4 ms·
Nothing surprising here. The cross products of countable set are countable and a bijection between N and NxN which you can then extend as been known for ages.
by WastingMyTime89 3y ago
Nothing surprising here.
The cross products of countable set are countable and a bijection between N and NxN which you can then extend as been known for ages.
The whole thing falls apart as soon as you use continuous set.
- chr1 3y agoThe cross product of continuum sets is also equivalent to a continuum, so it does not fall apart, it forms a space-filling curve on complex plane. See z-curve section of https://en.m.wikipedia.org/wiki/Quater-imaginary_base https://en.m.wikipedia.org/wiki/Quater-imaginary_base
- WastingMyTime89 3y agoYou learn something everyday. For whatever reason I was convinced there was no bijection between R and its cross-products which is extremely wrong.
- rocqua 3y agoIt is quite surprising to most people when they first learn that there are more real numbers than there are integers, but there are just as many pairs of integers as there are integers. In other words, infinity*infinity=infinity whilst 2^infinity>infinity The proofs are pretty easy, but that doesn't make the result less surprising to people who don't know it yet.