TeXipedia

coloncolonapprox

Represents a double colon followed by an approximation symbol, commonly used in mathematical logic and set theory to denote approximate definitions or relations.

Overview

Serves as a specialized relational operator combining the notion of definition (indicated by double colons) with approximation, particularly useful in formal mathematics and theoretical computer science.

  • Frequently appears in formal specifications where approximate definitions are needed
  • Used when describing relationships that are definitional but not exact
  • Common in papers and documents dealing with type theory and formal semantics
  • Helps distinguish between exact definitions (::) and approximate ones

Examples

Defining an approximation relation in category theory.

F∷≈GF \coloncolonapprox G 
F \coloncolonapprox G

Expressing an approximate natural transformation between functors.

η∷≈μ\eta \coloncolonapprox \mu 
\eta \coloncolonapprox \mu

Indicating an approximate morphism between mathematical objects.

X∷≈Y∷≈ZX \coloncolonapprox Y \coloncolonapprox Z 
X \coloncolonapprox Y \coloncolonapprox Z