TeXipedia

gtrapprox

Represents a mathematical relation indicating that one value is greater than and approximately equal to another value.

Overview

Serves as a specialized comparison operator in mathematical expressions where precise inequalities need to be combined with approximations.

  • Common in numerical analysis when discussing error bounds and estimates
  • Used in optimization problems where solutions converge to specific values
  • Appears in mathematical proofs and academic papers when describing asymptotic behavior
  • Particularly useful in describing algorithmic complexity bounds and numerical approximations

Examples

Comparing asymptotic growth rates in computational complexity analysis.

f(n)⪆n2f(n) \gtrapprox n^2 
f(n) \gtrapprox n^2

Expressing approximate inequalities in numerical analysis.

π⪆3.14159\pi \gtrapprox 3.14159 
\pi \gtrapprox 3.14159

Comparing series convergence rates in mathematical analysis.

∑n=1∞1n3⪆∑n=1∞1n4\sum_{n=1}^{\infty} \frac{1}{n^3} \gtrapprox \sum_{n=1}^{\infty} \frac{1}{n^4} 
\sum_{n=1}^{\infty} \frac{1}{n^3} \gtrapprox \sum_{n=1}^{\infty} \frac{1}{n^4}