TeXipedia

thickapprox

Denotes a stronger or more emphasized approximation relationship between mathematical expressions.

Overview

Provides a visually distinct, thicker version of the standard approximation symbol, useful when emphasizing approximate equality or when multiple levels of approximation need to be distinguished in mathematical writing.

  • Common in numerical analysis when highlighting primary or important approximations
  • Used in mathematical proofs and theoretical computer science to show stronger forms of approximation
  • Particularly useful in documents where regular and emphasized approximations need to be visually distinct
  • Often appears in optimization theory and computational mathematics

Examples

Expressing a rough numerical approximation with emphasis.

π≈3.14159\pi \thickapprox 3.14159 
\pi \thickapprox 3.14159

Indicating approximate equality between two expressions in statistical analysis.

μ^≈1n∑i=1nxi\hat{\mu} \thickapprox \frac{1}{n}\sum_{i=1}^n x_i 
\hat{\mu} \thickapprox \frac{1}{n}\sum_{i=1}^n x_i

Showing approximate equivalence in numerical methods.

f(x+h)≈f(x)+f′(x)hf(x + h) \thickapprox f(x) + f'(x)h 
f(x + h) \thickapprox f(x) + f'(x)h