Category:Examples of Inverses of Subsets
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This category contains examples of Inverse of Subset.
Monoid
Let $\struct {S, \circ}$ be a monoid whose identity is $e_S$.
Let $C \subseteq S$ be the set of cancellable elements of $S$.
Let $X \subseteq C$.
Then the inverse of the subset $X$ is defined as:
- $X^{-1} = \set {y \in S: \exists x \in X: x \circ y = e_S}$
That is, it is the set of all the inverses of all the elements of $X$.
Group
Let $\struct {G, \circ}$ be a group.
Let $X \subseteq G$.
Then the inverse of the subset $X$ is defined as:
- $X^{-1} = \set {x \in G: x^{-1} \in X}$
or equivalently:
- $X^{-1} = \set {x^{-1}: x \in X}$
Pages in category "Examples of Inverses of Subsets"
The following 2 pages are in this category, out of 2 total.