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succ

Denotes a strict successor relationship in mathematics, indicating that one element follows another in a given ordering.

Overview

Essential in mathematical logic, set theory, and order theory for expressing relationships between elements in ordered sets.

  • Commonly used in number theory to show one number directly follows another
  • Appears in proofs involving well-ordered sets and transfinite numbers
  • Useful in computer science when describing algorithms with sequential ordering
  • Often paired with its counterpart \prec to describe binary relations

Examples

Comparing elements in a strictly ordered set.

x≻y≻zx \succ y \succ z 
x \succ y \succ z

Expressing a successor relation in number theory.

n+1≻n for n∈Nn + 1 \succ n \text{ for } n \in \mathbb{N} 
n + 1 \succ n \text{ for } n \in \mathbb{N}

Denoting strict preference in decision theory.

A≻B≻C≻DA \succ B \succ C \succ D 
A \succ B \succ C \succ D