The Opposite of Infinity - Numberphile

Continuing to talk Infinitesimals, this time with Dr James Grime.
See last week's video: • The Infinitesimal Mona...
More links & stuff in full description below ↓↓↓
Dividing by Zero: • Problems with Zero - N...
James Grime: singingbanana.com
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[@regenald510]

I hated math in school but now i realize after watching these videos that it wasn't math I hated, it was the class.

[@el_kks_4361]

+

[@el_kks_4361]

+

[@brianmerritt5410]

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

[@NicksDomain101]

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.

[@johnsmith2848]

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.

[@williammickelson403]

Outfinity

[@HelloKittyFanMan.]

Haha!

[@JamesM1994]

Exfinity

[@devonqi]

outfoutity

[@JamesM1994]

@@devonqi interior:exterior infinity:exfinity

[@devonqi]

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

[@_nines8270]

And then the engineer comes along and says "Eh it's within 10%, it's fine..."

[@maheiramkhan]

buhahhahaha! XD

[@user-yb5if8kr3i]

Pi=3 e=3 Pi=е I'm a civil engineer 😎

[@Alguem387]

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

[@nickwilson3499]

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

[@StefanVeenstra]

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

[@serenes]

"let's say I have a circle"...draws lopsided potato edit: this is meant to be a humorous observation I have nothing against his theoretical circle

[@gnochhuos645]

Let’s see you try then

[@TXejas19]

😂😂😂

[@EE-wp9qr]

you aint got nothing on spongebob bro

[@DrWizardMother]

😂😂😂

[@ammyvl1]

He's a mathematician, not an artist

[@frosty1433]

My math teacher wouldn't accept work done in pen, and here this guy is using a permanent marker.

[@michaelmapple8201]

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

[@rakodlartv4565]

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

[@frosty1433]

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

[@143mailliw]

you cant erase water ink is a liquid

[@TheRadioactiveFX]

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

[@keithwilson6060]

I love the way James says "noooomba."

[@joaocesteil51]

omg me too

[@NoriMori1992]

I love the way he says everything.

[@myavuz3619]

also 'area'

[@franciscomoll-serrano8083]

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

[@markus-4383]

aaaaaaaarea

[@elfinthekitchen]

"There are lots of infinitesmals." Understatement of the century.

[@davidgumazon]

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

[@notfunny5021]

@@davidgumazon i dont think you got the joke

[@elfinthekitchen]

@Demi AngelCat 🤣🤣🤣🤣🤣🤣🤣

[@rohangeorge712]

@@davidgumazon infinity infintesmals = 1

[@user-kb8gm4tv4x]

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

[@stensoft]

Newton: I have invented calculus Leibniz: I have invented calculus Newton: That sounds derivative

[@BritishBeachcomber]

Leibniz: but integral to the problem...

[@nidhinbenny7975]

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

[@MrParry1976]

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

[@rohangeorge712]

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

[@NowhereManForever]

I like this sneaky way of teaching your viewers calculus without saying the scary C word.

[@Reydriel]

I was really enjoying that little calculus part XD

[@NowhereManForever]

It was all calculus

[@VicvicW]

Was it? Oooo interesting!

[@oldcowbb]

+Vicvic W calculus is always interesting

[@RFC3514]

+NowhereManForever - 6:45

[@grandmastarflash]

anyone that thinks they have found the worlds smallest number obviously haven't seen my bank balance

[@thewarlord6529]

Grand masterflash lol

[@blue9139]

Lol

[@JayTemple]

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

[@kungfuskull]

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

[@jwm239]

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

[@satanspotatoes]

My man just drew the worst circle ever and then proceeded to draw the most perfect f i have ever seen. You can see my amazement at 7:59

[@naysonbigelow6907]

7:00 He literally just summed up an entire semester of calculus in just a couple minutes This man is a genius

[@SpeakShibboleth]

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

[@grariee]

@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 .

[@tronalddump2267]

@Alt Account maybe it's a high school semester

[@critstixdarkspear5375]

The amount of theory in his brain has impinged so hard on on his motor functions that he can no longer draw shapes. Bless him for the sacrifices he has made.

[@aboriani]

Smart people usually have the worst calligraphy

[@MrOdsplut]

F

[@jonboshears7767]

Whoosh

[@o.steinman3855]

I’ve never seen that word before lol

[@tonytrizz7421]

Loooool

[@jackie2691]

I love how all the people in these videos are so excited to talk about these things.

[@jackie2691]

xD

[@mafiosomath7888]

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

[@jackie2691]

Mafioso Math haha! xP

[@AlistairRiddochSHBEW]

+Jackie ditto.

[@JorgetePanete]

so YOU HAVE A LOT OF this infiniTESimals...

[@Vidi]

Dr. Grime's enthusiasm is immensely encouraging. Even the least curious among us must find his presentation engaging. I wonder whether any single person fortunate enough to have studied under his personal direction did not succeed. Bravo!

[@griplimit]

Infinitesimals: “I’m the smallest thing” Mandelbrot set: “hold my fractals!”

[@lukedavis6711]

I dont get it

[@davidgumazon]

Weeb Fractals: Your fractals are so lewd...

[@RoryStarr]

@@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.

[@fabianp.2986]

The golden ratio: Amatuers

[@Perririri]

Normie

[@mva2997]

4 AM on a work night, a video about the opposite of infinity? BRING IT

[@AC_Blanco]

Planing at night to occupy more countries?

[@johnathan1784]

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

[@tallevi2000]

+ZeroSum Game boy, that escalated quickly!!

[@GuiltyGearRockYou]

+Masha Vasilchikova haha good luck ;D

[@TacoSt8]

.l.

[@manual1415]

I will become a mathematician, just so i can write on brown paper with green sharpies.

[@blue9139]

Manuel Pilarczyk Lol

[@HelloKittyFanMan.]

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

[@olipolygon]

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

[@sherllymentalism4756]

Did you?

[@bogogaming7736]

This is literally the basics of Calculus and I never really realized it until now Edit: I commented literally right before he started going over calculus. Wack

[@avishankarsardar6981]

With teachers like him one can never hate maths

[@TheFrewah]

I always loved math but not necessarily all of my teachers

[@RenoLuke]

Little known fact: George and Fred Weasley aren’t twins, they are in fact triplets and the third became a mathmagician

[@someone4650]

They’re twins again now.

[@kekorulesatlab3133]

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

[@kingigzorn7680]

That took a second

[@n0ame1u1]

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

[@HN-kr1nf]

@@n0ame1u1 THE QUAGMIRES

[@TiagoSeiler]

Teachers in school go: "Area of a circle is 2pi r^2". The kids ask why, and teachers just say "because it is". Two weeks after class everybody's already forgotten what the formula was. If we were taught WHY in school (just like this three minute segment at the start) we would never forget these things.

[@EmperorZelos]

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

[@KPopsicleSNSD]

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.

[@saintguel23]

+EmperorZelos ./.

[@EmperorZelos]

Miguel Sambaan ?

[@ulluubloo]

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

[@seven9399]

This guy is awesome he literally breathes life into Mathematics for those who hate maths, now find out it was probably just the class you was in.

[@greendeathification]

I honestly had no idea what this person was talking about for the majority of this video, but I watched whole thing because I enjoyed watching his genuine enthusiasm for the topic and for math

[@13StJimmy]

I’m pretty confident that if I had Dr. Grimes as a teacher I wouldn’t have switched majors and gone on to Calculus II

[@lacroixemmanuel9684]

Je

[@cygnus3543]

can't stop the fire

[@marcusderinger8892]

Why can't you just flatten the curve line

[@marcusderinger8892]

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

[@rahimeozsoy4244]

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.

[@kakalimukherjee3297]

8:58 You are a damn genius. You taught why the derivative is the inverse of the integral and what slope has to do with area in less than 30 seconds

[@erdo4321]

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

[@Ztingjammer]

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

[@jordantheoneandonly3880]

Ztingjammer same

[@kakalimukherjee3297]

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

[@samklemm822]

Kakali Mukherjee 2nd Fundamental Theorem of Calculus ftw

[@alperyoloyilmaz5388]

I recommend the book written by Keisler named Elementary Calculus. It uses infinitesimals to teach calculus. Also great video! I made a presentation and speech about this for school this year and seeing this made me really happy that the area is more popular than I thought.

[@Gabriel-pd8sv]

Thanks!

[@cedricgist7614]

I enjoy the work of Numberphile - Dr Grimes et al. You guys really love your work and it's infectious. Thank you.

[@SuburbAllied]

When I started to watch this video I had a finite amount of brain cells. When returning to my math homework, I realized I actually had an infinitesimal amount of brain cells.

[@georgeabreu6392]

SuburbAllied Was this an intended pun?

[@BlueSquad00]

you had to check the spelling of infinitesimal, didnt u

[@discordant8543]

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

[@namelastname4077]

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.

[@giraculum9981]

10:00 "They discovered that Newton came up with it first. Leibniz then died..." what, like, immediately? That's harsh.

[@Defectivania]

they roasted him straight into the grave

[@feralcatgirl]

about three and a half years later, apparently

[@maxwellsequation4887]

dx/100

[@MMaker738]

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

[@luctapia]

Wow, i remember watching these videos as a kid, not understanding literally anything, now im on calc 3 and this is a really nice summary!!!! It really shows your teaching abilities when you can captivate a kid with no knowledge or conception of calculus and do it again to the same person many years later!!!!! Thank you

[@sageriver7669]

"You're not fooling me Sonny...It's Turtles all the way down!!"

[@weebo1612]

Never Liked math until I started watching this channel.

[@jay.ahre1]

Never liked math.

[@Dark88Dragon]

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. -.-

[@Dark88Dragon]

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

[@Dark88Dragon]

It is indeed, Hideo Kojima ftw! ^^

[@groszak1]

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

[@FishKungfu]

It'd be cool if there were Numberphile action figures, or even just 3D printed figurines of 3D full body scans of our Numberphiles Heros. This would definitely include a "Brady" with a replaceable exploding head for every time his mind is blown.

[@FernieCanto]

+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.

[@tirsoacuna1356]

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

[@MarkusHobelsberger]

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

[@umbreon8527]

+Fernie Canto CLIFF. STOLL.

[@AstaMuratti]

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

[@SirMo]

OMG I love this! So many concepts explained in such a short succinct and clear manner.

[@josephjackson1956]

I find it amazing that Newton and Leibniz both came up with Calculus independently.

[@MuffinsAPlenty]

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.)

[@infinitejinpachi]

the opposite of infinity is my will to live

[@purpleice2343]

Deep.

[@georgeabreu6392]

infinitejinpachi :0

[@user-rd3jw7pv7i]

AHAHAHAHAH WHY IS THIS RELATABLE

[@BO-pf9wi]

The Golden Carpenter Depression

[@_BangDroid_]

gravestone quote

[@folumb]

Thanks for giving Leibniz some shine, he also has some very interesting philosophical works if you enjoy logic employed in a different way

[@PersimmonHurmo]

Mathematicians are great philosophers

[@StillMusician]

Plus: The bisquit is tasty!

[@rogersledz6793]

Thank you so much for uploading this video. It is helping me get through the pandemic!

[@shahrukhs1637]

Before starting video, I was thinking, oh that's so simple. This guy's going to teach us about limits. Lim(1/X) ,X→∞ Then as the video started, "oh is it something different? Seems like he is going towards integration by the end of the video, I'm happy, and also realized I'm rusty. Thankyou

[@d4nielDayZContent]

I love this guy. - Am I alone?

[@AntonioBarba_TheKaneB]

+PunktKommaNull Prof. James Grime is awesome!

[@redsalmon9966]

You are not alone

[@simonwilliamdavidson5660]

James is like the Ainsley Harriott of mathematics.

[@falmanna]

+PunktKommaNull we are shy to say this :p

[@d4nielDayZContent]

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

[@BearshiMisnes]

"I'm so rich, I can throw pennies around." Great job Dr. Grime

[@Perririri]

One pence coins, not one cent coins.

[@topilinkala1594]

In multivariable calculus one calculates with differentials as they were just ordinary variables and it all works out and is rigorous and consistent. But differentials are not numbers.

[@alice_in_wonderland42]

Or are they?

[@ninja8flash742]

Vsauce music plays

[@pokedart9001]

Enter... the *hyperreals.*

[@heartache5742]

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

[@bobob1292]

@@heartache5742 Sir this is a Wendy's

[@philh4807]

Even though I have been out of college since 1989 when I got my BS in chemistry, this guy might have made me change my major to math.

[@General12th]

I loved that demonstration of the fundamental theorem of calculus. Absolutely beautiful and simple and excellent!

[@General12th]

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

[@largolagrande7837]

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

[@eaglehorse3323]

Isn't the opposite to infinity finity

[@RWBHere]

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

[@tgbrowning3002]

By that reasoning it should be out finity. :)

[@grabern]

XD

[@TheRandomBiscuit]

Nah, it's ytinifni

[@ManHeyuan]

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. 🙂

[@mayursoowamber7549]

I wish I had this man during Uni 😭 The amount of understanding that just occurred in just 15 mins

[@Vethreth]

This is why we need passionate people to teach us instead of teachers with no passion. I wish I had access to such quality content during my scholarship (and that my English would allow me to understand, of course). Anyway, it's still really interesting. I didn't know I'd actually have fun learning about mathematics. Thanks for this gem! =)

[@jakeequilar5476]

I saw what you did there at 4:22 Numberphile

[@jakeequilar5476]

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

[@sorlag110]

+Jake Equilar kepler 39? the planetary system?

[@thomask.2726]

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

[@madokaonline]

+Thomas Korbacher indeed who is he? O _ o

[@thomask.2726]

warwick capper haha

[@areadenial2343]

An interesting thing I found on Wikipedia is the projectively extended real line, where the number line is wrapped around into a circle, and the point where they meet is infinity, which is neither positive nor negative. In this system, x/0 is equal to infinity, and x/infinity is equal to zero. The coolest part is that it would also work with complex numbers if you wrapped the plane of real and complex numbers into a sphere, which is the Riemann sphere.

[@R0llingHard]

I always thought x/infinity would be equal to infinitesimal

[@DanielRossellSolanes]

@@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)

[@edwardpotereiko]

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.

[@MuffinsAPlenty]

@@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!

[@omnipresentcatgod245]

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

[@stephenlandrum2262]

The entire thing I was just waiting for the next time he says “area” he holds out the a and it’s awesome

[@LLO227]

Man this video still rocks the cerebrum after 5 years! Needed this refreshing thinking exercise.

[@hiimapop7755]

"...cos I'm so rich I can throw my pennies around." Ahh taking quotes in 2019, amirite?

[@mk_rexx]

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

[@MultiWafflemaster]

Wouldn't the mathematical opposite of infinity be negative infinity? I would consider an infinitesimal to be the inverse of infinity.

[@numberphile]

+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.

[@TheGingeize]

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

[@L0LWTF1337]

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.

[@lachiagnew4292]

+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!

[@nal8503]

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

[@BadassBeazly]

My comprehension of the maths is at best, very rudimentary. I acknowledge that mathematics IS the universe(s). I admire those who are able to comprehend and play with numbers so easily. Yours is a vision that I cannot see, but I can "feel" this beauty and can admire it from afar. Thank you for sharing your passion.

[@Narutodumbo111]

"1/0 is not infinity, we would never do that" Me studying stability of transfer functions using final values: 👁️👄👁️

[@Quasihamster]

"There's soomthing about it that makes you ooncoompfable!" Love that accent :D

[@llucer3505]

'8' is the opposite of infinity ;-)

[@loginid7108]

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

[@damplamp]

thatsthejoke.jpeg

[@tjw_]

infinity * i = 8

[@Russtopia]

... ∞i (complex infinity) ? :)

[@XanderFenikkusu]

Devendra S wooooooosh

[@thomasking7659]

Thank you Fred Weasley, these videos are really interesting.

[@anastasistzaras7389]

What the haha

[@adibanti]

Interestingly using the slices underneath a curve in calculus is a very similar concept to how we record audio digitally. You take little rectangular chunks of the sound wave in exactly that way missing little bits at a time and convert them to bits of information. Any wonder why 8bit music sounds like that? It's because the rectangles used are really big so much of the sound is missing. Science and maths will always be best mates.

[@ThomasGodart]

Thank you James Grime for saying that 1/infinitesimal is infinity, which means that the other Numberphile videos about 1/infinity equals 0 are false! The good way to see infinity is that one that you just used: 1/infinity equals infinitesimal and defines infinitesimal, and 1/0 having no answer

[@douggwyn9656]

+Thomas Godart Except that it is wrong.

[@MoltenMetal613]

+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.

[@douggwyn9656]

+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]

the feeling of "it works for daily usage but somehow im not happy cause I disregarded a little fact" is what bothered me in school so much

[@gimpdoctor8362]

+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.

[@douggwyn9656]

+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."

[@Jameshazfisher]

I prefer the circle area proof that rearranges the wedges in an alternating zig-zag to form a rectangle, with one side r and the other side pi*r. It's a cleaner proof because it doesn't skew the wedges, and the area of a rectangle is slightly more trivial than the area of a triangle.

[@abdi8543]

Because of him i changed my major. I was only 14 years old when i had to make the decision, now 3 years later iam happy i met him.

[@technoultimategaming2999]

Smallest possible number that's still bigger than 0.... Just look at my exam results

[@IntergalacticPotato]

Fair

[@headcanon6408]

Technoultimategaming at least yours are bigger than zero

[@pathikghugare]

Meanwhile me : Laughing in negative 😂

[@SeriousApache]

Plank distance.

[@sameash3153]

@@Enter_channel_name farts on your screen

[@ImJustACowLol]

The opposite of infinity is finity. The end.

[@MadaxeMunkeee]

Cool.

[@Th3BlackLotus]

+MadaxeMunkeee story

[@maj.peppers3332]

+Leon Gerity Bro

[@tristanscott6774]

+ImJustACowLol Sir you are a true genius.

[@ImJustACowLol]

+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?

[@dollarbill8959]

Thank you for that knowledge, I gave never heard about hyperreals before.

[@priyanshupokhriyal1677]

I used to hate maths until I discovered your channel, thank you! ♥️

[@BarendNieuwoudtZA]

Honestly if it was explained to me this way, I would actually have understood what I was doing at uni

[@KaneCowboyCo]

mathematics such as calculus are difficult to many because too many have been taught since they first entered grade school that math is a memorization game.

[@RMeitzen]

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

[@laughy38247357075834]

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

[@KaneCowboyCo]

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

[@JITCompilation]

+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

[@thalesn]

Watching this video made me go back... Back to my first semester in college, when they threw us into a Calculus class without any care. I didn't hate Calculus, but Calculus is full of concepts that aren't intuitive at all. This video does a great job at explaining why those concepts aren't intuitive. I failed that class and, in the very next semester, I took the class again and then I aced it. I didn't suddenly got smarter, I just understood those very basic (albeit not intuitive) concepts.

[@SlimJimJoey]

This guy has the brain of The Brain, but the voice of Pinky 😂😂😂 Narf!

[@hatebreeder999]

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

[@shanestevens5194]

Similar physical attributes as pinky also hahaaaa

[@meyupme9854]

Did any one noticed the picture that got mixed with Kepler's photo in 4:22 XD

[@robertbell2159]

Warrick Capper, an AFL star and meme

[@meyupme9854]

@@robertbell2159 thanks for the clarification dude

[@McAllen07]

@@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.

[@adamestrada7610]

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.

[@oskarpaulander4027]

Happy to see a video about this! Wrote my bachelor's thesis on this very subject. It's an interesting area of mathematics that I hope will get more visibility. Specifically we looked at Picard's theorem and how much simpler the proof is by using non standard analysis (I'm far from competent enough to understand the standard proof). It's beautiful, massively useful and intuitive in a way that limits aren't. That being said. Both are needed

[@jannickharambe8550]

Dr James Grime is the best. He is amazing!

[@comochinganconesto]

I used stuff like this in calculus and physics way too much, didn't even know that they were a legitimate math concept just that it kinda worked and made certain problems easier to understand.

[@aliaqarahimi5410]

Whenever im super tired or need sth to entertain my soul, i watch the clips of this channel. Thank you :-)

[@leonardoacuna8970]

Am I the only person who spends his days watching videos like this not knowing wtf these people are talking about but still liking them

[@valentinaescalante4074]

Leonardo Acuna you are not alone, bro

[@grovergodwin3649]

Maybe theres apart of you that dose know

[@loopyllama6897]

Leonardo Acuna same here ^•^

[@dotherightthingandy5217]

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

[@ryan0348]

Leonardo Acuna I'm with u

[@Supertimegamingify]

I was wondering about this earlier, thanks!

[@daveayerstdavies]

If you alternate the orientation of the small triangles, you don't need to stretch them. You end up with a regular rectangle with height r and base pi r. Simpler and more convincing than the stretched triangles method.

[@newtonrhapson1453]

The problem of Math teacher in school are they teach only about calculating instead appliance and conceptual meaning. I'm not fond with Math in HS until go to college and learn about actual calculus from my lecturer and how they can be discovered

[@dmsanct]

I yearn for the day I can say "Yo guys have you heard, infinitesimals made a comeback!" and have people look at me like I finally lost it

[@enshk79]

I love the fact the original mathemations decided to just ignore the curve parts

[@user-fg6ng7ej6w]

his guy has a talent of explaining tricky concepts. great! thanks

[@tweedyburd007]

7:00 unknowingly makes pi

[@anushrao882]

I see it!?!

[@BroArmyCommander]

@@KaliFissure what is the what?

[@Bollibompa]

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

[@dominictwaites2721]

How? I don't see it

[@Seth_M-T]

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

[@Tymon0000]

Who is the guy 4:21 with 39 on his back?

[@ObeseYeti]

+Tymon0000 I think it's Capper

[@ikbeneenpop1]

+ObeseYeti Kepler*

[@ObeseYeti]

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

[@Tymon0000]

ObeseYeti Do you happen to know why he is there?

[@ITR]

+Tymon0000 Pun on the name, maybe?

[@DanielDaniel-xz2yp]

At the end when he talked about fans of the system (and that people that use it say its better) it kinda felt like i was watching a review for some math theories and i'm about to buy one

[@Jesyx]

I love this man's passion for Math

[@arandomchannel1101]

Infinity can't be rotated the opposite way... homever if you rotate it 90 degrees it will become 8.

[@jimbo9129]

damm.. mind blown. halarious tho

[@griseld]

this dude just broke math

[@nickpro8116]

But a ninety degree rotation is multiplying by i

[@SlenderMiner99]

Before watching the entire video: ∞/1 = ∞ 1/∞ = [opposite of ∞]

[@Schradermusic]

My guess is 10 to the power of minus infinite.

[@animejames7887]

Actually this is invers of infinity

[@fayezbayzidify]

I was going to say the same lol

[@andrewdavis4295]

Thats the recipicle of infinity

[@mihaispan4765]

You can’t divide by infinity

[@MarianoRodriguez]

Does Zeno´s paradox has something to do with this?

[@DanDart]

Great circle, James.

[@strengthxphilosophy]

Amazing!!

[@4MediaTV]

+Strength And Philosophy nice channel

[@strengthxphilosophy]

+Amanda Vicious thanks!

[@johnathan1784]

I subbed to your channel bruv.. not really into that motivational BS, but I love your approach... guys check this guys ch out!

[@strengthxphilosophy]

+johnathan1784 Thanks Johna - appreciate that!

[@Magnogen]

I think I understand... Is it: infinitesimal = 1/∞ ???

[@user-rd7jv4du1w]

Basically

[@brianheight]

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

[@MsAlfred1996]

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

[@4ka07_muhammadrizky]

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

[@paulpaul5972]

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

[@siamvat]

Infinitesimals, yeah! I love them, they are just like single points on a line, comparing them to whole numbers is just like comparing whole numbers to infinity, or omegas. Infinitesimals are the opposite of counting Alephs and The Inaccesible cardinals. We are reaching out to discover how big can mathematic really be. It's huge.

[@rrrfrdd4497]

Mathematicians are not the kind of people you usually imagine going "ignore the curvy bits, its close enough".

[@arvee3451]

"...it could be thrown out from theory" *lies back* "...they make a comeback" *goddammit*

[@matsv201]

"I have a circle" Sorry, i would call that a blob ;) "Now it turns into a triangle, you see that triangle" Sorry, i would call that a blob ;)

[@yelwinaung9296]

Very instructive.

[@Femaiden]

this is something i never thought about, but before watching the video, the first thing I thought of was 0.0 with an infinite number of 0's after it, but with a 1 at the end. this theoretical number has a 1 at the very end, but it also has an infinite number of zeroes in between, so you would never ever reach the 1 and yet somehow must be able to reach the 1 if you went far enough because the 1 is there, yet somehow unreachable, but reachable at the same time. now to actually watch the video and see how close my imagination is to what the video actually says. . .