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@tylerthurman2366 Says:
I thought this video was pointless until the geometry point in the video and now I just realize im too stupid
@kulturfreund6631 Says:
Awesome. Thanks for another great episode.
@Stugga_LiveXfreak Says:
anybody want to make a video on why i watch so my hours of vidoes like this even tho i barley went to school,
@kindlethumper Says:
Isn't cantors creating a new number between 0 and 1 method flawed? Write those numbers in order. That will show that is your try and add "1" anywhere, meaning at any digit in the number, it will already be on the list.
If the list of numbers on his "list" is truly infinite then any number he can create is already there. This isn't debatable.
@eamonquinn5188 Says:
Why are we calculating with infinity? How can anything make sense if you use that within a calculation? Old fashioned non-scientist here, but conventually if a calculation ends up with infinity, it's nonsense, so shouldn't starting with it also be nonsense? Excuse me, I'm very tired.
@eric81757 Says:
I thought it was funny that I was able to guess you were going to randomly choose 37 simply because I just watched a video about how 37 is one of if not the most common numbers that people give when asked for a random number.
@taoistsimple9671 Says:
That number would actually be on his list of infinite real numbers, he just didn’t write out infinite numbers. Changing one digit wouldn’t matter when you already have every number. 5:24
@garcesjohan Says:
This was Ramanujan!!!!!!! Not Cantor, Cantor published his ideas, come on man. A little credability lost here
@behtashs Says:
The benefit of changing titles is that it makes you want to watch it again as you should
@TheGuyWhoAsked72 Says:
Infinity is an idea not a number. Infinity goes on for infinity infinitely fast. No infinity is bigger than another.
@Albertobelmonte9 Says:
I don't think my college professor understood me when I had a existential crisis on the matter.
@Doesitmatter0probnot Says:
At about 3:13, how is it that the square of 16 is 269 and not 256? 17^2 is 324 and not 289? I hate to be so particular, but I believe that most of us appreciate your videos and do not refer to the backup/supporting information. Therefore, something as simple as wrong squares starts to raise questions on validity of the story/main point...
@simoncurtis3779 Says:
Infinity is not a size or a number.
@AxleBolt-u9m Says:
Encoded Abundances
@CoenRegnier Says:
Is there a reason you can’t just order it by adding digits?
Start at
0, 0.1, 0.2, 0.3… 0.9
0.01, 0.02… 0.09, 0.11
Is the issue that there’s too much room for error or something, in not repeating the 0.10?
Edit*
I think I just talked myself out of that because you can just set the rule that the last digit can’t be 0?
I haven’t even finished the video, I’ll probably be back
Edit, edit*
I think I’ve decided I’m right and that mathematicians are just creating problems because their lives are too easy
@RebelScumNE Says:
I need to know what marker he’s using
@konstmonst Says:
Maybe there is no infinity, it is just an abstraction of a very big amount. And countable infinity is a discrete set and uncountable is something not discrete. And the second thing is also an abstraction because as far as I understand everything in the world is discrete on some level (if you zoom in enough). If you calculate with big numbers, like limits, then infinity is some arbitrary huge enough number for the purpose of calculation. I mean just like calculating with floating point numbers: if the number have similar order, you get very precise results, if not - you can discard the smaller operands or replace them with zero.
@AnEngagedNormie Says:
At 24:56 why is just adding back in that missing section? It kind of seems like an arbitrary move without any reason which makes the rest possible.
@CokeGoblin27 Says:
9:28 why does that guy look like Sheldon
@matthewdancz9152 Says:
The axom of choice on a sphere is not producing infinite spheres. It is producing infinite paths on one sphere. Which is how the real world works.
@gregsmachines8386 Says:
@3:12 if 19^2 =400 then anything is possible!
@gregsmachines8386 Says:
@3:12 if 19^2 =then anything is possible!
@I-AM-BETTER-THAN-YOU-ARE Says:
This is stupid
@jovisha69 Says:
27:49
"... and before you know it... you've got infinite balls."
That is a remarkable statement:) 😊
@karyemaitrealiffemd7241 Says:
So, the corollary postulate that naturally arises is~ "God had infinite balls, and this empowered him to create universes."
@lilyoda333 Says:
An infinity can hold and infinite amount of infinities 😊
@DaveBoatBuilder Says:
So, it appears that it's a nonsense to talk of adding an infinite number of points with no length to make a line segment, or adding an infinite number of points with no volume to make a volume.
@AungMinKhant-c4s Says:
Type shi I watch instead of studying
@paulkohl9267 Says:
33:00 Reductio ad absurdum, there is no axiom of choice.
@hardygunsalus9897 Says:
4:00 I’ve never really agreed with this in a practical way. I get what they are saying. But I think it’s just semantics. Never ending is never ending. So by that definition they are the same. But maybe for math there needs to be a semantic game played so they can communicate that it’s different infinities. But at the end of the day, infinity means going on forever, there is not one “greater” or “larger” than the other, only in semantics and jumble word salad (or in this case math salad).
@EricPhan-m9k Says:
That is why if you organized and make law so no one can do anything and the Pentagon is 5 side shape just like a human body had no head , no hand , no leg then human body is a Pentagon
@dsbarclayeng1 Says:
Mathameticians forget that math is simply a ''model'' that we have invented, a tool. That sometimes reflects the Universe and sometimes not.
@phexlink Says:
I don't know how you generate your cartoons for this video (AI??), but at least you could have made sure that the correct title of Cantor's publication (08:10) was used, esp. since you tried to emulate the setting of the title from the original publication from 1883 (that's the copy I have).
@thibaultsall1240 Says:
You should have mentioned Hardin-Taylor in this video, which imo is the most striking application of axiom of choice, namely that you can pretty much predict the future of any process outside of a countable subset of timestamps using only the observed past.
Also not mentioning that Cantor stole his diagonal proof from Dedekind is a bit...
@ig2d Says:
i start to lose the argument at 7:40 where you say that "there are other ways to well order the natural numbers". the problem i have here is that the first ordering is clearly countable - every finite natural number being clearly mapped to a finite integer - but in your second ordering none of the negative numbers will ever be reached because there are an infinite number of positive integers to be counted first.
In short the concept of a countable infinite set is easy to understand but the concept of a well ordered infinite set is for me problematic. Maybe the type of world i wish to live in is one where the axiom of choice doesnt hold
@-30h-work-week Says:
Ridiculous.
:-)
@Lovayn12 Says:
Remind s me of the movie Primer. Beyond my understanding but fun to watch
@Heybro1048kid Says:
Watching this a second time, I may be a socrates but I kinda feel like that its not those axioms that are wrong or ANY theory, I think its just how math is built, I mean so random history happend and some random dude from the past thought of numbers for money, then have vaule, but these vaules are still correct, later, where the hell did muiltplication come from? or somewhat kind of ∑, or some random symbols, this kinda makes the origin of math wrong, that means there aren't any infinent rules, that kinda means math is limited execpt we haven't reach the limit of discovery or whatever you call it. Which is breaking the world.
@James_Bowie Says:
I was lost after "There is a rule ..."
@Shalmaneser1 Says:
Want to frighten scientists? Show them something new. It's wierd: for people who want to find the unknown, they are oddly emotional whenever it happens. Maybe the problem is that they want to be the one.
@CafeMuyCaliente Says:
Not using the axiom of choice and proving all step by step in mathematics seems to be comparable to using the wave function in physics or looking at the particles. So the axiom of choice is something like a mathematical double slit, you can look in countable steps at the details but you don't have to. What you get is what you want.
@jimmyr545 Says:
22:30 I thought 0 times infinity was indeterminate, as in could be any number, so could be 2 for example.
@Youllhavethatyesyouwill Says:
Once again upon visiting Veritasium, mind blown...
@Cineres Says:
The real issue with infinities is that mathematicians for some inane reason seem obsessed with the absurd notion that infinity is a number at all. "How long is the set of all integers?" should be answered with "It has no length", rather than "Length of infinity". What we think of as infinity is a motion, not a number. The set of all integers with the set of all squares removed still contains infinitely many numbers. But you can keep counting both the integer set and the squares set for infinity.
Stop the madness. Stop thinking infinities are actual numbers in any way, shape or form. They are not.
@panshulhumad9638 Says:
7:34 how can the sets be the same size
I mean the natural numbers go as 1,2 ... and they CLEARLY don't include the negatives
Am i missing something here?
@edbehn3617 Says:
There's a mistake at 3:12. At 16 the squares go goofy.
@spazic1493 Says:
I'm not going to claim I know anything more than the genuises working on these proofs, but I would like to know how mathematicians say it's not possible to duplicate a shape, as that seems to imply superposition reasoning, and would really suggest that more of our reality is in a super position than just the quantum-applicable conjecture?
So, is our reality really mirrored in overlap, and we can only measure part of it?
@LL3L. Says:
Obviously either Cantor was rich and didn't need a job or he had a lot of time being unemployed...
@wassollderscheiss33 Says:
You actually appear dumb from drugs. But I may be mistaken.
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