TeXipedia

trianglelefteq

Represents a triangle-shaped less-than-or-equal-to relation commonly used in mathematical expressions and set theory.

Overview

Serves as a specialized mathematical relation symbol that combines a triangular shape with the familiar less-than-or-equal concept, particularly useful in advanced mathematics and formal logic.

  • Frequently appears in order theory and abstract algebra
  • Used to denote specific partial ordering relationships
  • Common in proofs and theoretical mathematics where standard inequality symbols are insufficient
  • Often appears alongside other triangle-based relation symbols for consistent notation

Examples

Expressing a less than or equal to relationship with a triangular symbol in a set theory context.

A⊴B  ⟹  ∣A∣≤∣B∣A \trianglelefteq B \implies |A| \leq |B| 
A \trianglelefteq B \implies |A| \leq |B|

Showing a partial ordering relationship between mathematical objects.

P1⊴P2⊴P3P_1 \trianglelefteq P_2 \trianglelefteq P_3 
P_1 \trianglelefteq P_2 \trianglelefteq P_3

Defining a specialized ordering in abstract algebra.

∀x,y∈R:x⊴y  ⟺  x2≤y2\forall x,y \in R: x \trianglelefteq y \iff x^2 \leq y^2 
\forall x,y \in R: x \trianglelefteq y \iff x^2 \leq y^2