ThmDex – An index of mathematical definitions, results, and conjectures.

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▼	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

▶	D20: Enclosed binary operation
▶	D5319: 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 $x + y$ .