TeXipedia

varsubsetneqq

Denotes a strict subset relationship with an additional emphasis on inequality, commonly used in set theory and mathematical proofs.

Overview

Serves as a variant form of the strict subset notation, providing a visually distinct way to emphasize proper subset relationships in mathematical expressions.

  • Particularly useful in advanced set theory when multiple subset relationships need clear visual distinction
  • Often employed in formal mathematical proofs where precise set relationships must be unambiguously conveyed
  • Frequently appears in academic papers and advanced mathematics textbooks where subtle distinctions between different types of subset relations are important

Examples

Showing a strict subset relationship between two number sets.

N⫋Z⫋Q\mathbb{N} \varsubsetneqq \mathbb{Z} \varsubsetneqq \mathbb{Q} 
\mathbb{N} \varsubsetneqq \mathbb{Z} \varsubsetneqq \mathbb{Q}

Demonstrating proper subset relationship between vector spaces.

V1⫋V2⫋RnV_1 \varsubsetneqq V_2 \varsubsetneqq \mathbb{R}^n 
V_1 \varsubsetneqq V_2 \varsubsetneqq \mathbb{R}^n

Expressing nested subset relationships in set theory.

A⫋B  ⟹  ∣A∣<∣B∣A \varsubsetneqq B \implies |A| < |B| 
A \varsubsetneqq B \implies |A| < |B|