TeXipedia

nprec

Represents a negated precedes relation in mathematical notation, indicating that one element does not precede another in a given ordering.

Overview

Serves as a fundamental symbol in order theory and related mathematical fields where precise expression of non-precedence relationships is required.

  • Common in abstract algebra and set theory for describing order relationships
  • Used when constructing proofs involving partial orders
  • Particularly useful in contexts where showing non-precedence is as important as showing precedence
  • Often appears alongside other order relation symbols in formal mathematical writing

Examples

Showing that sequence A is not precisely less than sequence B.

{an}⊀{bn}\{a_n\} \nprec \{b_n\} 
\{a_n\} \nprec \{b_n\}

Demonstrating non-precedence in a partial ordering of sets.

A⊀B  ⟹  ∃x∈A:x∉BA \nprec B \implies \exists x \in A : x \notin B 
A \nprec B \implies \exists x \in A : x \notin B

Expressing that one function does not asymptotically precede another.

f(x)⊀g(x) as x→∞f(x) \nprec g(x) \text{ as } x \to \infty 
f(x) \nprec g(x) \text{ as } x \to \infty