TeXipedia

Rightarrow

Represents a logical implication or material conditional in mathematical proofs and logical statements.

Overview

Serves as a fundamental symbol in mathematical logic, set theory, and formal proofs to indicate that one statement leads to or implies another.

  • Commonly used in theorem statements and mathematical reasoning
  • Essential in expressing logical consequences and conditional relationships
  • Appears frequently in computer science for logical programming and algorithm specifications
  • Distinguished from the shorter arrow (→) by conveying stronger logical necessity

Examples

Logical implication in a mathematical statement

x>0⇒x2>0x > 0 \Rightarrow x^2 > 0 
x > 0 \Rightarrow x^2 > 0

Showing steps in a mathematical derivation

a=b⇒a2=b2⇒a2−b2=0a = b \Rightarrow a^2 = b^2 \Rightarrow a^2 - b^2 = 0 
a = b \Rightarrow a^2 = b^2 \Rightarrow a^2 - b^2 = 0

Expressing a conditional relationship between sets

A⊆B⇒∣A∣≤∣B∣A \subseteq B \Rightarrow |A| \leq |B| 
A \subseteq B \Rightarrow |A| \leq |B|