Surjective function

Let $f\colon A\to B$ be a function . Then $f$ is surjective (or onto) if

Surjectivity is the statement that the image of the whole domain equals the codomain : $f(A)=B$.

Examples:

• $f\colon\mathbb{R}\to[0,\infty)$ given by $f(x)=x^2$ is surjective.
• The projection $\pi\colon\mathbb{R}^2\to\mathbb{R}$, $\pi(x,y)=x$, is surjective.
• The exponential map $\exp\colon\mathbb{R}\to\mathbb{R}$ is not surjective (no negative values occur).