Inverse
When an operation ‡ is defined in a set E, the inverse of a non-zero element x of E is an element denoted by [latex]n^{-1}[/latex], such that n ‡ [latex]n^{-1}[/latex] = 1.
Example
- The inverse of [latex]\dfrac{4}{9}[/latex] is [latex]\dfrac{9}{4}[/latex], since [latex]\dfrac{4}{9}\space × \space\dfrac{9}{4}\space = \space 1[/latex].
- Consider the set E = {a, b, c} and the union set operation denoted by [latex]\bigcup [/latex]. We have {a, b} [latex]\bigcup[/latex] {a, b}’ = E, where E is the identity element for the operation of union.