TeXipedia

leftleftarrows

Represents a double leftward arrow notation commonly used to indicate repeated or sequential leftward movement or relationships in mathematical expressions.

Overview

Serves as a specialized mathematical arrow notation particularly useful in advanced mathematics and theoretical computer science.

  • Often employed in category theory to denote specific morphisms or transformations
  • Used in abstract algebra to indicate repeated operations or compositions
  • Appears in formal logic and set theory to represent specific relationships or mappings
  • Helpful in describing algorithmic processes or state transitions moving leftward

Examples

Showing a double left shift operation in a mathematical sequence.

xn⇇xn+2x_n \leftleftarrows x_{n+2} 
x_n \leftleftarrows x_{n+2}

Indicating a two-step backward transformation in group theory.

G⇇Hwhere G=f(f(H))G \leftleftarrows H \quad \text{where } G = f(f(H)) 
G \leftleftarrows H \quad \text{where } G = f(f(H))

Representing a double reverse implication in logical notation.

P⇇Qmeans P⇐(Q⇐R)P \leftleftarrows Q \quad \text{means } P \Leftarrow (Q \Leftarrow R) 
P \leftleftarrows Q \quad \text{means } P \Leftarrow (Q \Leftarrow R)