Definition of Binary Operation
When an operation, such as addition or multiplication is performed on a set, two elements in the set combine to form a third element. Since two elements combine, such an operation is called a binary operation.

If we denote the operation with an asterisk (∗) we can use the following symbolic notation to describe its behavior in a set, S:

x,y ∈ S: x ∗ y = z, where z ∈ S

Common arithmetic operations like addition and multiplication of real numbers are examples of binary operations.

We can also perform binary operations on finite sets and display the result in a table. For example, consider a set S = {0,1,2,3,4}. with binary operation (+) to denote modular addition.