A <function> where the <domain (function)> is the same as the <codomain>.


Endofunction

{wiki}

= Injection
{synonym}

= Injective
{synonym}

Mnemonic: in means into. So we are going into a <codomain> that is large enough so that we can have a different image for every input.


Injective function

{wiki}

= Surjection
{synonym}

= Surjective
{synonym}

Mnemonic: sur means over. So we are going over the <codomain>, and covering it entirely.


Surjective function

{wiki}

Vs: <image (mathematics)>: the codomain is the set that the function might reach.

The <image (mathematics)> is the exact set that it actually reaches.

E.g. the function:
$$
f(x) = x^2
$$
could have:
* codomain $\R$
* image $\R_{+}$

Note that the definition of the codomain is somewhat arbitrary, e.g. $x^2$ could as well technically have codomain:
$$
\R \bigcup \R^2
$$
even though it will obviously never reach any value in $\R^2$.

The exact image is in general therefore harder to characterize.


Ciro Santilli @cirosantilli 37

 Incoming links: Codomain