Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Structure
Algebraic structure
Right identity element
Formulation 0
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 right identity element in $S$ if and only if \begin{equation} \forall \, x \in X : x y = x \end{equation}
Formulation 1
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 right identity element in $S$ if and only if \begin{equation} \forall \, x \in X : x + y = 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 right identity element in $S$ if and only if \begin{equation} \forall \, x \in X : f(x, y) = x \end{equation}