The Alexander Sphere

i dont mean to sound crude or stupid but wat the hell is this!?

i can do that with my fingers

finite volume, with infinite surface area? I don't understand the implications of what you've just said, but its very intriguing.

I'm a greduate mathematics student currently taking a topology course. We haven't looked at anything like this, and the semester is almost finished. I wish that we did investigate things like this. Only point-set.

boring

beautiful and obvious!! 5 stars!!!

awsome idea

is this the most unbreakable shit in the universe?

I guess so xD

the main issue is that theoretically you should both be able to get smaller and smaller, but also have a smallest distance. if you accept the concept of the planck length, then technically you would eventually be unable to tell whether or not they are touching because they would shrink to such a small size that it would be impossible to know if they even exist. there is no real life vs. theory because real life expectations are in themselves purely theoretical.