TeXipedia

nleftarrow

Represents a negated left arrow, indicating a relationship or implication that does not hold in the leftward direction.

Overview

Commonly used in mathematical logic, set theory, and abstract algebra to denote non-implications or the absence of specific relationships between elements or statements.

  • Essential in proof writing to show that certain properties or relationships do not hold
  • Frequently appears alongside regular arrows to contrast valid and invalid relationships
  • Particularly useful in advanced mathematics when discussing mappings, functions, or logical implications that fail in one direction

Examples

Showing that a sequence does not converge to a limit.

xn↚Lx_n \nleftarrow L 
x_n \nleftarrow L

Indicating non-implication in logical statements.

A↚BA \nleftarrow B 
A \nleftarrow B

Denoting that a function is not a left inverse.

f∘g↚idXf \circ g \nleftarrow id_X 
f \circ g \nleftarrow id_X