TeXipedia

precnsim

Represents a negated precedes and similar to relation in mathematical notation, combining both non-precedence and non-similarity concepts.

Overview

Serves as a specialized mathematical relation symbol primarily used in order theory and abstract algebra to denote when one element neither precedes nor is similar to another.

  • Common in formal mathematical proofs and theoretical computer science.
  • Particularly useful when discussing partial orders and equivalence relations simultaneously.
  • Often appears alongside other order-theoretic symbols to express complex relationships between mathematical objects.
  • Frequently used in advanced set theory and category theory discussions.

Examples

Expressing that sequence A is not asymptotically equivalent to sequence B.

An⋨Bnas n→∞A_n \precnsim B_n \quad \text{as } n \to \infty 
A_n \precnsim B_n \quad \text{as } n \to \infty

Denoting non-asymptotic precedence in complexity analysis.

f(n)⋨g(n)f(n) \precnsim g(n) 
f(n) \precnsim g(n)

Indicating that one function does not precede and is not asymptotically similar to another.

log⁡n⋨n1/2\log n \precnsim n^{1/2} 
\log n \precnsim n^{1/2}