Category:Inverses of Mappings
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This category contains results about Inverses of Mappings.
Definitions specific to this category can be found in Definitions/Inverses of Mappings.
Let $f: S \to T$ be a mapping.
The inverse of $f$ is its inverse relation, defined as:
- $f^{-1} := \set {\tuple {t, s}: \map f s = t}$
That is:
- $f^{-1} := \set {\tuple {t, s}: \tuple {s, t} \in f}$
That is, $f^{-1} \subseteq T \times S$ is the relation which satisfies:
- $\forall s \in S: \forall t \in T: \tuple {t, s} \in f^{-1} \iff \tuple {s, t} \in f$
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