The Opposite of Infinity - Numberphile
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- Опубліковано 7 вер 2015
- 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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I hated math in school but now i realize after watching these videos that it wasn't math I hated, it was the class.
+
+
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.
Outfinity
Haha!
Exfinity
outfoutity
@@devonqi interior:exterior infinity:exfinity
@@JamesM1994 i understand hehe.. im just makin a lil' lul bruv..
And then the engineer comes along and says
"Eh it's within 10%, it's fine..."
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 say I have a circle"...draws lopsided potato
edit: this is meant to be a humorous observation I have nothing against his theoretical circle
Let’s see you try then
😂😂😂
you aint got nothing on spongebob bro
😂😂😂
He's a mathematician, not an artist
My math teacher wouldn't accept work done in pen, and here this guy is using a permanent marker.
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 like this sneaky way of teaching your viewers calculus without saying the scary C word.
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
"There are lots of infinitesmals."
Understatement of the century.
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.
Newton: I have invented calculus
Leibniz: I have invented calculus
Newton: That sounds derivative
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
I love the way James says "noooomba."
omg me too
I love the way he says everything.
also 'area'
noomba sounds like a kind of goomba in a spooky level.
aaaaaaaarea
anyone that thinks they have found the worlds smallest number obviously haven't seen my bank balance
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.
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
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!
I love how all the people in these videos are so excited to talk about these things.
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...
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.
Smart people usually have the worst calligraphy
F
Whoosh
I’ve never seen that word before lol
Loooool
7:00
He literally just summed up an entire semester of calculus in just a couple minutes
This man is a genius
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
Infinitesimals: “I’m the smallest thing”
Mandelbrot set: “hold my fractals!”
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
4 AM on a work night, a video about the opposite of infinity? BRING IT
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.
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
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.
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.
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
Little known fact: George and Fred Weasley aren’t twins, they are in fact triplets and the third became a mathmagician
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
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.
+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.
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
With teachers like him one can never hate maths
I always loved math but not necessarily all of my teachers
10:00 "They discovered that Newton came up with it first. Leibniz then died..." what, like, immediately? That's harsh.
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...
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
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
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.
Thanks!
I enjoy the work of Numberphile - Dr Grimes et al. You guys really love your work and it's infectious. Thank you.
I will become a mathematician, just so i can write on brown paper with green sharpies.
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?
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.
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.
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.
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
OMG I love this! So many concepts explained in such a short succinct and clear manner.
Never Liked math until I started watching this channel.
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.
Isn't the opposite to infinity finity
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. 🙂
Thank you so much for uploading this video. It is helping me get through the pandemic!
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
the opposite of infinity is my will to live
Deep.
infinitejinpachi :0
AHAHAHAHAH WHY IS THIS RELATABLE
The Golden Carpenter
Depression
gravestone quote
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.
+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)))
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.
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.
Wouldn't the mathematical opposite of infinity be negative infinity? I would consider an infinitesimal to be the inverse of infinity.
+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.
Thanks for giving Leibniz some shine, he also has some very interesting philosophical works if you enjoy logic employed in a different way
Mathematicians are great philosophers
Plus: The bisquit is tasty!
"You're not fooling me Sonny...It's Turtles all the way down!!"
I find it amazing that Newton and Leibniz both came up with Calculus independently.
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.)
'8' is the opposite of infinity ;-)
or it is rotation at 90deg ( counter or clockwise)
thatsthejoke.jpeg
infinity * i = 8
... ∞i (complex infinity) ? :)
Devendra S wooooooosh
I saw what you did there at 4:22 Numberphile
+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
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! =)
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
"I'm so rich, I can throw pennies around."
Great job Dr. Grime
One pence coins, not one cent coins.
I love this guy. - Am I alone?
+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! :)
I wish I had this man during Uni 😭 The amount of understanding that just occurred in just 15 mins
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.
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.
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.
I loved that demonstration of the fundamental theorem of calculus. Absolutely beautiful and simple and excellent!
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.
6:20 You can’t get an *_ABSOLUTE_* volume; but, assuming the heights are same for those 2 stacks, you can get a *_RELATIVE_* or *_COMPARATIVE_* volume (”Stack A > Stack B” / ”Stack A = Stack B” / ”Stack A < Stack B”). Actually, those 2 stacks of pennies *_DON’T_* have the same height: The straight cylinder has 19 pennies, while the jumbled-up cylinder has 16 pennies. I *_KNEW_* they weren’t quite the same.
The entire thing I was just waiting for the next time he says “area” he holds out the a and it’s awesome
Did any one noticed the picture that got mixed with Kepler's photo in 4:22 XD
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.
Smallest possible number that's still bigger than 0....
Just look at my exam results
Fair
Technoultimategaming at least yours are bigger than zero
Meanwhile me :
Laughing in negative 😂
Plank distance.
@@Enter_channel_name farts on your screen
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.
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.
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
+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.
"There's soomthing about it that makes you ooncoompfable!"
Love that accent :D
You even find infinitesimal spaces on graphs, for example the x and y axes on a graph of y = 1/x is in an infinitesimal space that doesn't intersect the curve at any point. If you moved them even slightly, they would intersect the curve but they don't.
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.
Honestly if it was explained to me this way, I would actually have understood what I was doing at uni
The opposite of infinity is finity. The end.
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?
Man this video still rocks the cerebrum after 5 years! Needed this refreshing thinking exercise.
Thank you for that knowledge, I gave never heard about hyperreals before.
I think I understand...
Is it:
infinitesimal = 1/∞
???
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
"...cos I'm so rich I can throw my pennies around."
Ahh taking quotes in 2019, amirite?
But if I throw my pennies around, I would get arrested.
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. . .
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.
Whenever im super tired or need sth to entertain my soul, i watch the clips of this channel. Thank you :-)
Infinity can't be rotated the opposite way... homever if you rotate it 90 degrees it will become 8.
damm.. mind blown. halarious tho
this dude just broke math
But a ninety degree rotation is multiplying by i
That is the way a lot of area/volume things are calculated for circular shapes. E.g. cutting a circle into really skinny isosceles triangles such that you can assume the curve is straight and the height is the radius, then laying them out in a line 2*pi*r long and using the triangle area formula to get 2*pi*r*r*1/2
Similarly for a sphere, you can use lots of tall skinny pyramids or cones pointing into the centre and using the 1/3 height x base area (which tots up to 4*pi*r^2) to get 4/3*pi*r^3
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.
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
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.
+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
In honor of John Conway, who invented surreal numbers, there is an inverse cardinal 1/omega which is smaller than every positive real number, yet not the smallest among cardinals. It uses Dedekind cuts and some partial order which goes beyond my imagination. But fascinating
Epsilon is used in programming for dealing with floating point numbers where (0.1+0.2)-0.3 does not equal 0 but the absolute value is less than epsilon. But be aware that floating point errors compound so you really want to avoid programs where a floating point number is modified where you want to know if it is almost an integer accurately, and never use it for currency always use an integer and then translate it to a presentational float (like 123 pence converted to £1.23 but that 1.23 is never operated on).
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
Who is the guy 4:21 with 39 on his back?
+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?
I was wondering about this earlier, thanks!
Thank you Fred Weasley, these videos are really interesting.
What the haha
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
+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."
7:00 unknowingly makes pi
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. :)
"Inifintesimal" is also a concept in calculus. Not diectly connected to real numbers, but to functions. A function is said to be an infinitesimal to another if the limit of their ratio is 0. Then you can also define to what order
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
So how does this change that old problem of: "Is 1 equal to 0.9999-repeating?"
If they are an infinitesimal apart then in the hyper-real system they are not equal?
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.
2 years later and I finally realize why the base of the triangle isn't infinitely long.
It has infinitesimals which is an infinite number of slices. Each slice can be sliced in two again, meaning you can never run out of slices, so why isn't the base infinitely long?
Well, every time you slice the slices, they'll be half the size, so the length of the base have not changed at all. Stacking two triangles with a base of 1 is the same as stacking one of length 2 or 4 of length 0.5, so it doesn't matter how many times you split it, the length will always be the same. So the length is the same, the height is always the radius and therefore the area will not be infinite.
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?
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.
I used to hate maths until I discovered your channel, thank you! ♥️
Before watching the entire video:
∞/1 = ∞
1/∞ = [opposite of ∞]
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
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
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
"1/0 is not infinity, we would never do that"
Me studying stability of transfer functions using final values: 👁️👄👁️
This guy has the brain of The Brain, but the voice of Pinky 😂😂😂 Narf!
Ahh the pinky and the brain.
Very famous cartoon here in India during early 2000s😇
Similar physical attributes as pinky also hahaaaa
*sees f(x)* *PTSD fires up*
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
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
Por favor podrías subir tus videos con subtitulo en español, se ve que tus clases son bien animadas y muy explicadas, gracias
Cantor's Diagonal Proof showed that there were always "wedged-in" values between any two Rational Number fractions, however small, to form the Real Numbers. Thus, the basics for this topic were there ever since he came up with that proof.