TeXipedia

Colonsim

Represents a colon-like relation symbol with a tilde above it, commonly used in mathematical notation to denote similarity or correspondence.

Overview

Serves as a specialized relational operator in mathematical writing, particularly useful in category theory, abstract algebra, and formal mathematics.

  • Often employed to indicate a special kind of correspondence or mapping between mathematical objects.
  • Appears in contexts where both similarity and relation need to be expressed simultaneously.
  • Frequently used in advanced mathematical proofs and theoretical computer science.
  • Provides a more specific alternative to simple colons or similarity symbols when precise mathematical relationships need to be conveyed.

Examples

Defining an equivalence relation using the 'colon similar to' symbol.

xy    f(x)f(y)x \Colonsim y \iff f(x) \sim f(y)
x \Colonsim y \iff f(x) \sim f(y)

Expressing a congruence relation in number theory.

ab(modn)a \Colonsim b \pmod{n}
a \Colonsim b \pmod{n}

Denoting a special similarity relationship between matrices.

AB    det(A)=det(B)A \Colonsim B \implies \det(A) = \det(B)
A \Colonsim B \implies \det(A) = \det(B)