Successors

A successor refers to a person or thing that follows another in time, order, sequence, or hierarchy. A successor may inherit a title, office, property, or responsibilities, or simply occupy the next position in a chain of events. The term is paired with predecessor, the one who comes before.

In mathematics and logic, the successor of a number is the next number in the natural-number sequence, typically S(n) = n + 1. In order theory, the successor of an element x is the least element greater than x; in ordinal arithmetic, the successor of an ordinal α is α + 1.

In law and politics, succession governs who assumes authority, title, or estate after a vacancy. Line of succession lists the ranked individuals eligible to succeed, with rules often based on inheritance, proximity of relation, or appointment. Some jurisdictions have formal succession laws and constitutional provisions governing monarchy, presidency, or office.

In business and organizations, succession planning identifies potential successors for critical roles and prepares them to assume responsibilities, reducing disruption during transitions. This may involve training, mentorship, and staged elevation.

In computing and information science, an edge or transition from one state to another is described as a successor relation in automata and state machines; in data structures, the successor of a node is the next node in a sequence.