Addition

Addition is an elementary binary operation, written \(a + b\) (pronounced "\(a\) plus \(b\)"). It can be informally defined as the total number of objects when \(a\) objects are combined with \(b\) more. Formally, it means the cardinality of a set formed by the union of two disjoint sets with cardinalities \(a\) and \(b\). \(a\) and \(b\) are called the summands, and \(a + b\) is called the sum.

Addition is : \(a + b = b + a\) for all values of \(a\) and \(b\). It is also, meaning that \((a + b) + c = a + (b + c)\). Repeated addition is called multiplication.

\(0 + n = n\)

In the fast-growing hierarchy, addition grows faster than \(f_0(n)\).

It is the first hyper operator, and forms the basis of all following hyper operators.