Question 54
Let $n$ be a strictly positive integer and let $A = \{1, 2, \dots, n\}$. Find the number of the increasing functions $f : A \to A$ which satisfy the property
$$
|f(x) - f(y)| \le |x - y|,
$$
for any $x, y \in A$.
$$
|f(x) - f(y)| \le |x - y|,
$$
for any $x, y \in A$.