Surjection/Definition

Given a function $f:X\rightarrow Y$, we say $f$ is surjective if:

• $$\forall y\in Y\exists x\in X[f(x)=y]$$
• Equivalently $$\forall y\in Y$$ the set $$f^{-1}(y)$$ is non-empty. That is $$f^{-1}(y)\ne\emptyset$$