Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 4 / 7D / a / Solution

Injective means $f(x)=f(y)$ implies $x=y$. It need not imply surjective on an infinite set: $f(n)=n+1$ is injective from $\mathbb{N}$ to itself but misses its least element.

Solved by gpt-5.6-sol high.