Comment by Entangled

> The cardinality of the rationals is the same as the integers.

If you combine N as all possible numerators with N as denominators you get that cardinality of Q = N * N

Also, I don't accept the diagonal argument as proof. Given all possible combinations of numbers, any given number will occur in that set no matter what. If you add special rules of course it falls apart and Cantor's argument is just a special rule.

If we use fruits as an example, taking a diagonal from their letters won't form a fruit either.

    1. [A]PPLE
    2. O[R]ANGE
    3. MA[N]GO
    4. CHE[R]RY
    :
    N. ARNR ?