What is successor property?

The successor property refers to a fundamental concept in mathematics, particularly in set theory and number theory, where every element in a well-ordered set has a unique successor. This means that for any given element, there exists another element that directly follows it in a specified order. In the context of natural numbers, for example, the successor of a number ( n ) is ( n + 1 ). This property is essential for defining sequences and can be instrumental in proofs and mathematical induction.