TeXipedia

triangledown

Represents a downward-pointing triangular symbol commonly used in mathematical notation and technical diagrams.

Overview

Serves as a geometric operator or marker in mathematical expressions, particularly useful in advanced mathematics and theoretical physics.

  • Often employed to denote specific operations or transformations in abstract algebra
  • Used in diagram notation for category theory and advanced topology
  • Appears in technical documentation where directional indicators are needed
  • Frequently paired with other geometric symbols like \triangle for expressing mathematical relationships

Examples

Representing a downward-pointing triangle operator in a mathematical expression.

∇×F=▽×F\nabla \times F = \triangledown \times F 
\nabla \times F = \triangledown \times F

Using the triangle-down symbol in a set theory expression.

A▽B={x∈A:x∉B}A \triangledown B = \{x \in A : x \notin B\} 
A \triangledown B = \{x \in A : x \notin B\}

Showing a decreasing sequence with a triangle-down indicator.

{an}n=1∞▽→0\{a_n\}_{n=1}^\infty \triangledown \to 0 
\{a_n\}_{n=1}^\infty \triangledown \to 0