TeXipedia

Colonapprox

Represents a relation that combines a colon with an approximation symbol, commonly used in mathematical proofs and formal definitions.

Overview

Serves as a specialized mathematical operator combining the semantic meaning of both a colon and an approximation, particularly useful in advanced mathematics and theoretical computer science.

  • Frequently appears in formal mathematical writing when defining approximate relationships or correspondences
  • Used in contexts where a definition or relation is approximate rather than exact
  • Common in theoretical papers and academic publications where precise mathematical notation is essential
  • Helps express nuanced mathematical concepts where traditional equality or definition symbols are too strict

Examples

Defining a function using the colonapprox relation symbol.

f(x)∷≈x2+2x+1f(x) \Colonapprox x^2 + 2x + 1 
f(x) \Colonapprox x^2 + 2x + 1

Expressing an approximate definition in set theory.

A∷≈{x∈R:∣x∣<1}A \Colonapprox \{x \in \mathbb{R} : |x| < 1\} 
A \Colonapprox \{x \in \mathbb{R} : |x| < 1\}

Showing an approximate recursive relation.

an+1∷≈2an+1na_{n+1} \Colonapprox 2a_n + \frac{1}{n} 
a_{n+1} \Colonapprox 2a_n + \frac{1}{n}