Definition:Inflationary Mapping

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

Let $\phi: S \to S$ be a mapping.

Then $\phi$ is inflationary iff:


 * $\forall s \in S: s \preceq \phi \left({s}\right)$

Also known as
An inflationary mapping can also be called progressive or progressing.