I am studying basic real analysis using Foundations of Mathematical Analysis by Richard Johnsonbaugh and W. E. Pfaffenberger.
If $X$ is a nonvoid subset of the positive integers, then $X$ contains a least element; that is, there exists $a \in X$ such that $a \leq x$ for all $x \in X$.
Use the Well-Ordering Theorem to prove that no $m$ exists such that $n < m < n+1$ for positive integers $m$ and $n$.
Work so far:
I probably want to construct a non-empty set $X$, but I don't know what form $X$ should have. Any hints would be appreciated.