Question

Can I get help with one to one correspondence for the following? {4,8,12,16,...} and {...1/4,1/3,1/2,1,2,3,4,...} ? Thank you.

Answer 1

First of all, we know that this is possible since \(\mathbb{Q}\) is countable.

Answer 2

yeah i just forget the formula to go from one to the other. i know the diagnonal bit, but i think there is some piecewise thing you write to go form natural numbers to fractions.
whatever it is all you do is divide by four first, so that is not a big deal