TeXipedia

notni

Represents the negation of set membership, indicating that an element is not contained within a specified set.

Overview

Essential in set theory and mathematical logic for expressing non-membership relationships between elements and sets. Commonly appears in:

  • Mathematical proofs where set exclusion needs to be demonstrated
  • Formal logic statements and set-theoretic expressions
  • Computer science contexts, particularly in formal specifications and algorithm analysis
  • Academic papers and textbooks dealing with set operations and relationships

Examples

Expressing that an element is not a member of a set complement.

x∌Ac  ⟹  x∈Ax \notni A^c \implies x \in A 
x \notni A^c \implies x \in A

Showing non-membership in the set of natural numbers.

π∌N\pi \notni \mathbb{N} 
\pi \notni \mathbb{N}

Demonstrating that a complex number is not in the real number set.

i∌Ri \notni \mathbb{R} 
i \notni \mathbb{R}