Question 32
a) Let $A$ be a finite, nonempty set and $f: A \rightarrow A$ an injective function. Show that $f$ is surjective.
b) Let $f: \{1,2,3, \ldots, 63\} \rightarrow \{1,2,3, \ldots, 63\}$ be a function such that $f(1)+f(2)+f(3)+\cdots+f(63)-1=2016$. Show that $f$ is not injective.
b) Let $f: \{1,2,3, \ldots, 63\} \rightarrow \{1,2,3, \ldots, 63\}$ be a function such that $f(1)+f(2)+f(3)+\cdots+f(63)-1=2016$. Show that $f$ is not injective.