Binary Operation

definitionabstract-algebra

Definition

A binary operation on $X$ is a function $\sigma :X\times X\to X$.

For all $x,y\in X$, we have $\sigma (x,y)\in X$. We can denote $\sigma (x,y)$ as $x\ast y$.

Examples

1. Usual addition, subtraction, or multiplication on integers, rationals, or real numbers.
2. $\cup ,\cap ,\setminus$ are all binary operations on the power set of a set.