TeXipedia

Subset

Denotes a proper subset relationship with a double line underneath, emphasizing a stronger containment relationship between sets.

Overview

Serves as a specialized variant of the standard subset symbol, primarily used in advanced mathematics and set theory to indicate a more emphatic or specific subset relationship.

  • Common in formal mathematical proofs and abstract algebra where precise set relationships need emphasis
  • Often employed to distinguish from regular subset notation when additional mathematical properties or conditions apply
  • Particularly useful in topology and analysis when describing nested sequences of sets
  • Frequently appears alongside other set-theoretic notation in academic papers and advanced textbooks

Examples

Showing a proper subset relationship between nested sets.

A⋐B⋐CA \Subset B \Subset C 
A \Subset B \Subset C

Expressing a strict subset relationship in set theory with additional context.

{1,2}⋐{1,2,3}⋐N\{1,2\} \Subset \{1,2,3\} \Subset \mathbb{N} 
\{1,2\} \Subset \{1,2,3\} \Subset \mathbb{N}

Comparing nested subspaces in linear algebra.

V1⋐V2⋐V3⊆RnV_1 \Subset V_2 \Subset V_3 \subseteq \mathbb{R}^n 
V_1 \Subset V_2 \Subset V_3 \subseteq \mathbb{R}^n