TeXipedia

sqsubset

Denotes a strict subset relationship using a square-shaped symbol, commonly used in set theory and mathematical logic.

Overview

Serves as a specialized mathematical relation symbol that indicates a proper subset relationship with distinct visual emphasis compared to standard subset notation.

  • Popular in formal mathematical proofs and set-theoretic arguments
  • Often used alongside its complement \sqsupset for expressing strict containment relationships
  • Particularly useful in contexts where visual distinction from regular subset symbols is important
  • Common in advanced algebra, topology, and theoretical computer science where precise set relationships need to be clearly distinguished

Examples

Showing a proper subset relationship between sets using the square subset symbol.

A⊏B  ⟹  ∣A∣<∣B∣A \sqsubset B \implies |A| < |B| 
A \sqsubset B \implies |A| < |B|

Comparing nested vector spaces with the square subset notation.

V1⊏V2⊏V3V_1 \sqsubset V_2 \sqsubset V_3 
V_1 \sqsubset V_2 \sqsubset V_3

Expressing strict inclusion of mathematical structures.

N⊏Z⊏Q⊏R\mathbb{N} \sqsubset \mathbb{Z} \sqsubset \mathbb{Q} \sqsubset \mathbb{R} 
\mathbb{N} \sqsubset \mathbb{Z} \sqsubset \mathbb{Q} \sqsubset \mathbb{R}