ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Definition D554
Binary operation
Formulation 0
Let $X$ be a D11: Set.
A D18: Map $f : Y \to Z$ is a binary operation on $X$ if and only if \begin{equation} Y = X \times X \end{equation}
Children
Enclosed binary operation
Idempotent binary operation
Conventions
Convention 0 (Multiplicative notation)
Let $X \neq \emptyset$ be a D11: Set and let $f : X \times X \to Y$ be a D554: Binary operation on $X$. If $x, y \in X$, then the convention in multiplicative notation is to denote the element $f(x, y)$ by $x y$.
Convention 1 (Additive notation)
Let $X \neq \emptyset$ be a D11: Set and let $f : X \times X \to Y$ be a D554: Binary operation on $X$. If $x, y \in X$, then the convention in additive notation is to denote the element $f(x, y)$ by $x + y$.