TeXipedia

blacktriangle

Represents a solid black upward-pointing triangular symbol commonly used in mathematical notation and technical diagrams.

Overview

Serves as a distinctive mathematical marker or indicator, particularly useful in formal proofs, logical reasoning, and technical documentation.

  • Often employed to denote special relations or highlight important steps in mathematical proofs
  • Used in diagram annotations and technical illustrations where directional emphasis is needed
  • Appears in computer science literature for representing hierarchical relationships or indicating progression
  • Valuable in set theory and abstract mathematics for denoting specific operations or properties

Examples

Representing an increasing trend or upward direction in mathematical analysis.

f(x)▲g(x) as x→∞f(x) \blacktriangle g(x) \text{ as } x \to \infty 
f(x) \blacktriangle g(x) \text{ as } x \to \infty

Indicating a strictly greater than relationship in order theory.

a▲b  ⟹  a>ba \blacktriangle b \implies a > b 
a \blacktriangle b \implies a > b

Denoting an upward-pointing operator in quantum mechanics.

H^∣ψ⟩=E▲∣ψ⟩\hat{H} |\psi\rangle = E \blacktriangle |\psi\rangle 
\hat{H} |\psi\rangle = E \blacktriangle |\psi\rangle