▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Structure
▾ Algebraic structure
▾ Identity element
Left inverse element
Formulation 0
Let $S = (X, +)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $0_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if \begin{equation} y + x = 0_S \end{equation}
Formulation 1
Let $S = (X, \times)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $1_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if \begin{equation} y x = 1_S \end{equation}
Formulation 2
Let $S = (X, f)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $I_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if \begin{equation} f(y, x) = I_S \end{equation}
Child definitions
» D525: Left inverse map