The Opposite of Infinity - Numberphile 

Haha!

Exfinity

outfoutity

@@devonqi interior:exterior infinity:exfinity

​@@JamesM1994 i understand hehe.. im just makin a lil' lul bruv..

+

+

Yeah, many people can't see the forest past the trees.

I always thought that if we learned math not from other or from a book, but invented math ourselves under proper guidance, than we could all understand math very easily.

But imagine if everyone had to be a genius to create 1000's of years of math progress. That system doesn't work, just like our own system.

buhahhahaha! XD

Pi=3 e=3 Pi=е I'm a civil engineer 😎

@@user-yb5if8kr3i pi = 5 if it breaks it ain't my fault

@@Alguem387 just round everything to 1 or 0. Pi = 1

@@user-yb5if8kr3i You can have Euler's π but you may not eat it.

Let’s see you try then

😂😂😂

you aint got nothing on spongebob bro

😂😂😂

He's a mathematician, not an artist

ummmm doing symbolic math is annoying AF to do with computer so why he doesn't accept pens? Our proffessor uses old projector and markers at uni

I think Shea means he wouldn't accept it in pen, but in pencil. There's a difference you know.

I don't remember why, but pen doesn't erase.

you cant erase water ink is a liquid

My teacher wouldn't accept work done in anything other than pen.

I was really enjoying that little calculus part XD

It was all calculus

Was it? Oooo interesting!

+Vicvic W calculus is always interesting

+NowhereManForever - 6:45

infinite of infinitesimals = infinite Uhhhhhhhhh.....................................................................................

@@davidgumazon i dont think you got the joke

@Demi AngelCat 🤣🤣🤣🤣🤣🤣🤣

@@davidgumazon infinity infintesmals = 1

there are as many infinitesmals as real numbers. number of hyperreals is also same as real numbers.

omg me too

I love the way he says everything.

also 'area'

noomba sounds like a kind of goomba in a spooky level.

aaaaaaaarea

Smart people usually have the worst calligraphy

F

Whoosh

I’ve never seen that word before lol

Loooool

Leibniz: but integral to the problem...

@@BritishBeachcomber Damn I was gonna say something like this...

let's set a limit to the level they can go down fighting

@@MrParry1976 it may never end, there maybe no limit

xD

+Jackie I'm always excited to tell my family this stuff but they look at me like, "AHHHHH!"

Mafioso Math haha! xP

+Jackie ditto.

so YOU HAVE A LOT OF this infiniTESimals...

Grand masterflash lol

Lol

Mine's not small. It's large. And negative.

I was really expecting that to end in a genitals joke. :p

...hmm... a finite candidate for smallest positive number is the reciprocal of a googleplex raised to the googleplex power a googleplex times.

Either you had a really terrible calculus class or you were a terrible student if that's all you learned in a semester.

@Alt Account some mathematics teachers don't really know mathematical concepts that well . so , some of the students aren't exposed to this correct explanation . instead , the teachers only teach their students formulas of calculus .

@Alt Account maybe it's a high school semester

what? he didnt say anything special.. what do you mean?

@@erdo4321 my guess is just that James described it in such a clear and intuitive way. Always love videos with James!

Ztingjammer same

He basically said that when you differentiate an integral, what you get is the function. This makes clear the fact that differentiation and integration are, by definition, opposite operations

Kakali Mukherjee 2nd Fundamental Theorem of Calculus ftw

they roasted him straight into the grave

about three and a half years later, apparently

dx/100

Just correlation or causation - for some measurements we will probably never know...

I dont get it

Weeb Fractals: Your fractals are so lewd...

@@lukedavis6711 they are infinitely repeating designs. So, the smallest piece is dependent purely on resolution. In other words, theoretically, the fractal is infinitely recursive in the same area and not even really distinct in the way infinitesimals are. I don't have a math degree though, so maybe someone else will be a bit more accurate.

The golden ratio: Amatuers

Normie

I always loved math but not necessarily all of my teachers

Planing at night to occupy more countries?

+ZeroSum Game Lmaooooo I see what you did there... must be Ukrainian aren't you? lml!

+ZeroSum Game boy, that escalated quickly!!

+Masha Vasilchikova haha good luck ;D

.l.

Manuel Pilarczyk Lol

...As long as you do it without using random commas like the one here between "mathematician" and "just."

@@HelloKittyFanMan. They said mathematician, not an English major 😊

Did you?

Je

can't stop the fire

Why can't you just flatten the curve line

You can find the distance of the curved line flatten it out and set it above to the lowest height point

I had a horrible teacher but I am in calc 2. I studied myself, didnt listen teacher. İt is your failure. Blaming your teacher is not a solution.

They’re twins again now.

@@someone4650 duuudde..... I was getting over it and now you've ruined it

That took a second

@@someone4650 They're still triplets; the death of one does not change the status of their birth.

@@n0ame1u1 THE QUAGMIRES

Thanks!

Or are they?

Vsauce music plays

Enter... the *hyperreals.*

deleuze borrows differentials from calculus he says that they are the infinitesimal blocks of change itself their relative magnitudes dictate the nature of encounters think of omicron notation, two functions come together and one may overwhelm the other and he says that the way they have been marginalised, the way "instantaneous change" has been termed an oxymoron instead of a generative paradox, is basically the attempt of state science to enforce thinking in terms of only being and identity as opposed to becoming and difference differentials will always be too small for state machinery, from this comes said machinery's imprecision, the inevitable "negligible" error to which pure difference has been relegated (dialecticians call this "negation") instead of putting up with this failure, the imperfection of the world compared to the actual numerical measurements with which we seek to capture it, deleuze says we have to finally start thinking of pure difference itself, because it is what drives being the way the derivative drives a function with infinitesimal steps

@@heartache5742 Sir this is a Wendy's

+Tiago Seiler Most students would still forget because most humans are ignorant peasents. I am hwoever pro-understanding education.

In this case... It kinda is. I mean Pi is a concept only understood when you understand that it is just a number derived from calculations.

+EmperorZelos ./.

Miguel Sambaan ?

+EmperorZelos I infer you are the type of person who contributes little to society, yet is in full capability to do so.

Never liked math.

Hm Shii, I am the complete opposite. In elementary school I was by far the best, but when I changed to "gymnasium" I was seriously fcked up and dropped to average. -.-

Yeah no problem, I also love to play games like MGS ;)

It is indeed, Hideo Kojima ftw! ^^

I loved math but hated this channel as it's mostly incorrect.

This actually happens a decent amount throughout the history of science and mathematics. Newton and Leibniz were both very intelligent people, but people today often view them as some sort of super mega geniuses who developed calculus all on their own. The state of mathematics when they both lived was ripe for the development of calculus. If Newton and Leibniz had not done it, someone else probably would have within the next 20 years or so anyway. The idea behind integrals (the method of exhaustion, like what is shown in this video to get the area of a circle) existed for millennia before Newton and Leibniz. About 50 years before Newton, René Descartes introduced coordinate geometry, which was a fundamental step toward developing calculus. Around the same time Pierre de Fermat posed the question of how to find the tangent line to a curve at any given point. Within about 20 years before Newton, James Gregory gave the first sort of argument for the Fundamental Theorem of Calculus - it was a highly geometric argument which connected areas under curves with the tangent lines of those curves. Later, Isaac Barrow developed the tool of infinitesimals and used it to solve Fermat's tangent line problem. Barrow also gave the first rudimentary proof of the Fundamental Theorem of Calculus using his infinitesimal techniques. Then we get to Newton. Isaac Newton was a student of Isaac Barrow and learned about infinitesimals (and how they relate to tangent lines and the big connection in the Fundamental Theorem of Calculus) from Barrow. Essentially, Newton was in exactly the right place at the right time to develop calculus. Pretty much all of the requisite tools had been developed right before he started his studies, and he learned directly how to use the last necessary tool from the very person who developed it. Newton saw how to put these tools together in a meaningful way, and more importantly, saw an application (physics). While Leibniz doesn't have the tools handed to him on a silver platter like Newton did, Leibniz still lived in the historical context where people knew about the method of exhaustion and already had coordinate geometry. People cared about Fermat's problem, and knew about Gregory's connection between area and slope. All it takes is for Leibniz to do the same thing Barrow did and just imagine the infinitely small and then run with it. This is what I mean when I say that the mathematics community was "ripe" for the development of calculus. The general trend of mathematical thinking and interest were moving toward calculus anyway and both Newton and Leibniz happened to be the right people living in the right places at the right time. Math and science are rarely developed solely by lone mega geniuses. (Another example of this phenomenon is the theory of relativity. Although we credit Einstein for the theory, he also lived in a context where people were studying and developing the same sorts of things. There are many mathematicians including Henri Poincaré and David Hilbert whose ideas about relativity were instrumental to getting the full theory. Yet science history tends to wipe away the contributions of everyone but Einstein and paint a faulty narrative of Einstein as a lone super mega genius who did everything without anyone's help. No, he lived in a context which was ripe for his ideas.)

SuburbAllied Was this an intended pun?

you had to check the spelling of infinitesimal, didnt u

SuburbAllied well you have to be more specific, what are you classifying as brain cells? Just neurons? Or any cell in the brain? It's been est that the adult male human brain, at an average of 1.5 kg, has 86 billion neurons and 85 billion non-neuronal cells

hang in there, my friend. newton described himself as a little boy on the beach, that, every once in a while, found a stone that was a bit more shiny than the rest.

Yes, but not in mathematics. Mathematicians are very strange people.

By that reasoning it should be out finity. :)

XD

Nah, it's ytinifni

The deception of logic: Take a wooden chopstick, with length measuring 20cm. Break it in half into 2 and we now get 2 sticks, each measuring 10cm in length. 20 = 10 + 10 20 - (10 + 10) = 0 What is lost in-between? Absolutely nothing! Suppose you were required to draw a line in the center of the original stick before cutting it in half. Where would you draw the line, with nothing in-between? To know what 3-D is exactly, first imagine 1-D and 2-D in their purest forms. Can anything possibly exist in just a 1-dimensional or 2-dimensional form? If 1-D and 2-D were totally imaginary, how real could a 3-D object be? 🤔 Are you able to reconcile 3-dimensional concept with reality? Theory: The entire Universe began from a single point. Now, what is the smallest possible point? It is impossible to reconcile this theory with logic as well. Can you draw a "perfect circle" using a compass, without the smallest possible point? Question nothing, to question everything. 🙂

Deep.

infinitejinpachi :0

AHAHAHAHAH WHY IS THIS RELATABLE

The Golden Carpenter Depression

gravestone quote

+Fish Kungfu I feel there should be action figures for all of Brady's channel: James for Numberphile, Prof. Polyakoff for Periodic Videos, Prof. Moriarty for Sixty Symbols... Ooh, this would be so fun.

+Fernie Canto I'd definitely buy a figurine of James!

+Fernie Canto Don't forget the legendary Keith from the Royal Society from Objectivity ;)

+Fernie Canto CLIFF. STOLL.

+Fish Kungfu it would be a great idea for kickstarter project) definitely for it)))

+PunktKommaNull Prof. James Grime is awesome!

You are not alone

James is like the Ainsley Harriott of mathematics.

+PunktKommaNull we are shy to say this :p

hakkihan tunbak Thanks for the hint! Didn't know that yet! :)

+MultiWafflemaster I feel like I get what he was saying.... What is the opposite of the "biggest thing" - it is the "smallest thing" or "negative the biggest thing". I guess it is like what is the opposite of being unimaginably rich? Is it being really poor, or being in debt? Both arguments hold water for me. The problem with "negative the big thing" is that it still has a kind of great magnitude in my mind. Just one man's musings.

+MultiWafflemaster Infinity is a concept, not a number. Surely the opposite of something too big to measure is something too small to measure?

The inverse of an number depends on the group you are in. If it is addition, then the negative value is the inverse. If it is multiplication it is one divided by the value. If it is NxN matrix then you inverse the matrix. If it is MxN matrix, then you need a pseudo inverse.

+MultiWafflemaster No it wouldn't because they both have the same magnitude but in different directions. If that makes sense? Like if I asked what would be the opposite of the word huge you wouldn't say oh negative huge!

+Lachi Agnew Read +L0LWTF1337 's post. Both answers are right, due to lack of further specification.

Mathematicians are great philosophers

Plus: The bisquit is tasty!

One pence coins, not one cent coins.

or it is rotation at 90deg ( counter or clockwise)

thatsthejoke.jpeg

infinity * i = 8

... ∞i (complex infinity) ? :)

Devendra S wooooooosh

+stingersplash16 watch it again, pay real close attention to the video and you'll see it!

+Jake Equilar kepler 39? the planetary system?

+Jake Equilar Who is this guy having the number 39 on his back?

+Thomas Korbacher indeed who is he? O _ o

warwick capper haha

I always thought x/infinity would be equal to infinitesimal

@@R0llingHard and that's because infinitesimal IS equal to zero. the usual definition of infinitesimal is "a number that's as close as possible to zero without being zero" problem is that such number can't exist since we can always get the average between zero and whatever number you believe to be infinitesimal. but, if you define infinitesimal as "the smallest non-negative irrational" then, infinitesimal = 0. the only difference between both definitions is the inclusion of 0 and that you can't use the average trick anymore. the issue of the cylinder, shown in the video, having volume while it's cross sections have heigh zero can be explained because we have infinite cross sections so they add to 0*infinity (which isn't defined)

The infinitesimal is not equal to zero as the hyper reals can show. And the infinitesimal is also not a number, an all-too-common misconception.

@@DanielRossellSolanes "the usual definition of infinitesimal is "a number that's as close as possible to zero without being zero"" Usual definition in which context? I have typically seen infinitesimals described as something like "positive numbers which are smaller than every positive real number." But I may not have experienced the same contexts as you, so I'm genuinely curious!

​@@edwardpotereikoWe're talking about standard real numbers system, No field extensions are related to it.

Fair

Technoultimategaming at least yours are bigger than zero

Meanwhile me : Laughing in negative 😂

Plank distance.

@@Enter_channel_name farts on your screen

Valera 8 No, I don't have to do anything.

No estaría 'troleando' a nadie, sólo escribiendo mal. 2 pequeñas correcciones si me permites: *I'm really sorry *Not Spanish but Spaniard. Saludos.

Warrick Capper, an AFL star and meme

@@robertbell2159 thanks for the clarification dude

@@meyupme9854 This isn't the only time I've seen his picture show up in an academic video. He shows up the same way in the Teaching Company series about the American Civil War I think.

A little late but I think this is also a clever reference to Kepler-39, 39 being the number on the jersey worn by Warrick Capper. Could be coincidental, tho.

Ahh the pinky and the brain. Very famous cartoon here in India during early 2000s😇

Similar physical attributes as pinky also hahaaaa

What the haha

+pantheryou Not really, if you understand the principle you don't need to memorize anything.

It's not difficult. It's only difficult if you don't want to learn it

R. Rain re-read my post. what you have typed is precisely my point.

+pantheryou i absolutely agree. Math is really just logic and philosophy. If you understand the logic behind it without the numbers, then you can do the math but most people believe that math is a dark magic where stuff just gets pulled out of mathematicians hats

I see it!?!

@@KaliFissure what is the what?

@@KaliFissure No. The Planck length is a fundamental metric of the dimension of length. Asking for an opposite is a non-sequitur.

How? I don't see it

@dominic twaites When he draws the two outer vertical lines, it sort of looks like the symbol for pi. :)

Cool.

+MadaxeMunkeee story

+Leon Gerity Bro

+ImJustACowLol Sir you are a true genius.

+This Could Be You!!! Thank you, thank you. I just received word that I am nominated for the Nobel Price of Mathematics. It is the first time such a nobel price is going to be given, as prior to this date the Nobel Price for Mathematics did not exist yet. Awesome, right?

Basically

That's what I always thought, and the only reason I came to the comments!

NO You can not divide by infinity, it is not a number

@@MsAlfred1996 you are right it can only happen in limits

Sorry for my bad English! 0,0=infinitesimal ∞=infinitely large 0=naught ᴑ=impossible

But if I throw my pennies around, I would get arrested.

damm.. mind blown. halarious tho

this dude just broke math

But a ninety degree rotation is multiplying by i

+Tymon0000 I think it's Capper

+ObeseYeti Kepler*

ikbeneenpop1 The guy with the 39 on his back is Warwick Capper

ObeseYeti Do you happen to know why he is there?

+Tymon0000 Pun on the name, maybe?

+Thomas Godart Except that it is wrong.

+Thomas Godart lim x-->infinity 1/x=0 lim x-->0 (+) 1/x=infinity lim x-->0 (-) 1=x= - infinity Infinity is not a number, meaning that problems that involve it have to use limits.

+BlackSkullRacer613 One-sided limits are often useful. Since the whole infinitesimal/illimited etc. discussion has been confined to the nonnegative numbers, the limit while approaching 0 from above is relevant.

+teekanne15 well limits get around the error by just essentially saying "i bet that you can't make that error ever give me a wrong answer because i can always draw enough triangles" hence the standard epsilon-delta proofs.

+Ben Nutley What we actually do is the equivalent of "Tell me how much error in the result you will allow, and we'll find a small enough delta (or large enough N, in some cases), that our procedure will be at least that accurate."

Blan Morrison reminds them of awful high school math classes

Unit circle fires up my ptsd

💀

2pir made me habe flashbacks

yes i was there, a suicide bomber detonated during the exams @@katyameowmeow

My guess is 10 to the power of minus infinite.

Actually this is invers of infinity

I was going to say the same lol

Thats the recipicle of infinity

You can’t divide by infinity

Leonardo Acuna you are not alone, bro

Maybe theres apart of you that dose know

Leonardo Acuna same here ^•^

I like to pretend I understand.... I just enjoy watching somebody enjoy such a mad subject. He's great!

Leonardo Acuna I'm with u

The basketball player!!!

[ 4:20 + 0:02= ? ]

39?

I had to Google it, but the 39 on the guy's jersey + mentioning Kepler might be a reference to the brown dwarf star Kepler-39. Edited to add: someone else on here ID'ed the guy as Australian footballer Warwick Capper.

Yeah whats that about....

they aren’t an infinitesimal apart, they are the same number. it is just an artifact of a base 10 number system.

.3 repeating is what? What about that number multiplied by 3?

@@ar_xiv never thought of it like that

Ok so we all agree that for every integer execpt zero n/n = 1. So 1/3 = 0.3 repeating. 2/3 = 0.6 repeating. So 3/3 has to be 0.9 repeating right. But every n/n = 1.... thus 3/3 = 1 = 0.9 repeating

Yea, I don't like that saying. Topologically speaking, 0.9 repeating is in the open interval (0,1), while 1 is not.

the triangles go around the circle so when you add up the triangles bases it equals the circumferences of the circle so imagine the circumference is 3 the 3 is divided infinitely so the base of each triangle is 3/(inf) now to form the triangle we want to add all the base together and because the base of each triangle is the same we can multiply by how many triangles there is which is infinity so we get (3/inf)*inf the 2 infinitys cancel and we are left with 3

Welcome to the Super Task

Welcome to convergent infinite series. Heard of Zeno's paradox?