Injective function

Let $f\colon A\to B$ be a function . Then $f$ is injective (or one-to-one) if

Injectivity means distinct inputs never collide under $f$. Equivalently, each element of the image has at most one preimage .

Examples:

• The inclusion map $\iota\colon\{1,2\}\to\{1,2,3\}$ is injective.
• The function $f\colon\mathbb{Z}\to\mathbb{Z}$ given by $f(n)=2n$ is injective.
• The function $g\colon\mathbb{R}\to\mathbb{R}$ given by $g(x)=x^2$ is not injective since $g(1)=g(-1)$.