similar with electric fields so there are some uses of infinity in physics.
You are right that stars are about the same density at any point in space (the same number of stars per any specific volume) what they were saying is within the observable universe, as far as light has travelled since the big bang, there is a very large but finite number of stars. We can't tell how far it extends beyond this.
There are no exceptions in mathematics. A number divided by a number equals a number. The idea that a number divided by itself is defined to be equal to one is flawed due to how trends work, but regardless a number divided by itself equals one. 0/0 = R, which contains 1, so consistency is preserved. Also: 0/∞ = 0. Notice that commutatively, that means 0/0 = ∞, which is consistent with 0/0 equaling R. R is all real numbers.
Countable infinities are those whose members are countable when you impose limits, e.g. there is an infinite number of multiples of 2, but there are only five between 1 and 10. An example of an uncountable infinity would be Real numbers (Real in the strict mathematical sense, i.e. all numbers, positive and negative, whole and fraction/decimal) - there are an infinite number of these, but also if you pick any two numbers, there are still an infinite number of Real numbers between these.
No, Brady Haran is the same person as Brady Haran, they're not just two people randomly having the same name. Also, most of the people in the sixtysymbols videos have already been in a few numberphile videos, and the same goes the other way around.
I had a comment before this explaining that (apart from -1^2 actually being -1 and (-1)^2 being 1), the opposite of squaring x is actually taking the positive or negative square root of x, and therefore your conclusion is incorrect, and not just generally taking the square root, whereas the opposite of dividing something by y is just multiplying it by y.
ö. . , Yeah, and how do you fill a hotel with infinite amount of rooms in the first place? And if you do, and this scenario of moving from room to room happens it takes an eternity - like literally. And did they finish building of the hotel in the first place - I hear the construction is still going on there... last night when I checked in:)
Ups looks like I said that the size of a singularity is also infinite. What I actually meant was that the formulas give an answer of zero or "infinitesimally small" (which again doesn't make sense and is impossible to grasp).
Heh, glad to see I'm not the only math major who was shaking his head sadly at the 3/0 equals infinity bit. And of course the hotel had a countably infinite number of rooms so if an uncountably infinite number of new guests showed up (ie one for each real number) the hotel couldn't fit them in.
Perhaps a good analogy would be an infinitely long tape measure - the number of ticks is infinite, since the tape measure has infinite length, but you can count the number of ticks along any given length of the tape. There are also an infinite number of places where you *could* draw ticks along the edge of the tape, and even between two ticks, there is still an infinite number of positions you could draw more ticks. That would be an uncountable infinity.
Once when he was still quite small my son asked me what the largest number was. I of course replied that there wasn't one. Upon his insistence that there must be I told to imagine that he take the largest number, whatever it was, and then add one to it.
His eyes went wide and his jaw literally dropped. The look of someone who has just seen over the edge. Priceless.
SlideRulePirate Until you have aleph-null...
Or until you get a bit 8-bit about that. :)
The largest infinity might be the number of numbers in total, not
including that number itself (all the ordinals, cardinals, surreal
numbers, etc.)
I am that son.
1:20 *matt parker voice* pfft physicists
What,,, there is no such voice
I heard it.
I think the concept of 0 is even more profound than that of infinity. It's hard to imagine something going on forever, but even harder for me to imagine nothingness. No matter, no energy, no space, no anything. Profound.
To work out the answer to an integer divided by zero, you need to first define the number set that you are talking about. For natural numbers (N), whole numbers (W), integers (Z), rational numbers (Q), real numbers (R) and complex numbers (C), the answer is undefined, because there is no element of the set which satisfies the problem. However, when you start using limits and extended real and complex number systems, infinity is defined and can be a solution to the problem. (also see alephs!).
A great example of the math/physics divide is when you're making a Taylor series approximation. Once you write out a few terms, a physicist would say that the remainder is negligible, while a mathematician would worry very much about whether those remainder terms do in fact vanish.
I love this zoom in on Wallace's face. It starts innocently, then quickly becomes "I will destroy you. Infinitely."
> "Very, very big" is as far from the infinity as you can get.
Oh, this is going to be one of my favourite quotes of all time, ever.
I spent some time learning catastrophe theory at University because it helped removed irritating singularities from my calculations in theoretical Chemistry.
It used to be the hip theory in the 1970s but by the time I was at University it was a great tool for dealing with infinities.
When he was about three years old my child started talking about "the end of the number". I soon realised that he was talking about the concept of infinity. And I was surprised because I was planning to introduce this concept to him a bit later. He didn't have the right word then, so he made up his own.
i like a lot the way this professor explains everything, very clear
@9hello123 A graph of a non-continous function approaches infinity near the asymptote, the asymptote itself is a point sized hole in the graph, which is why 3/0 is an undefined constant.
@Haiguise1
Take the example of 1/f noise (i.e, signal). It exist in the physiological data such as heart rate, EEG, eye movements. At what scale you take measurements you still see self similarity.
great videos, link and info, thanks
@immrgrunty1363: there is no such thing as dividing a number endless times. You can define infinity as the limit of 3/x as x approaches 0 from the right, but then you are dealing with limits and not regular division. Also, you must explicitly state whether you are coming from the left or right, as in the two cases you end up with + or - infinity (in this case those are different things).
If you define 3/0 in regular division, then regular algebra breaks and you cannot solve anything.
@itsmanofpopsicle Yes it does, If we're talking about f(Y) = 3/X, then the asymptote is still 0, it would take an infinite value of Y to reach X. Even if Y is a negative number.
In fact if you go to Wikipedia and go to the asymptote article, there's a graph of such a function drawn out.
tavi921 Mathematically, no, 3/0 does not equal infinity because, as you say, it leads to various paradoxes which break maths. That, however, is a problem with algebraic maths, rather than 3/0 not actually being equal to infinity. The problem is that algebraic maths cannot describe infinity adequately. Its like saying 3/0 = banana, and 7/0 = banana so 3 = 7. Thats just what happens when you use a term in algebraic maths that has no mathematical value.
Obviously, you can divide 3 by 0 an infinite number of times. This is all that statement means. It has no mathematical value, so you don't do it, but fundamentally its demonstrably true.
Mathematically, 3/0 = undefined. And the reason it is undefined is because no one knows how to define it.
We define it by the term "infinity".
oh_no_mrbill Define it mathematically so that you can do calculations with it.
***** What I meant is that infinity is a term that describes a concept, not a number. There is no number infinity. So "=" is understood in a logical sense instead of a mathematical sense. Actually I think you were making the same point.
oh_no_mrbill You literally just said what I explained in my original comment, yes.
***** I just wanted to clear it up, when you said "no one knows how to define" infinity it does have a very clear logical definition.
@kristijanadrian No, undefined is a synonym for unknown. ie: either there is no known answer or the question is illogical. Zero and infinity are opposite mathematical concepts, the only thing they have in common is that neither fits neatly into the human mind because of our lack of physical experience with them.
Loving it .......superb.
@madadane123 i think its actually undefined if you want to get technical, because if you plot it on a graph the gradient shoots off towards infinity and infinitesimal
The limit as x approaches 0+ of 3/x is infinity, but the limit as it approaches 0- is negative infinity, therefore you cannot associate a value to a number divided by zero, hence the term "undefined".
@THERaikami1 The natural numbers are infinite, but countable - 1, 2, 3, etc. But there are an infinite number of numbers in between 1 and 2, which are uncountable. This is because there are a finite number of natural numbers between any two natural numbers (if x and y are natural numbers and x < y, then there are (y-x)-1 natural numbers in between them), but an infinite number of numbers between any two numbers in general.
for instantaneous velocity it is valid to say that it is the velocity an object will have if from the moment we are interested in it performs uniform linear motion (ΣF=0). the same for acceleration (obviously in this case ΣF=constant)
@Lunarsight Graph f(x)=1/x. The reason a constant divided by 0 is undefined is entirely dependent upon which side the number is coming from--either the positive or the negative. For example, the limit as x approaches 0 from the positive side is +infinity, but the limit as x approaches 0 from the negative side is -infinity. The reason it's undefined is because the two points do not meet.
A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined. Thus, it is sometimes useful to think of a/0, where a ≠ 0, as being Infinity. This infinity can be either positive, negative, or unsigned, depending on context.
@Xerotaerg
What's wrong with it?
Is it because it's zero?
But, does zero ever start or stop?
What's the definition of infinity?
@krypekeeper no? would you mind elaborating?
@MarkArandjus The problem with that theory is that it doesn't take into account negative numbers- which are smaller than 0.0001. Rather than being a slope down, it actually is a parabola that stops at infinity and goes to -3 and slopes upward.
Iv reciently just watched your video on the speed of light, and it was saying that the speed of light does not stack if you shine a torch from a moving train. But in that sence the speed of light is also infinate? because c + 100m/s is also c.
but it has a set value (3x10*8), and infinity has infinate value.
...so does that mean c is a countable infinity?
@TriMiro8107 3/0 is undefined because the in that circumstance, infinity is treated as '0' dividing '3' an endless number of times. so yes, 'infinity,' in a sense, works in that circumstance.
@pigrogromitus Xeno's paradox is hella crazy, but very interesting. Do you know if that has been resolved? It seems to me that if one makes time discrete (i.e, a "Planck time," or what have you), then the paradox is solved--past the Planck time, divisions are either theoretically impossible, or just plain meaningless.
You, Sir, made my day. :)
@LamaPaj A better way to put it is that 3/t tends towards infinity as t tends to 0.
@123Fusselbirne the range is how far the effect is able to reach. and as no matter how far away you get from an object, gravity still interacts. that means it's range is infinite
@MrSuednym
Other way around. Mathematicians are applied Physicists. That is a little unfair because both are independent or can be, but they both need each other to get anywhere.
@bohngat But they are mathematical constructions, If you take a snowflake for example there still is a minimum 'resolution' for the fractal which is at the size of the water molecules.
@bitt3r0blivion I'm not a calc whiz, but I seem to rember that L'Hopital's Rule specifically applies to limits.
@123Fusselbirne Yes the limit is 0, but a graph like that has no Y value for x=0.
There are cardinal numbers, ordinal numbers, hyper-real numbers, numbers from smooth analysis, and surreal numbers. Those are structures that can be used to discuss infinities within mathematics.
is (1/0 = infinty) greater or (2/0 = infinty ) greater ?
another (infinty + 1 = infinty or greater number that have another special name)?
As soon as we use numbers in association with Geometry we soon come up against the problem of Infinity. The Natural Numbers 1, 2, 3, 4,., are used to count discrete objects. In the two-dimensional plane we assume that any point can be represented by a pair of numbers (a, b). Considering a straight line of length one unit, we assume that it consists of points.
However, a point has zero width. One then has the problem of how many points you need to form the line. Dedekind and Cantor considered this problem, and the different types of Infinity. However does this Cartesian System of Geometry correctly model the space in which we live? (The Cartesian System assumes that space is continuous).
Leibniz considered this problem, and felt that space was NOT continuous; he developed the concept of Infinitesmals and his Differential Calculus from this different concept of space. Perhaps Leibniz had stumbled upon a vague sense of the Planck length.
infinite rooms? hate to be the roomcleaner at that hotel
There's just one room cleaner, despite the size of the hotel. You'd think that would be a problem, and that the hotel is ridiculously understaffed, but the room cleaner has a clever way of getting around this issue. He cleans each room in half the time as he cleaned the last. He spends one hour on the first room, half an hour on the second, one quarter of an hour on the third, ect. Eventually, he gets all rooms cleaned within 2 hours.
@@katiekatie6289 what
the definition of the base unit, ampere "the constant current that will produce an attractive force of 2 × 10-7 newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum" which contains infinity and can we can think of negligible cross section as an infinitecimal?
@OhhSoulz I'm glad it helped.
@LamaPaj That's correct. ∞ is actually the limit of y=3/x when x approaches 0 (if x approaches from the left, if it is negative, then the limit is - ∞). He just wrote it that way to make it more easily understandable. I'm pretty sure he knows that ;)
@MarkArandjus Never thought of it that way. Sorry for the inconvenience
Me: Oh hey I've seen a Numberphile video on this already
0:25 - "You shouldn't really be talking to a scientist you should be talking to a mathematician"
Me: ...I knew it
@Yunituber Maybe. It certainly means that some parts of particle physics is wrong.
well thanks for the help, cleared it up a bit!
...ill have to go read up on special relativity.
Sorry im still a bit of a newbie when it comes to physics - im only at my A levels at the moment!
Thanks again.
Indeterminate is undefined, just that it is possible to assign it any value, though it isn't very helpful. When it comes to something that is undefined, there just isn't a value that can be used to represent it yet. For a time SQRT(-1) was undefined, but now we use i or j. Same thing applies to 1/0, which you can prove a value for if anyone ever payed attention to factorials.
According to calculus isn't x/0 = +/- infinity (+ from the positive side and - from the negative aside)?
@kristijanadrian Actually an infinte pound bill would have the interesting property that no matter what you bought with it you would always get an infinite pound note as change. The problem with issuing infinite pound notes is social, not mathematical.
@thelegendxp Do you think Wiki is some kind of bible?
@OhhSoulz Is a constant an infinity? Well you could see a constant as an infinite sum of infinitesimals. But there's no need to look at them that way. Let a constant just be a finite constant and everything works out fine.
@ray123ification I don't know. Could be, but I'm fairly certain that whatever can be imagined, can be expressed one way or another. Doesn't mean it's going to be easy, or that anyone will understand what it is you're actually expressing, but it is doable. :>
Infinity, more or less (un)countability is often used in computation theory (the mathematical part of computer science) and used to describe problems and their computable complexity (won't go into details). It's not useless and not just something of the mind as it helps us in many ways (like knowing what to put effort into in algorithmics) and can be shown to be there for instance in the proof of the halting problem with use of diagonalisaton (look it up).
@cooltokes Good question. I have absolutely no idea :P
very comforting video. i still dont get that infinite hotel, it is said that every room is full at arrival. where/how/why would you find an empty room then to move someone into?
It's like thinking about infinity plus one. It's still infinity.
Always think about infinity as a concept rather than a number so obviously 2+1 isn't 2 but infinity +1 is still infinity, so they don't use the same rules
it is said that every room is occupied. doesnt matter how many there are. if you make up another room, it will be occupied as well. at least that is what "every" means to me. if, for whatever reason, you can make up an empty room, why would you move all people already there one room further? just give it to the person arriving last.
It's inifnity. You don't have to finish the task of "move all people to the n*2 room" because there is no finish. If you check on the people at any point in time, you will see a whole bunch of people walking around at one part of the hotel, and this traffic is moving along the room numbers. In a normal hotel, there would be an end where half the guests are now stuck and have no idea what they are supposed to do. But in an infinitly large hotel there can be no end and therefore nobody is ever complaining about "not having a new room".
Here's another little thing showing that thinking about the "end" is somewhat pointless when dealing with infinity:
Imagine you have a lamp that can be turned on and off in an instant. Now you turn the lamp on and wait a minute. Turn it off and wait half a minute. Turn it on and wait a quarter of a minute. After 2 minutes, you will have turned the lamp on and off an infinite amount of times. Now here's the question: Is the lamp now on or off?
Hm, interesting. I guess I didn't understand that bit about black holes at all. I'll have to look into it. Thanks for your insight!
Just a suggestion but what would be really good is a whole channel dedicated to mathematics :)!
@thelegendxp 3/0 is not a defined *number*. Infinity is not a number.
Where did you get that top hat for the cat? Or is it photo shopped? I want to get one for my brother's fat cat and a monocle and the bow tie.
@123Fusselbirne and why did you take down your comment? and i don't really see how you can have a different perspective on science
1:28 NOOOOOOOOOOOOOOOOOOOOOOOO
I was about to post the same comment (7 years later though).
Indeed, 3 divided by 0 is not INFINITY !!!!!!!!!!!!!!!!
It may have been wiser to ask the question to mathematicians.
@123Fusselbirne exactly. it's kinda funny because you don't really use the symbol for infinity in physics because if you did then F=0 and then the range wouldn't be truly infinite. but like you mention you can have an unimaginably large number for the distance and no matter how much larger you make it there will still be a force. mathematicaly you just can't use the symbol infinite ^^
"Wot?" I love that!
@ 2:11 please note the Egyptian symbol he shows for infinity is partially the same as the glyph/symbol for KA or the body double, your shadow that follows you around for an eternity.
The ka as a spiritual double was born with every man and lived on after he died as long as it had a place to live.
After death the ka became supreme. Kings thus claimed to have multiple kas. Rameses II announced that he had over 20.
science is a religion >> U do know that?
@Versudan 2:10 correction in the bar
great videos
(:
By definition a countably infinite set is a set that can be put into one-to-one correspondence with the set of natural numbers. For example, you can put the natural numbers and the odd naturals into such a correspondence.
0:29 so will you be making a numberphile video about infinity?
So, the distinction between Mathematicians and Physicists is wether you are concerned with axial-tangential sync-duration limits or compound relative-timing duration wave-particle type measurements, and philosophically, of course it's the same indeterminate qa principle of the perceived meaning of Actuality.., the degree/proportions of Cultural Relativism inherent in "truth in labeling, lawful-ness".
I've written this also as a comment to another Brady's video: Physical world can be described with rational complex numbers. There's no need for irrational numbers as using Plank's measurements all measurements are quantified. But you still need complex numbers to easily describe for example elecro-magnetic fields.
On the other hand as a mathematician I'm fascinated by the worlds that are created by imagining infinities that are between aleph0 and aleph1 or lager than aleph1 but not part of the power series of alephs. And that there is such thing as Banch-Tarski paradox which is impossible in nature as one never can cut anything the way the paradox cuts things up.
@megaelliott That's not quite true either. lim 3/x, x-> 0+ = ∞, yes, but lim 3/x, x->0- = -∞. Technically the limit doesn't actually exist because the left- and right-hand limits are disjoint.
@conneelyb You're probably right :P I'll admit right away that the explanation i got is very simplistic, and as you say, its most likley not correct for every aspect of math.
i think you're talking about the limit of 1/x, which is undefined as x approaches 0 for the reasons you stated - the left and right sides of the limit aren't equal to each other.
you could say 1/x^2 is defined as infinity as x approaches 0 because both sides of the limit equal each other, but you must remember we are talking about a limiting function and not simple division such as 1/0 (with limits we are talking about 1/a number really really really really close to 0)
1/0 is undefined
6:18
I'm as far to a mathematician as you can think (I'm a sociologist) but I too hate when physicists and astronomers misuse the term infinity. It's one of the few complains I have anyway. Otherwise I love them and admire them deeply :-)
@l0rdoflol I can see the logic in your teacher's explanation: taking 0 people out each time allows for infinite iteration. However, translate to an algorithm & u have a conditional expression & recursive function i.e. for each iteration, if X != 0, take X people out then return to calling function, Else do nothing and return to calling function. So you would have infinite iterations of that recursive function but the amount of people taken out is a running total i.e. countable.
I thought the gravitational force that acts between two masses has a range from 0 to infinity 1/r^2 law, it is similar with electric fields so there are some uses of infinity in physics.
@JiminyN Fundamental really, right?
You are right that stars are about the same density at any point in space (the same number of stars per any specific volume) what they were saying is within the observable universe, as far as light has travelled since the big bang, there is a very large but finite number of stars. We can't tell how far it extends beyond this.
There are no exceptions in mathematics.
A number divided by a number equals a number.
The idea that a number divided by itself is defined to be equal to one is flawed due to how trends work, but regardless a number divided by itself equals one. 0/0 = R, which contains 1, so consistency is preserved.
Also: 0/∞ = 0. Notice that commutatively, that means 0/0 = ∞, which is consistent with 0/0 equaling R.
R is all real numbers.
0:25 "You shouldn't really be talking to scientists...need to talk to mathematicians."
SNAP!
Countable infinities are those whose members are countable when you impose limits, e.g. there is an infinite number of multiples of 2, but there are only five between 1 and 10. An example of an uncountable infinity would be Real numbers (Real in the strict mathematical sense, i.e. all numbers, positive and negative, whole and fraction/decimal) - there are an infinite number of these, but also if you pick any two numbers, there are still an infinite number of Real numbers between these.
No, Brady Haran is the same person as Brady Haran, they're not just two people randomly having the same name. Also, most of the people in the sixtysymbols videos have already been in a few numberphile videos, and the same goes the other way around.
@morningsweet666 Why always Chuck Norris???
I had a comment before this explaining that (apart from -1^2 actually being -1 and (-1)^2 being 1), the opposite of squaring x is actually taking the positive or negative square root of x, and therefore your conclusion is incorrect, and not just generally taking the square root, whereas the opposite of dividing something by y is just multiplying it by y.
Worst hotel ever. Everytime someone checks in you have to move... you won't get any sleep there.
ö. . , Yeah, and how do you fill a hotel with infinite amount of rooms in the first place? And if you do, and this scenario of moving from room to room happens it takes an eternity - like literally. And did they finish building of the hotel in the first place - I hear the construction is still going on there... last night when I checked in:)
how acn infinity have a beginning...room one. what about room -1 ?
5:53 what word was that?
have you guys thought of releasing a Math's youtube channel ??
Thanks for the answer
@ray123ification It can't, I guess, but what you can do is you can set a point in infinity to use as a start point, and work from there.
How do you get 0=0?
3 divided by 0 isn't infinity, it's indeterminate.
The limit of 3/x when x approches 0 is plus or minus infinity.
Ups looks like I said that the size of a singularity is also infinite. What I actually meant was that the formulas give an answer of zero or "infinitesimally small" (which again doesn't make sense and is impossible to grasp).
I love how at 1:18 he says "and divide it by zero" as if he had a choice...
Heh, glad to see I'm not the only math major who was shaking his head sadly at the 3/0 equals infinity bit. And of course the hotel had a countably infinite number of rooms so if an uncountably infinite number of new guests showed up (ie one for each real number) the hotel couldn't fit them in.
the picture is called grafix cat
Very popular on image boards for editing, so to answer your questions, it's photoshopped
@Zmrdaciq What kind of a silly answer is that? Take that number and double it, what's your name for THAT?
@AngelixArch Yeah, those fanatics.
Perhaps a good analogy would be an infinitely long tape measure - the number of ticks is infinite, since the tape measure has infinite length, but you can count the number of ticks along any given length of the tape. There are also an infinite number of places where you *could* draw ticks along the edge of the tape, and even between two ticks, there is still an infinite number of positions you could draw more ticks. That would be an uncountable infinity.