The Number of Integers between Two Integers

In the setting of The Integers and the Rational Numbers, with the Natural Numbers and the Integers Identified with Subsets of the Rationals, let $a,b\in\mathbb{Z}$ with $a\le b$.

¶ $b-a+1\in\mathbb{N}$, and the set $\{x\in\mathbb{Z}:a\le x\le b\}$ is finite with number of elements $\#\{x\in\mathbb{Z}:a\le x\le b\}=b-a+1$.