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nsubseteqq

Denotes a negated double-line subset or equal relationship between sets, indicating that one set is not a subset of or equal to another.

Overview

Serves as a fundamental symbol in set theory and mathematical logic for expressing non-containment relationships between sets with additional emphasis through double lines.

  • Commonly used in advanced mathematical proofs and formal set theory.
  • Provides a more visually distinct alternative to the single-line variant.
  • Particularly useful when writing formal mathematical statements that need to emphasize strict set relationships.
  • Often appears alongside other set theory notation in academic papers and advanced mathematics textbooks.

Examples

Showing that set A is not a proper subset of set B with equality.

A⊈BA \nsubseteqq B 
A \nsubseteqq B

Expressing a counterexample in number theory where the natural numbers are not a subset of or equal to the real numbers.

N⊈R\mathbb{N} \nsubseteqq \mathbb{R} 
\mathbb{N} \nsubseteqq \mathbb{R}

Demonstrating non-inclusion relationship between function spaces.

L1(Ω)⊈L2(Ω)L^1(\Omega) \nsubseteqq L^2(\Omega) 
L^1(\Omega) \nsubseteqq L^2(\Omega)