TeXipedia

nsubseteq

Denotes a negated subset relationship with equality, indicating that one set is not a subset of or equal to another set.

Overview

Essential in set theory and mathematical logic for expressing non-containment relationships between sets. This symbol combines the concepts of subset, equality, and negation to precisely communicate when one set is neither contained within nor equal to another set.

  • Commonly used in proofs and formal mathematical writing
  • Appears frequently in abstract algebra and topology
  • Helpful in expressing counterexamples and contradictions in set-theoretic arguments
  • Often paired with other set relation symbols like \subseteq and \subset for comprehensive set comparisons

Examples

Showing that one set is not a subset of another with natural numbers.

{1,2,3}⊈{2,4,6}\{1,2,3\} \nsubseteq \{2,4,6\} 
\{1,2,3\} \nsubseteq \{2,4,6\}

Demonstrating non-subset relationship between vector spaces.

V⊈W since v∈V but v∉WV \nsubseteq W \text{ since } v \in V \text{ but } v \notin W 
V \nsubseteq W \text{ since } v \in V \text{ but } v \notin W

Expressing that the set of irrational numbers is not a subset of rational numbers.

I⊈Q\mathbb{I} \nsubseteq \mathbb{Q} 
\mathbb{I} \nsubseteq \mathbb{Q}