Definition:Strictly Progressing Mapping/Definition 1
Jump to navigation
Jump to search
Definition
Let $g$ be a class mapping.
$g$ is a strictly progressing mapping if and only if:
- $\forall x \in \Dom g: x \subsetneqq \map g x$
That is, if $x$ is a proper subset of its image under $g$ for all $x$.
Also see
- Results about strictly progressing mappings can be found here.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 2$ Superinduction and double superinduction