Difference between revisions of "Function"

Revision as of 19:57, 28 February 2015

A function $f$ is a special kind of relation

Domain

A function ought be defined for everything in its domain, that's for every point in the domain the function maps the point to something.

Examples

(See domain below first if you do not know what the domain is)

• $$f:\mathbb{R}\rightarrow\mathbb{R}$$ given by $$f(x)=\frac{1}{x}$$ isn't defined at $$0$$
• $$f:\mathbb{R}\rightarrow\mathbb{R}$$ given by $$f(x)=x^2$$ is correct, it is not surjective though, because nothing maps onto the negative numbers, however $$f:\mathbb{R}\rightarrow\mathbb{R}_{\ge 0}$$ with $$f(x)=x^2$$ is a surjection. It is not an injective function as only $$0$$ maps to one point.

Notation

A function $f$ from a domain $X$ to a set $Y$ is denoted $f:X\rightarrow Y$

TODO: Come back after the relation page and fill this out