Definition:Inverse Mapping/Also defined as
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Definition
Let $S$ and $T$ be sets.
Let $f: S \to T$ be an injection.
Then its inverse mapping is the mapping $g$ such that:
Thus $f$ is seen to be a surjection by tacit use of Restriction of Mapping to Image is Surjection.
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Also see
- Results about inverse mappings can be found here.
Sources
- 1999: András Hajnal and Peter Hamburger: Set Theory ... (previous) ... (next): $1$. Notation, Conventions: $10$