> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/260-function-theory/topics/division-of-functions.md).

# Division of functions

All properties of functions

* wrt relations
  * functional relation
  * relations that are left-unique and right-serial
  * Fn ⊆ Rel ⊆ Dom⨯Cod (elements are ordered pairs)
  * a rel R: xRy ≡ (x,y) ∈ R, R = {(x,y) | x ∈ A ∧ y ∈ B}
* by involved sets
  * domain
    * preimage
  * codomain
    * range
    * image
* by injectivity
  * (a relation ↓)
  * (a function ↓)
  * surjection  ↓ onto
  * injection   ↓ one-to-one
  * bijection   ↓ one-to-one correspondence
* by totality
  * total functions
  * partial functions