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.

In googology, it is the first hyper operator, and forms the basis of all following hyper operators.

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

Zero is the additive identity, meaning that \(0 + n = n\) for all \(n\).

In other notations Edit

Notation Representation
Up-arrow notation \(a \uparrow^{-1} b\)
Fast-growing hierarchy \(f_0^b(a)\)
Hardy hierarchy \(H_{b}(a)\)
Slow-growing hierarchy \(g_{\omega+b}(a)\)

See also Edit