Successor function ($S$)

In mathematics, particularly in the context of set theory and number theory, the successor function is used to define the concept of "next" numbers in a sequence. For natural numbers, the successor function takes a natural number \( n \) and gives the next natural number \( n + 1 \). For example: - If \( n = 0 \), then the successor of \( n \) (often denoted as \( S(n) \)) is 1.