The successor function is a mathematical concept used primarily in set theory and number theory. It defines the next number in a sequence, typically represented as S(n) , where n is a natural number. For example, the successor of 3 is 4, indicating that 4 follows 3 in the natural number sequence. In formal systems like Peano axioms, the successor function is essential for defining natural numbers. It helps establish the properties of numbers, such as addition and ordering. The function ensures that every natural number has a unique successor, which is fundamental for constructing the set of natural numbers.