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@exploiter_ Says:
new intro?
@TechniclyTapri Says:
2:46 Holly rip off of tralaleo tralala😭🥀✌️
@Jason-qy4rt Says:
Nah, imaginary numbers like -1 have a positive quantity, your adding -1 to an equation. So the smallest number would be 0, but the next bigger number would be both its positive and imaginary counterpart, canceling eachother out, so the 2nd smallest number is also 0.
@panther105 Says:
What was that weird idea going around about a decade ago (maybe older) that showed measurable (just barely) ability of the human brain to affect a computer random number generator?
@AnonymousCaller-f1f Says:
The curse of 37 follows us everywhere
@leethompson6070 Says:
In the physical world (machinists) you have to have a designated point of acceptance or stopping otherwise you would never get anything accomplished or built…all these extra things aren’t what the real world are built out of…all these conjectures are waisting time of operation and getting stuff to where it needs to go.
@kaushikneeladri Says:
Each time I start a new veritasium video, I feel I'm probably gonna get this. Somewhere along the way I am lost and I build my hope I'll get the next one perhaps.
@SJohnTrombley Says:
People often describe axioms as assumptions, but I prefer the interpretation where they're properties of all objects in the domain of discourse. So instead of "we assume sets have these properties" it's "a set is precisely any object that has these properties."
@DePhoegonIsle Says:
Ehhh.... all I take from this is 'The axiom of choices' is little more than thought wanking, requiring any implementation of it to require extreme amounts of energy to produce such things.
At what point does it really matter? All you've proven is that you've taken logical traces, measurements of a thing, and reproduced it. Maybe the entire point of transporters, but at that point... Axiom of choice, or extreme LOD at such levels that the distinction doesn't matter. Where the logistics are literally 'priming scanning' and the extreme energy it'd take to 'make a copy' is on the literal magnitudes of where the easiest source is the scanned target, and would bring into question more variables & data storage/processing than is ever manageable with anything even closely related to what we know, even at the higher near theory crafted end.
Like, even the thought experiments assume sheer perfection to a degree that REALLY is impossible, or that it is nothing more than copying something with raw energy as the thing mimicking a physical template. >.>
They need a term for those who math wank to this level where the point is entirely missed and the abuse of 'uncountable' really needs to stop >.> sure 'unknowable' to a point that is meaningless is a thing, but ... up it's own **s if you know what I mean.
It's like a Cicle saying to a sphere, 'You literally can't understand how many points I have' ... Like ... Brother .. you're nothing but a theory crafted item existing in a dimensional reality that includes infinately more points than your pressious little existance could even grasp, and at some point you reach the 'It really doesn't bloody matter, and the practical difference to any affect is nothing, or if at all a story told around you meant to wank the tellers off rather than make any point worth making.
- It'd be like telling a computer you spent more money on a part that was 2-10x more for something that is electrically identical, to remain cooler.... in a space where it never went above 40- 60 °C anyway, for a part rated for 80-90'c constant lifetime use.
@rotorblade9508 Says:
omega numbers is like saying after the natural numbers set it comes the Real numbers set by definition.
@rotorblade9508 Says:
to me almost everything looks like a mess
I understand limits to ∞ , for example 1/x with x->∞ tends to +0
but I cannot say there are more R than N numbers. R simply has let’s say a higher resolution
you can get into trouble with infinitesimals but you just follow some intuitive rules or do some tricks to fix it
@BrentBayl33tspock-z1c Says:
Here I thought we'd be contesting the idea of 0
@MrXsnuff Says:
so if your things dont work out, make up a rule to make it work
@UnpromptedGenocide Says:
Good video, but the AoC section implies that indexing an uncountable set is the same as indexing the integers which is untrue. It is a fundamentally different map.
@devongrey4135 Says:
"They run an algorithm on your current local time... " WRONG.
@niety5914 Says:
0:38 ‘37’ you say? 👀
@geeshta Says:
6:47 noooo the starting point if natural numbers is 0 😭
@bobbun9630 Says:
"Computers can't generate random numbers". Often said, but a rather suspect claim. You could certainly build a component for a computer that senses random inputs from the environment, such as decays from a radioactive source, and the computer then uses that input to generate a random stream of output. I think what's meant is that a deterministic process (not a computer) can't generate random numbers. So an idealized computer like a Turing machine can't generate random output, but a practical realization of a computer built with actual hardware should be able to do so if designed with that capability in mind.
@G70P Says:
Yep, Axioms are reliable if proven of choice equals Konstant
@ReyanshsAccount-pm1ln Says:
5:03 I suppose this process can be repeated infinitely to create an infinite amount of numbers by also applying the same thing on the final digit of the new number formed
@LostShot1238 Says:
at 3:10 the square numbers are all wrong after 225
@scottscotty1660 Says:
This all seems like mathematical masturbation. What is the practical use of any of this in the real world?
@heart.9889 Says:
I have a master in mathematics and I knew about all the underlying theory but little about the people involved except their names (since theorems etc are often named after them) so let me tell you at 10:45 I gasped a gasp and got excited bc I realized what must happen next 😂 this video made me very happy, thank you
@ReubenKoki-Kaweesa-xb7td Says:
me rewatching my 1st ever veritasium video
@R_Y_Z_E_N Says:
I used axiom of choice to select this video from my feed , seems like I was right
@angelstrawn5493 Says:
The diagonalization proof has a great flaw that seems to defy identification. When a comprehensive list of the real numbers is set next to the natural numbers, the list will include the diagonalized number, by definition. If you list every real number, how can it be that one was not included? Just look at that number. It isn't special. The way to construct the reals is the critical step. You have to start with the smallest and proceed to the largest. If you randomly input the numbers, the chance of missing one is assured, which is how the proof is constructed.
@BogdanTudor-h5b Says:
Just in case anyone is curious, I'm not contradicting Cantor. I don't have to. He contradicted himself.
@BogdanTudor-h5b Says:
I've always admired your videos, but what if a non-mathematician (from the 21st century) tells you Cantor's set theory is fundamentally flawed and consequestly FALSE? By the way, I'm not just saying that; I can also prove it.
@erikolsen1333 Says:
Dededikin cut 3:55
@erikolsen1333 Says:
Epsilon 2:05
@erikolsen1333 Says:
0:34 the AC, axiom of choice
@anonymous5573 Says:
I always watch this video when I am unable to sleep and zzzzzzzz........
@jwmarquez Says:
3:11 16 squared doesn't equal 269.
@mathexplainedreal Says:
a sphere with no lengths??
@Sam-b9c4s Says:
For the smallest number after 1, I would pick 2-.9repeating
@W1nterS0ldierE Says:
Question. If you’re randomly choosing from what point to cut the sphere from each time, doesn’t matter being mostly empty space influence something about this in some way?
@nofriendsgg Says:
Please explain what I'm missing here. According to Cantor's diagonalization proof, as presented in this video, a set is considered larger than the set of natural numbers if, having mapped each natural number one-to-one with a member of that set, a unique as-yet unmapped member can be identified. That is, constructing a new real number using the diagonalization procedure proves that there are more real numbers than there are natural numbers.
Well, let's map each natural number to the set of even numbers {2, 4, 6, 8, ...} - this is trivial to do: simply map each natural number to the even number that is double its value, i.e. 1 --> 2; 2 --> 4, 3 --> 6, 4 --> 8 etc. Thus the set of even numbers is the same size as the set of natural numbers. However, now take the set of even numbers and for each member, append to the set its value subtract one. We have now added to that set a series of values that weren't already in that set, and therefore weren't already mapped to the natural numbers: {1, 3, 5, 7,...}, and have therefore increased the size of the set, following the same logic as the diagonalization proof.
However, this set, which is supposedly larger than the set of natural numbers, contains the same values as the set of natural numbers {1, 2, 3, 4, ...}. Therefore the set of natural numbers is larger than itself. What gives?
@jessysavard2133 Says:
i have an other theory watch this. infinity is infinity , if its to hard for people to wrap there head around that then find an other world in that monkey language that english, sorry tto be rude i wanted to be clear , there not more possibility between 0 & 1 and between 1 and infinity if you keep adding digit... com on now those mathematicien lost it in the process that just ragebait at this point and it work jesus christ
@Cloudscape Says:
Thanks, I don’t think my brain works anymore
@djreaves13 Says:
lim n->0+ n
take that
@blokmuscle Says:
Oh you don’t think I have enough infinity? To infinity and beyond bro. Double infinity.
@Nairolf.182 Says:
0:33 "I can plug random numbers from my head" also him literally the next moment "37"
@haddonsdad1829 Says:
You're smart by 3/4
@ardanmichaelblum Says:
❤❤❤❤❤❤❤❤❤❤❤❤
@rraiderr17395 Says:
Choosing 37 or 42 as the ,,random numbers,, was a nice touch.
@josephsummer777 Says:
Everyone always chooses 37.
@bladefearawksttm Says:
And in our generation the only infinity we care about is the infinity war
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