I just wanted to know what's wrong in the following argument:
Say I take a number and rewrite as a binary. e.g 155 = 10011011
Then I can relate the number with a subset of N, which contains the exponents of 2 where the 1's appear in binary form.
So
$155 = 2^0 + 2^1 + 2^3 + 2^4 + 2^7 \Rightarrow \{0,1,3,4,7\}$
$64 = 2^6 \Rightarrow \{6\}$
$122 = 2^4 + 2^5 + 2^6 \Rightarrow \{4,5,6\}$
$0 \Rightarrow \{\} $
Now since every number has unique binary decomposition, and the map is a surjection, it is a bijection between the power set of N and N...