TeXipedia

lessapprox

Denotes a less than or approximately equal to relationship between mathematical expressions.

Overview

Serves as a specialized comparison operator in mathematical notation, combining the concepts of "less than" and "approximately equal to" into a single symbol. Particularly useful in:

  • Numerical analysis when discussing error bounds and approximations
  • Mathematical proofs where precise inequalities need to be relaxed
  • Statistical comparisons where exact values are not required
  • Optimization problems when describing near-optimal solutions that satisfy specific constraints

Examples

Comparing asymptotic growth rates of functions.

f(n)⪅g(n)as n→∞f(n) \lessapprox g(n) \quad \text{as } n \to \infty 
f(n) \lessapprox g(n) \quad \text{as } n \to \infty

Expressing approximate inequalities in numerical analysis.

3.14159⪅π3.14159 \lessapprox \pi 
3.14159 \lessapprox \pi

Comparing approximate bounds in mathematical analysis.

∫01f(x) dx⪅M\int_0^1 f(x)\,dx \lessapprox M 
\int_0^1 f(x)\,dx \lessapprox M