# Definition:Filter/Proper Filter

## Definition

Let $\left({S, \preccurlyeq}\right)$ be an ordered set.

Let $\mathcal F$ be a filter on $\left({S, \preccurlyeq}\right)$.

Then $\mathcal F$ is a proper filter on $S$ if and only if $\mathcal F \ne S$.

That is, if and only if $\mathcal F$ is a proper subset of $S$.

## Also see

• Results about filters can be found here.