TeXipedia

longleftarrow

Represents a long leftward-pointing arrow used to indicate extended relationships, implications, or mappings in mathematical expressions.

Overview

Serves as an elongated version of the standard leftward arrow, providing enhanced visual emphasis in mathematical notation and formal proofs.

  • Commonly used in set theory and abstract algebra to show reverse mappings or inverse relationships
  • Appears in logical proofs to indicate reverse implications or consequences
  • Useful in diagram notation where extended arrows improve readability
  • Often employed in computer science and category theory to denote backward relationships or dependencies

Examples

Showing logical implication in reverse direction (necessary condition).

qpq \longleftarrow p
q \longleftarrow p

Indicating a limit approaching from the right.

xa+x \longleftarrow a^+
x \longleftarrow a^+

Representing a leftward mapping between sets.

BAB \longleftarrow A
B \longleftarrow A