binary operation

let $\text{[math]}$ be a set, a binary operation on $\text{[math]}$ is a function that assigns each ordered pair of elements of $\text{[math]}$ an element of $\text{[math]}$ .
[cite:;from @abstract_gallian_2021 chapter 2 groups; definition binary operation]

a /binary operation on a set $\text{[math]}$ is a function mapping $\text{[math]}$ into $\text{[math]}$ .
[cite:;taken from @topology_munkres_2014 chapter 1 set theory and logic]