While reading the section on countability from Ralph Boa's book 'A Primer on real functions', I came across this sentence 'While those sets cannot be counted can be thought of 'bigger' than those that can be counted. This made me wonder if the following is true 'For any countable set A and an u countable set B, does there exist an injection from A to B?
Now my above conjecture obviously reduces to commenting on existence of injection from $\mathbb{N}$ to $B$(as defined above ), as any countable set has a bijection with the set of natural numbers . Now I am unable to proceed. Please help.Thanks.