A binary operation is a mathematical operation that combines two elements from a set to produce another element from the same set. Common examples of binary operations include addition, subtraction, multiplication, and division. These operations take two inputs, often referred to as operands, and apply a specific rule to generate a result. In formal terms, a binary operation on a set S is a function that maps pairs of elements from S to a single element in S. For instance, in the set of integers Z, the operation of addition takes two integers and returns their sum, which is also an integer.