Say that I have infinity rooms labeled 1, 2, 3, 4, 5... and so on. If I decide to give you all of them, I have no rooms left. So, infinity - infinity = 0. If I decide to give you all the even numbered rooms, I still have infinity rooms. So, infinity - infinity = infinity. If I decide to give you all but the first three rooms, I have 3 rooms left. So infinity - infinity = 3 (constant).
It can in some cases. Infinity is a limit. So if you do infinity1 - infinity2, if infinity1 is approaching infinity faster than infinity2 is approaching infinity, you will have a positive constant. And visa versa.
It has to do with the rate at which the number increases. Like if the equation is n raised to the n power, divided by n raised to the 2nd power, where n is a growing constant from 1 to infinity, then the top would eventually cancel out the bottom. It's slightly difficult to explain, but if you take Calculus 2, you'll learn about it.
I hated math when I was in school. I kept telling myself "when am I ever going to use this in real life?" And then I became an X-Ray Technician and now all I do is fractions and equations in my head all day long to figure out technical factors lol.
all the math up to highschool is academic math. degree is Pure Math, math for the sake of math. it's retarded because highschool math teachers doesn't emphasize the different between pure and actuarial (applied) despite their own math degrees
I remember when I moved states and the new school I went to had a different maths curriculum to my previous school and were comparatively behind - and they said 'you can only take a smaller number from a bigger number.' I said 'well actually....' and then I got kicked out of class :(
Some infinities grow at a similar rate as others, so one never really overtakes the other. Take for example (x+20) / x. If you put a small number in for x, you'll clearly see that the top part is bigger than the bottom because of that +20. However, if you make x really big (approach infinity), the difference that the +20 makes gets smaller and smaller (approaches zero) and thus will not make a difference as x->infinity. So as x approaches infinity, the quotient approaches 1 (constant).
I know, I just gave an example of a larger topic in calculus. The example I gave can be resolved using l'Hopital's rule, which applies to other indeterminate forms including: infinity/infinity, 0/0, 0*infinity, infinity-infinity and infinity^infinity. Yes, raising infinity to the infinity power can also get you either infinity, zero or a constant. :D
The n/0 is in fact a set up for the lure on movement speed in space and time in witch if you divine by 0 you get over the speed of light, that is imposible because if you hit that kind of speed you will comeback at the end of time and space, at least that's why my phisics teacher thinks they teach kids to ignore the possibility of dividing by 0
It's not always though. Day9 gave a perfect example in this video. We are all taught n/0 is undefined where n = ℝ. But it's actually possible to do in some physics applications. Same with infinity. There are some circumstances where we can manipulate infinity. I believe it can be done through manipulation using set theory and cardinal numbers/aleph numbers that you learn about in 400+ level classes. Think of it this way. sqrt(-1) isn't "real", but can still be used and manipulated like a real #
a good question is "what is the reciprocal of infinity," i looked it up and it would be the smallest possible number greater than 0. infinity/1--------1/infinity
I think rather than the answer being always and thus 'infinity', the answer is never and thus it simply cannot and does not happen (ever) hence the operation is undefined and/or meaningless except when dividing by ±0 which is merely to influence the sign of the output.
Sure knowledge of "advanced math" is not a necessary condition to play the game, but understanding differential equations is huge for understanding economy in supcom fa.
Yeah, I know that, but I thought he was talking purely about infinity minus infinity, with no other constants in the beginning of the equation. Thanks for the clarification, though..
Actually wether you can do this or that depends on which set of numbers you are in. E.g. in the natural numbers you can't subtract bigger numbers from smaller numbers, since this would lead to a result, which is not in the natural numbers. Still I agree that it is stupid to tell people they can't do that, only to later tell them the opposite. They should simply say "That's a topic which comes later." and leave it with that.
I am just wondering, how can infinity minus infinity be a constant? My logic is, if the first infinity is stronger, the equation is infinity. If the second infinity is stronger, it would be minus infinity. If both of them are the same, they would cancel each other out and the result would be zero. Am I missing something?
My favorite is when you take calculus and first learn about c they call it a placeholder. And then you get to differential equations and learn that c is a set of all real numbers and have to use it to solve most if not all differentials first order or more. Actually I think differential equations shattered about a shitton and a half of the boundaries lower math had created.
@goJesusandStarcraft Actually people are missing the most important thing. When the teacher says YOU CANT TAKE THE SQUARE ROOT OF A NEGATIVE they are completely right. WHEN YOU WORK ON REAL NUMBERS. Thats the source of a confusion, they just dont add this part and people generalize that sentence as 'in math u cant divide by zero'. Same for negative numbers, they DONT EXIST when You work on NATURAL NUMBERS. And so on...
I thought real numbers was what I think of as R , so negative numbers are part of this set. So complex numbers have nothing to do with what my initial comment stated. Though i can be wrong about what real numbers are, I am not used to english terms in mathematics. cheers :D
Schools need to be like mine. In 1st grade, when doing addition and subtraction, I had the kid-like inquisitiveness to ask "so what happens if I subtract 5 from 4???!!!" Instead of saying "shush that's not what we're here to teach", they moved me out of the math class to 2nd grade math, and then replaced P.E. for "gifted student" class, where we learned a lot faster and a lot more. This isn't to say the divide is good socially, but it keeps kids front getting stunted intellectually by schools.
what school tells kids that you CANT subtract say 20 from 12...? I knew about negative numbers before I even went to school and they never said I was wrong or said even that you can only subtract the smaller number
No hes not. He was joking, referring to what he said earlier about students being taught that negative numbers don't exist early in education. Negative numbers are "real numbers" anyway....
Infinite = 1*10^307 a friend ofmine got this. you might ask why exactly this number. well in school we have a pretty good math programm and he asked it what the root of Infinite^2 is. and well the program gave him this. (ps: if you ask it only Infinite = it gives you an error )
That's exactly what happens. And this is what Day9 is talking about. Your teacher told you to not worry about it, in fact he told you to completely ignore it. But if you continue to take physics and other high level maths, you will revisit this point and they'll say, "so let's learn to divide by 0" and everyone will be like "whhhaaattt?" And remember, I'm talking about learning these things in 400/500 level college classes, not high school or even freshman/sophomore in college level.
Like being told square root of negative 1 isnt a number. Then doing my last 2 years of school in the hardest math and that's what 90% of the work was on.
The concepts of advanced/basic math that you use don't really make sense. You can make differential equations as advanced as you want, there are plenty of open problems in the field. The point about supcom fa is that the economy is presented in terms of rates, which allows you to use the intuition you may have from solving diff eq. For people who never studied the subject the game forces them to learn the concepts, without actually telling them that they are doing diff eq.
It´s exatly the same in our country and not just with Math, but with Accounting and few other subjets as well. "Well, but what if we put this here and do it this way? "NO, you can´t.", then after the class it´s like: "So why can´t I do it like this? Because you know, eeeehh, we´re not supposed to learn this method, we will learn that next year."
that's so true lol, you are always lied to in math in school and given to simplistic explanations, so in the end for some people who don't get it nothing makes sense they go like -4 - 4, ok so minus and minus cancel out, and then I get +8
Well the answer would be an indefinition (that is when you don`t know the result). About the negative I never really heard it, but I think he said in a serious way, usually when we get to an indefinition we use the l`hopital`s rule.
I love how some people go like "Oh I learned about 'insert college/uni level maths topic here' in 5th grade, when in reality they just HEARD about it in that particular grade. Maybe from the teacher who just mentioned it once or told a very interested student about it on the side. I knew there was a thing called Linear Algebra way back in 2nd grade. Could I solve it? Naturally not. I couldn't even solve normal algebra at that point, barely even normal 1+1 maths. But I knew of it and I had even seen it. The reason I knew about it was because I was just naturally inquisitive, not necessarily interested. I sucked at math and I still do, at the age of 28, yet I somehow am doing a very late Engineering degree. Yet I still hear people saying nonsense such as how they learned various maths back in high school or even middle school that my Engineering level maths use today. And even if they DID teach that level, what use could a high schooler/Middle schooler even have for it? It'd be a complete waste of time.
Hahaha i wish big D would do a podcast about math i love his ideas. Negative numbers arent real. I wanna get him started on square roots of negative numbers. Thats like the square root of all evil
Can anyone explain me what does he mean by "quietly Jefferssoning" in 0:23? I think it's some local phrase in US i can't get but may be useful ;) Aaand what about an example of multiplying equasion to cancel infinity, anybody? Please? :) Last thing, that quote of the physicist at the very beggining, can someone re-type it here? It's hard to catch as non-native english speaker ;) Cheers!
I realise that - I should have said negative numbers strictly speaking don't exist. But in terms of the mathematical meaning of a 'real number', yes negative numbers are real. Sorry for the misunderstanding. :)
Algebra 1: NO U CAN'T TAKE THE SQUARE ROOT OF A NEGATIVE NUMBER IT DOESN'T EXIST YOU GET TEH PROBLEM WRONG! Algebra 2: "So you find the conjugate of this complex number, which is (3-4i)"
Let me explain Taedrin's joke: The Natural numbers are all the positive integers, that is 1,2,3,4,5... and so on. So when Taedrin said (paraphrased) "negative numbers aren't natural" he was correct, as natural numbers are only positive. It's also a play on words, since it sounds like you are saying negative numbers are unnatural. In conclusion, what Taedrin said was in fact a math joke, and it was in fact a good one.
They do the same thing in Chemistry, first saying that nothing's smaller than an atom, then they tell you about protons, neutrons, and electrons and say there's nothing smaller than that, then they talk about quarks...
when i learned about imaginary numbers in math class, i immediately turned to my friend in the desk next to me and pointed out "just because something's imaginary doesn't mean it's not rear!" (southpark reference? anyone?)
Infinity - infinity is exactly equal to a - b there are an infinite number of infinities. that is why it depends there is an infinite amount of numbers between 2 and 3, and twice as many between 2 and 4, but both are classified as infinity. infinity is nothing more than a variable for a number we can not write out no matter how hard we try. infinity - infinity is undefined, just like A / 0. it can literally be anything. there is no real answer for infinity - infinity which is why they say it can not be done. the only way to get a real number answer from infinity - infinity is to define those infinities, in which case, it can have a real answer, but its like saying A - A = 5, which is impossible since any number minus itself is 0. yet infinity - infinity if defined to do so could. it just does not make much sense.
![Day[9] - Accidental Date](http://i.ytimg.com/vi/L7Cj5AEk_LQ/mqdefault.jpg)
![Day[9] - Accidental Date](/img/tr.png)
Say that I have infinity rooms labeled 1, 2, 3, 4, 5... and so on.
If I decide to give you all of them, I have no rooms left. So, infinity - infinity = 0.
If I decide to give you all the even numbered rooms, I still have infinity rooms. So, infinity - infinity = infinity.
If I decide to give you all but the first three rooms, I have 3 rooms left. So infinity - infinity = 3 (constant).
+Sang yeop Jung Cantor's hotel.
seems legit
I like you.
there are different sizes of infinity
Well, I wouldn't say "sizes" of infinity.
"no one will ever marry you"
BigSean over here breaking those rules too.
2021 and I still miss the SC2 and Hearthstone content version of Day9.
Should have said:
"Can't be a negative number, though. Those aren't natural."
It can in some cases. Infinity is a limit. So if you do infinity1 - infinity2, if infinity1 is approaching infinity faster than infinity2 is approaching infinity, you will have a positive constant. And visa versa.
It has to do with the rate at which the number increases. Like if the equation is n raised to the n power, divided by n raised to the 2nd power, where n is a growing constant from 1 to infinity, then the top would eventually cancel out the bottom. It's slightly difficult to explain, but if you take Calculus 2, you'll learn about it.
I hated math when I was in school. I kept telling myself "when am I ever going to use this in real life?" And then I became an X-Ray Technician and now all I do is fractions and equations in my head all day long to figure out technical factors lol.
all the math up to highschool is academic math. degree is Pure Math, math for the sake of math. it's retarded because highschool math teachers doesn't emphasize the different between pure and actuarial (applied) despite their own math degrees
i like how the sound of him sipping out of a mug at the end is still part of the video. it fits in so perfectly! :)
some infinities are larger than other infinities.
THERE, SOMEONE SAID IT.
+TheWhovianMaster WOAH
WOAH.
TheWhovianMaster there is countable and uncountable infinities.
I remember when I moved states and the new school I went to had a different maths curriculum to my previous school and were comparatively behind - and they said 'you can only take a smaller number from a bigger number.' I said 'well actually....' and then I got kicked out of class :(
Some infinities grow at a similar rate as others, so one never really overtakes the other. Take for example (x+20) / x. If you put a small number in for x, you'll clearly see that the top part is bigger than the bottom because of that +20. However, if you make x really big (approach infinity), the difference that the +20 makes gets smaller and smaller (approaches zero) and thus will not make a difference as x->infinity. So as x approaches infinity, the quotient approaches 1 (constant).
I know, I just gave an example of a larger topic in calculus. The example I gave can be resolved using l'Hopital's rule, which applies to other indeterminate forms including: infinity/infinity, 0/0, 0*infinity, infinity-infinity and infinity^infinity. Yes, raising infinity to the infinity power can also get you either infinity, zero or a constant. :D
The n/0 is in fact a set up for the lure on movement speed in space and time in witch if you divine by 0 you get over the speed of light, that is imposible because if you hit that kind of speed you will comeback at the end of time and space, at least that's why my phisics teacher thinks they teach kids to ignore the possibility of dividing by 0
Day[9]’s “in math” sounds like “that one time, at band camp”
It's not always though. Day9 gave a perfect example in this video. We are all taught n/0 is undefined where n = ℝ. But it's actually possible to do in some physics applications. Same with infinity. There are some circumstances where we can manipulate infinity. I believe it can be done through manipulation using set theory and cardinal numbers/aleph numbers that you learn about in 400+ level classes. Think of it this way. sqrt(-1) isn't "real", but can still be used and manipulated like a real #
@geganobo he is alluding to what he said earlier when he said you can't take a lager number away from a bigger number.
a good question is "what is the reciprocal of infinity," i looked it up and it would be the smallest possible number greater than 0. infinity/1--------1/infinity
Yeah I was thinking the same. It's "Divided" and/ or Dividing.
I think rather than the answer being always and thus 'infinity', the answer is never and thus it simply cannot and does not happen (ever) hence the operation is undefined and/or meaningless except when dividing by ±0 which is merely to influence the sign of the output.
I think Vihart would like this video.
Wow. This was beautiful.
Sure knowledge of "advanced math" is not a necessary condition to play the game, but understanding differential equations is huge for understanding economy in supcom fa.
Sean should do stand up comedy, he is really tallented. I think he might be one of the best in America.
Yeah, I know that, but I thought he was talking purely about infinity minus infinity, with no other constants in the beginning of the equation. Thanks for the clarification, though..
I was laughing as soon as he said you can't divide by zero.
I am a physics major too. :)
take the limit as x->infinity of (x-x+1)
it's very obviously 1. That's how
Actually wether you can do this or that depends on which set of numbers you are in. E.g. in the natural numbers you can't subtract bigger numbers from smaller numbers, since this would lead to a result, which is not in the natural numbers.
Still I agree that it is stupid to tell people they can't do that, only to later tell them the opposite. They should simply say "That's a topic which comes later." and leave it with that.
GENIOUS genious Day9, as a comedian, he´s so smart to make his point in this one ... jesus academic things are stupid sometimes
I am just wondering, how can infinity minus infinity be a constant? My logic is, if the first infinity is stronger, the equation is infinity. If the second infinity is stronger, it would be minus infinity. If both of them are the same, they would cancel each other out and the result would be zero. Am I missing something?
My favorite is when you take calculus and first learn about c they call it a placeholder. And then you get to differential equations and learn that c is a set of all real numbers and have to use it to solve most if not all differentials first order or more. Actually I think differential equations shattered about a shitton and a half of the boundaries lower math had created.
@goJesusandStarcraft Actually people are missing the most important thing. When the teacher says YOU CANT TAKE THE SQUARE ROOT OF A NEGATIVE they are completely right. WHEN YOU WORK ON REAL NUMBERS. Thats the source of a confusion, they just dont add this part and people generalize that sentence as 'in math u cant divide by zero'. Same for negative numbers, they DONT EXIST when You work on NATURAL NUMBERS. And so on...
I thought real numbers was what I think of as R , so negative numbers are part of this set. So complex numbers have nothing to do with what my initial comment stated.
Though i can be wrong about what real numbers are, I am not used to english terms in mathematics.
cheers :D
About the division by 0 part: en.wikipedia.org/wiki/Wheel_theory
Schools need to be like mine. In 1st grade, when doing addition and subtraction, I had the kid-like inquisitiveness to ask "so what happens if I subtract 5 from 4???!!!"
Instead of saying "shush that's not what we're here to teach", they moved me out of the math class to 2nd grade math, and then replaced P.E. for "gifted student" class, where we learned a lot faster and a lot more.
This isn't to say the divide is good socially, but it keeps kids front getting stunted intellectually by schools.
what school tells kids that you CANT subtract say 20 from 12...? I knew about negative numbers before I even went to school and they never said I was wrong or said even that you can only subtract the smaller number
No hes not. He was joking, referring to what he said earlier about students being taught that negative numbers don't exist early in education. Negative numbers are "real numbers" anyway....
Infinite = 1*10^307
a friend ofmine got this.
you might ask why exactly this number.
well in school we have a pretty good math programm and he asked it what the root of Infinite^2 is. and well the program gave him this.
(ps: if you ask it only Infinite = it gives you an error )
How I want to write "negative numbers just don't exist! (source: day 9)" on my math test on monday :D
Depends if you're subtracting Aleph null or Aleph one, so...yeah I guess it depends.
That's exactly what happens. And this is what Day9 is talking about. Your teacher told you to not worry about it, in fact he told you to completely ignore it. But if you continue to take physics and other high level maths, you will revisit this point and they'll say, "so let's learn to divide by 0" and everyone will be like "whhhaaattt?" And remember, I'm talking about learning these things in 400/500 level college classes, not high school or even freshman/sophomore in college level.
Like being told square root of negative 1 isnt a number. Then doing my last 2 years of school in the hardest math and that's what 90% of the work was on.
The concepts of advanced/basic math that you use don't really make sense. You can make differential equations as advanced as you want, there are plenty of open problems in the field. The point about supcom fa is that the economy is presented in terms of rates, which allows you to use the intuition you may have from solving diff eq. For people who never studied the subject the game forces them to learn the concepts, without actually telling them that they are doing diff eq.
It´s exatly the same in our country and not just with Math, but with Accounting and few other subjets as well. "Well, but what if we put this here and do it this way? "NO, you can´t.", then after the class it´s like: "So why can´t I do it like this? Because you know, eeeehh, we´re not supposed to learn this method, we will learn that next year."
that's so true lol, you are always lied to in math in school and given to simplistic explanations, so in the end for some people who don't get it nothing makes sense
they go like -4 - 4, ok so minus and minus cancel out, and then I get +8
Well the answer would be an indefinition (that is when you don`t know the result). About the negative I never really heard it, but I think he said in a serious way, usually when we get to an indefinition we use the l`hopital`s rule.
"Can't be negative because those aren't natural." Fixed it for you.
I think I learned more math from Day 9 then in school.
Makes sense though! They do it so you don't get confused, it works.
I love how some people go like "Oh I learned about 'insert college/uni level maths topic here' in 5th grade, when in reality they just HEARD about it in that particular grade. Maybe from the teacher who just mentioned it once or told a very interested student about it on the side.
I knew there was a thing called Linear Algebra way back in 2nd grade. Could I solve it? Naturally not. I couldn't even solve normal algebra at that point, barely even normal 1+1 maths. But I knew of it and I had even seen it. The reason I knew about it was because I was just naturally inquisitive, not necessarily interested. I sucked at math and I still do, at the age of 28, yet I somehow am doing a very late Engineering degree.
Yet I still hear people saying nonsense such as how they learned various maths back in high school or even middle school that my Engineering level maths use today. And even if they DID teach that level, what use could a high schooler/Middle schooler even have for it? It'd be a complete waste of time.
Day9 should be a math teacher (after he's old), he has a degree right?
Hahaha i wish big D would do a podcast about math i love his ideas. Negative numbers arent real. I wanna get him started on square roots of negative numbers. Thats like the square root of all evil
Touché.
The result then. Anything divided by zero is always equal to zero.
Can anyone explain me what does he mean by "quietly Jefferssoning" in 0:23? I think it's some local phrase in US i can't get but may be useful ;)
Aaand what about an example of multiplying equasion to cancel infinity, anybody? Please? :)
Last thing, that quote of the physicist at the very beggining, can someone re-type it here? It's hard to catch as non-native english speaker ;)
Cheers!
Devide? seriously?
All you're doing is sabtracting from this guy's self-esteem. You're miltiplying his problems.
your* doing
you added too many periods. to represent a pause it is only three dots...
I realise that - I should have said negative numbers strictly speaking don't exist. But in terms of the mathematical meaning of a 'real number', yes negative numbers are real. Sorry for the misunderstanding. :)
cant we divide by zero in string theory?
This is coming out of the mouth of a math major!
386 part 2, its in the description
I hope negative numbers don't exist for architecture! Having a building that has a height of negative 200 feet would be a nightmare :D
he was talking about standard classes. pretty sure everybody into sc has been in honours programs instead :)
Same as you are told you cant have a sqrt of a negative number. Its too complex (lol) to teach to young kids.
negative numbers? What are those?
wouldn't that be an underground dungeon?
you aren't supposed to reveal your name in the internets.
-everyday i'm jefferson
definitely true. I assume that mletemps over there is in algebra 1 or lower, because he obviously hasn't taken calculus :/.
In some circumstances there is!
I think you guys missed this guys joke - negative numbers are real in the sense that they are not complex: (a + bi) for a and b integers.
Quietly here jeffersoning at "Devide"
@drizzt7dourden7 *frantically waving raised hand* LOW BATTERY?
Day9 is an Eternal Truth !
To us they at least said: "you can't do that YET".
And where do the demons show up?
Algebra 1: NO U CAN'T TAKE THE SQUARE ROOT OF A NEGATIVE NUMBER IT DOESN'T EXIST YOU GET TEH PROBLEM WRONG!
Algebra 2: "So you find the conjugate of this complex number, which is (3-4i)"
a) I do.
b) Joke? IT WAS A JOKE? :O OMMIGOT
c) Huh, clever choice.
d) Some day you'll get it.
Huehuehuehuehue
which daily # is this one?
Let me explain Taedrin's joke:
The Natural numbers are all the positive integers, that is 1,2,3,4,5... and so on.
So when Taedrin said (paraphrased) "negative numbers aren't natural" he was correct, as natural numbers are only positive. It's also a play on words, since it sounds like you are saying negative numbers are unnatural.
In conclusion, what Taedrin said was in fact a math joke, and it was in fact a good one.
it took you intil 7th grade to find out about negative numbers?
infinity minus infinity can be a negative number
It's funny, because I'm studying physics and just now we studied that you actually CAN divide by zero ^^
? What it equals to
the diefenbunker is an upsidedown hotel
I'm not drunk enough, yet, to understand this.
They do the same thing in Chemistry, first saying that nothing's smaller than an atom, then they tell you about protons, neutrons, and electrons and say there's nothing smaller than that, then they talk about quarks...
Dropping some knowledge
when i learned about imaginary numbers in math class, i immediately turned to my friend in the desk next to me and pointed out "just because something's imaginary doesn't mean it's not rear!" (southpark reference? anyone?)
titled*
'' Can't be a negative number, those aren't real''
Made a math mistake there :D
... A negative number is still a constant...
I hated math too. So I just taught myself how to program instead.
Programming is one of the few places math is actually useful...
i wish day9 was my college teacher
It produces asymptotic behavior at X=0.
infinity - infinity = infinity - infinity. DUUUUUHHHHHHHH!!!
oh man, when I'm finished with studying physics, I hopefully can laugh about this stuff haha :D it sounds so funny
Day9: "What if I substract Infinity minus Infinity?" ... Teacher: GG !
The answer to dividing any number by zero, is infinity.
Just sayan.
Infinity - infinity
is exactly equal to
a - b
there are an infinite number of infinities.
that is why it depends
there is an infinite amount of numbers between 2 and 3, and twice as many between 2 and 4, but both are classified as infinity.
infinity is nothing more than a variable for a number we can not write out no matter how hard we try.
infinity - infinity is undefined, just like A / 0. it can literally be anything. there is no real answer for infinity - infinity which is why they say it can not be done.
the only way to get a real number answer from infinity - infinity is to define those infinities, in which case, it can have a real answer, but its like saying A - A = 5, which is impossible since any number minus itself is 0. yet infinity - infinity if defined to do so could. it just does not make much sense.
5th? we learned about them in 2nd
Infinity minus infinity equals 7. I know this for a fact becouse it was carved on a table at my school.
"...deviding"?