TeXipedia

approxcoloncolon

Represents an approximation relationship using a double colon notation, commonly used in mathematical proofs and formal logic.

Overview

Serves as a specialized relational operator in mathematical writing, particularly useful in contexts involving approximate equivalences or mappings.

  • Often appears in advanced mathematical texts and formal logic proofs
  • Used to denote approximate correspondences between mathematical objects
  • Combines the concepts of approximation and relation in a single symbol
  • Particularly valuable in category theory and abstract algebra where approximate mappings need to be distinguished from exact ones

Examples

Expressing an approximate definition in type theory notation

N≈∷{0,1,2,...}\mathbb{N} \approxcoloncolon \{0, 1, 2, ...\} 
\mathbb{N} \approxcoloncolon \{0, 1, 2, ...\}

Indicating an approximate type assignment in programming language semantics

x≈∷Intx \approxcoloncolon \text{Int} 
x \approxcoloncolon \text{Int}

Representing fuzzy membership relation in set theory

A≈∷{x∣f(x)>0.5}A \approxcoloncolon \{x \mid f(x) > 0.5\} 
A \approxcoloncolon \{x \mid f(x) > 0.5\}