TeXipedia

approxeq

Denotes approximate equality with an additional curved line beneath the standard approximation symbol, indicating a stronger form of approximation.

Overview

Provides a more nuanced way to express approximate relationships in mathematical expressions, particularly useful when standard approximation notation isn't precise enough.

  • Common in numerical analysis when expressing convergence relationships
  • Used in mathematical proofs where the nature of approximation needs to be distinguished from simple approximation
  • Appears in statistical contexts when discussing asymptotic behavior
  • Helpful in physics and engineering when indicating close equivalence with theoretical values

Examples

Showing that two expressions are approximately equal in a numerical computation.

π≊3.14159\pi \approxeq 3.14159 
\pi \approxeq 3.14159

Indicating approximate equality in a physical measurement with uncertainty.

g≊9.81 m/s2g \approxeq 9.81 \text{ m/s}^2 
g \approxeq 9.81 \text{ m/s}^2

Demonstrating approximate equality in a series expansion.

sin⁡x≊x−x36+x5120 for small x\sin x \approxeq x - \frac{x^3}{6} + \frac{x^5}{120} \text{ for small } x 
\sin x \approxeq x - \frac{x^3}{6} + \frac{x^5}{120} \text{ for small } x