TeXipedia

minuscoloncolon

Represents a specialized mathematical operator combining a minus sign with a double colon, commonly used in formal logic and proof theory.

Overview

Serves as a specialized notation primarily found in advanced mathematical logic, proof theory, and formal reasoning systems where precise symbolic representation is crucial.

  • Often appears in sequent calculus and formal deduction systems
  • Used to denote specific logical relationships or inference rules
  • Particularly relevant in computer science logic and automated theorem proving
  • Functions as a variant of traditional turnstile notation with additional semantic meaning

Examples

Defining a negative relation in mathematical logic

A−∷B  ⟹  A is not related to BA \minuscoloncolon B \implies A \text{ is not related to } B 
A \minuscoloncolon B \implies A \text{ is not related to } B

Expressing a negative type constraint in type theory

f−∷X→Yf \minuscoloncolon X \to Y 
f \minuscoloncolon X \to Y

Indicating negative membership in set notation

x−∷S  ⟺  x∉Sx \minuscoloncolon S \iff x \notin S 
x \minuscoloncolon S \iff x \notin S