Successor function

For other uses, see Successor.

In mathematics, the successor function or successor operation is a primitive recursive function defined by

$S(n)=n+1. \,$

We have S(1) = 1 + 1 = 2, S(S(1)) = 2 + 1 = 3, ...

The successor function is used in the Peano axioms which define the natural numbers.

It is also one of the primitive functions used in the characterization of computability by recursive functions.

See also

• successor ordinal
• successor cardinal
• Increment