Question

Explain why the union of two countably infinite sets with nothing in common is also countably infinite.

I said that it was because the two sets are in one-to-one correspondence with each other. Is this right?

Answer 1

yes,

e.g. there are just as many even whole numbers, as are whole numbers
1-2
2-4
3-6
...
58978 - 117956
...
..

a 1-1 correspondence
for every whole number I can find a matching even number, and for every even number I can find a unique whole number.