TeXipedia

ni

Denotes set membership from right to left, indicating that an element contains or includes another element.

Overview

Serves as the reverse or mirror of the standard set membership operator, particularly useful in mathematical logic and set theory when expressing relationships from a container's perspective.

  • Common in formal mathematical proofs where emphasizing the containing set is important.
  • Often used to express "contains as an element" or "has as a member".
  • Appears frequently in abstract algebra and topology when describing properties of sets or classes.
  • Provides a natural way to state inclusion from the perspective of the larger set or collection.

Examples

Set membership expressed in reverse (set contains element)

N∋5\mathbb{N} \ni 5 
\mathbb{N} \ni 5

Multiple elements contained in a set

R∋x>0\mathbb{R} \ni x > 0 
\mathbb{R} \ni x > 0

Expressing domain conditions in function definition

f:R∋x↦x2f: \mathbb{R} \ni x \mapsto x^2 
f: \mathbb{R} \ni x \mapsto x^2