TeXipedia

downharpoonright

Represents a downward-pointing harpoon with a rightward barb, commonly used in mathematical notation and set theory.

Overview

Serves as a specialized mathematical operator primarily found in advanced mathematical contexts, particularly in set theory, order theory, and abstract algebra.

  • Often employed to denote specific mappings or relations between mathematical objects.
  • Frequently appears in academic papers and advanced mathematical texts.
  • Pairs naturally with \upharpoonright for expressing bidirectional relationships.
  • Used in conjunction with other arrow-like symbols to create more complex mathematical notation.

Examples

Defining a mathematical relation using the downward harpoon.

x⇂yx \downharpoonright y 
x \downharpoonright y

Representing a restriction operation in set theory.

f⇂A={(x,y)∈f:x∈A}f \downharpoonright A = \{(x,y) \in f : x \in A\} 
f \downharpoonright A = \{(x,y) \in f : x \in A\}

Indicating a projection or mapping in abstract algebra.

π⇂G:G→H\pi \downharpoonright G : G \to H 
\pi \downharpoonright G : G \to H