Possible Mistake in Hrbacek's "Introduction to Set Theory"

Question

In exercise $2.3$ on page $45$, the author writes:

$2.3$ Prove that there is a one to one mapping of $N$ onto a proper subset of $N$.

$N$ here denotes the set of all natural numbers. My question is, if you take any finite subset $A\subset N$, wouldn't that imply $N$ is finite as well ?

Answer 1

A proper subset need not necessarily be finite. For example, consider the proper subset $A=2\mathbb{N}=\{2n\mid n\in\mathbb{N}\}$. Can you find a one-to-one mapping from $\mathbb{N}$ onto $A$?