Things get weird at infinity

I just learned so much, and nothing at the same time

"Could you store every single picture?" No, the FBI would lock you up for life.

zach star is like the substitute teacher you'd have for a class taught by vsauce

"What happens at infinity?" Well this explanation's going to take forever...

“Size matters... That’s right” I think this is the best thing ever

Is there a general pattern for an "infinity paradox generator"? 1. Take infinity which is NOT A NUMBER. 2. Put infinity into a mathematical expression where it is treated as a number. 3. ???? 4. PARADOX!!!

"Here's a question you didn't ask!" I already knew this was going to be a good one

Zack Star: SIZE MATTERS Also Zack Star: 1 is the same size as infinity. my wife: 😒

That [0,1) question was in my real analysis class but I never understood the thought process of it so I ended up just memorizing the answer. Only now do I understand how to actually do it

Associative property: exists Infinity: We don't do that here

Zach Star is by far the best creator for math content! I love how his videos are so clear and concise, and how there is such a wide range of topics that he covers.

“Take whatever numbers you want, add or subtract them forever, math happens different. Weird.”

Cool. That's understandable. Have a nice day

(-inf,inf) and (0,1) Zach: they are the same picture

13:25 This reminded me of Hilbert's Infinite Hotel. There you have a hotel with an infinite no. of rooms and every time a guest comes, you make them go to an occupied room. It's occupant is shifted to another room and so on, forever. Here we map 0 to 1/2, 1/2 to 1/4, and so on... . Every 1 / 2^n to 1/ 2^(n+1). The remaining numbers map to themselves. Pretty cool solution actually.

I have watched so many videos on YouTube which concern themselves with explaining novel concepts in math. I mean everything I can find, from Numberphile to Mathologer to 3 Blue 1 Brown to lectures from university courses at Yale and Stanford to podcasts and interviews with mathematicians and popular STEM educators like Neil Degrasse Tyson and VSauce and Veritasium to presentations at institutions like the Royal Institute and on and on and on.... Yet I find that I grasp concepts and model them in my mind's eye much better after you present them to me. From glimpsing four spatial demonsions for the first time after your demonstration of how a Klein bottle can be made from a cylinder to seeing exactly how conditional convergence can be maniuulated to produce counterintuitive sums, you are so much better at explaining these things than anyone else I have found.

"Can you store every image that was ever created on your computer?" Depends on the compression level

I think it would be helpful to clarify that these rules and definitions for how infinities work are chosen, not discovered. We could define infinity sizes in different ways, for example. Not that these definitions were chosen without reason, mind you; they were chosen because they are useful. Still, I think the, uh, artificial nature of Infinities is worth pointing out.

Interesting. Infinity sure is an interesting concept. I truly wonder if we will ever have the means of achieving such one day. Awesome work!

i loved the moment when i first understood this in math classes. nostalgia