- Note that if $A, B$ sets s.t $|A| \leq |B|$ then there exists an injection $f: A \rightarrow B$.
Let $A$ be a set and suppose that there exists a proper subset of $A$, denoted $B$,
which satifies $ |A| \leq |B| $. Prove that $\mathbb{N} \leq A $.
So far I've noticed the fact that $B$ has to satisfy the same property as $A$. It smells like induction, since we can argue the same about $B$, and so on. However, I struggle to see how it's connected.
Thanks