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.
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.
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.