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.

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.

anonymous · Answer

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

anonymous · Answer

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