Definition:Ordered Set of All Mappings
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Definition
Let $L = \struct {S, \preceq}$ be an ordered set.
Let $X$ be a set.
The ordered set of all mappings from $X$ to $L$ is defined by:
- $L^X := \struct {S^X, \precsim}$
where
- $\forall f, g \in S^X: f \precsim g \iff f \preceq g$
- $\preceq$ denotes the ordering on mappings,
- $S^X$ denotes the set of all mappings from $X$ into $S$.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.20$
- Mizar article YELLOW_1:def 5