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prec

Denotes a strict precedence or ordering relationship between mathematical objects, indicating that one element precedes another.

Overview

Essential in mathematical logic, set theory, and order theory for expressing strict partial orders and comparing elements.

  • Common in formal mathematics to define ordering relationships between sets, numbers, or abstract objects
  • Used in proofs and theoretical computer science when describing algorithms' complexity relationships
  • Appears frequently in abstract algebra when discussing ordered structures
  • Often paired with similar relations like succeeds (\succ) to establish complete ordering systems

Examples

Comparing elements in a partially ordered set.

a≺b≺ca \prec b \prec c 
a \prec b \prec c

Expressing strict precedence in mathematical relations.

x1≺x2≺x3≺⋯≺xnx_1 \prec x_2 \prec x_3 \prec \cdots \prec x_n 
x_1 \prec x_2 \prec x_3 \prec \cdots \prec x_n

Showing proper subset relationship with precedence.

A⊂B≺CA \subset B \prec C 
A \subset B \prec C