Definition:Proper Extension of Mapping
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Definition
Let $f$ and $g$ be mappings such that:
- $g$ is an extension of $f$
- $f \ne g$
That is:
- $f \subsetneqq g$
Then $g$ is a proper extension of $f$.
Also see
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $6$: Order Isomorphism and Transfinite Recursion: $\S 1$ A few preliminaries