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