TeXipedia

Uparrow

Represents a double upward arrow symbol commonly used in mathematical logic and set theory to indicate logical implications or ordering relations.

Overview

Serves as a vital notation in formal mathematics and theoretical computer science, particularly when expressing logical relationships or ordered structures.

  • Frequently used to denote upward double implications in logical proofs
  • Appears in order theory to represent strict hierarchical relationships
  • Common in formal specifications and mathematical reasoning
  • Often paired with \Downarrow for bidirectional relationships
  • Distinguished from the single arrow (\uparrow) when stronger emphasis or formal distinction is needed

Examples

Logical implication with double upward arrow in a formal logic expression

p⇑q≡¬(p↑q)p \Uparrow q \equiv \neg(p \uparrow q) 
p \Uparrow q \equiv \neg(p \uparrow q)

Double arrow notation in matrix algebra showing upward relationship

A⇑B=CA \Uparrow B = C 
A \Uparrow B = C

Vertical double arrow in a mathematical inequality chain

x<y⇑z<wx < y \Uparrow z < w 
x < y \Uparrow z < w