Definition:Set of All Mappings
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Definition
Let $S$ and $T$ be sets.
The set of (all) mappings from $S$ to $T$ is:
- $T^S := \left\{{f: S \to T: f \ \text{is a mapping}}\right\}$
Also known as
It is sometimes unwieldy to write $T^S$; particularly when $T$ and/or $S$ have themselves superscripts or subscripts attached.
In these cases, it is convenient to write $\left[{S \to T}\right]$ for the set of mappings from $S$ to $T$.
Also see
Sources
- Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 8$: Functions
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 1$
