Inverse Element

Inverse Element

The inverse element of an element x from a set E for an operation ⊕ defined on E is the element x‘ of E such that x ⊕ x‘ = n where n ∈ E is the identity element for the operation ⊕.

Examples

• The additive inverse of x for addition in $$\mathbb{R}$$ is the inverse element of x for this operation
• The inverse of x for multiplication in $$\mathbb{R}$$ is the inverse element of x for this operation.
• The reciprocal relationship $$f^{-1}$$ of a function $$f$$ defined in $$\mathbb{R}$$ is the inverse element of $$f$$ for the composition of functions, since $$f^{-1}\space ο\space f = I_{\mathbb{R}}$$, where $$I_{\mathbb{R}}$$ is the identity relation on $$\mathbb{R}$$.