A Finite Set of Real Numbers Has Exactly One Increasing Listing

In the setting of The Real Line: Standing Notation and Background for Calculus on Intervals, let $N\in\mathbb{N}_{0}$, let $[N]$ be as in Intervals of Natural Numbers (ii), and let $A$ be a subset of $\mathbb{R}$ such that there is a bijection from $[N]$ onto $A$; thus $A$ is finite.

(i) There is exactly one bijection $x:[N]\to A$ such that $x(i)<x(j)$ for all $i,j\in[N]$ with $i<j$.