I have problem with one-to-one correspondance
"One-to-one correspondence with the set (B) of all tags possible being represented with their binary representation (i.e. 0, 01, 00, 010101, 11000, 01010, 11 etc.) and the set of natural numbers. Prove that this is impossible."
It looks to me this is possible. Because I can make a bijaction btw N and B exept 1 condition. For 1 there are 2^1 tags in B. {0,1} For 2 there are 2^2 tags in B. {00,01,10,11} and it goes on ..
Could you help me with this problem?