Predicate to prove a set is countably infinite Hi I have this question and have been struggling to find an answer.


  Prove that the set of numbers which are powers of 2 (i.e. $\{1, 2, 4, 8, 16, 32, \ldots\}$) is a countably infinite set.


Not sure if I've been over thinking it but I've been trying it for the last week and haven't got anywhere with it.
Hint: $f:\mathbb N \rightarrow A, f(n)=2^n$ is a bijection, where $A=\{1,2,4,8,..\}$

Assuming $\mathbb N$ contains zero.
This question has two parts: 


Is the set infinite?
Is the set countable?


Number 1. you can do by contradiction, much like how Euclid proved that there are infinitely many primes. For 2., the definition of countable is that there exists a one-to-one function from your set to the integers. Inclusion is such a function in this case.