surjective function

let $\text{[math]}$ be a function
$\text{[math]}$ is surjective if for every $\text{[math]}$ there exists atleast a single $\text{[math]}$ such that $\text{[math]}$ , which means $\text{[math]}$

its cool to think of a surjective function as one whose image is "stretched out" to fit its range

a function $\text{[math]}$ is surjective if every element in $\text{[math]}$ comes from applying $\text{[math]}$ to some element in $\text{[math]}$ :
$\text{[math]}$ [cite:;taken from @tao_analysis_1 definition 3.3.20]