TeXipedia

blacktriangleleft

Represents a solid black triangular arrow pointing leftward, commonly used in mathematical notation to indicate specific relationships or directional concepts.

Overview

Serves as a specialized mathematical symbol primarily used in advanced mathematics and theoretical computer science to denote specific relations or operations.

  • Often employed in category theory and abstract algebra to represent particular mappings or transformations
  • Used in formal logic and set theory to denote specialized relations between elements
  • Appears in proofs and theoretical papers where precise symbolic notation is required
  • Sometimes utilized in computer science literature for describing algorithms or state transitions

Examples

Showing a strict ordering relation between elements.

x◀y◀zx \blacktriangleleft y \blacktriangleleft z 
x \blacktriangleleft y \blacktriangleleft z

Indicating a one-way implication or dependency in a mathematical statement.

A◀B  ⟹  f(A)<f(B)A \blacktriangleleft B \implies f(A) < f(B) 
A \blacktriangleleft B \implies f(A) < f(B)

Representing a strict partial order in set theory.

{1,2}◀{1,2,3}◀{1,2,3,4}\{1,2\} \blacktriangleleft \{1,2,3\} \blacktriangleleft \{1,2,3,4\} 
\{1,2\} \blacktriangleleft \{1,2,3\} \blacktriangleleft \{1,2,3,4\}