TeXipedia

gnapprox

Represents a negated greater-than and approximately equal relationship between mathematical expressions.

Overview

Serves as a specialized mathematical comparison operator combining both inequality and approximation concepts in a negated form. Commonly found in:

  • Advanced mathematical proofs where precise relationships between quantities need to be expressed
  • Analysis and topology contexts when discussing sequences and limits
  • Theoretical computer science for describing algorithmic bounds
  • Mathematical logic and set theory for expressing complex relationships between elements

Examples

Expressing that one sequence is not asymptotically greater than another.

f(n)⪊g(n) as n→∞f(n) \gnapprox g(n) \text{ as } n \to \infty 
f(n) \gnapprox g(n) \text{ as } n \to \infty

Showing a function's growth rate is not greater than exponential.

h(x)⪊ex for x>0h(x) \gnapprox e^x \text{ for } x > 0 
h(x) \gnapprox e^x \text{ for } x > 0

Comparing computational complexity classes.

O(nlog⁡n)⪊O(n2)O(n\log n) \gnapprox O(n^2) 
O(n\log n) \gnapprox O(n^2)