TeXipedia

varsupsetneq

Denotes a strict superset relationship with an emphasized gap, indicating one set properly contains another with additional elements.

Overview

Serves as a variant of the standard strict superset symbol, providing a more visually distinct notation in set theory and mathematical logic.

  • Commonly used in advanced set theory to emphasize proper containment
  • Particularly useful when multiple set relationships need to be visually distinguished in the same context
  • Often appears in formal mathematical proofs and academic papers where precise set relationships must be clearly indicated
  • Preferred in contexts where the standard superset notation might not provide sufficient visual emphasis

Examples

Showing a proper superset relationship between two infinite sets.

R⊋Q\mathbb{R} \varsupsetneq \mathbb{Q} 
\mathbb{R} \varsupsetneq \mathbb{Q}

Demonstrating strict set containment in power sets.

P(A)⊋{∅,A}\mathcal{P}(A) \varsupsetneq \{\emptyset, A\} 
\mathcal{P}(A) \varsupsetneq \{\emptyset, A\}

Expressing proper superset relation between vector spaces.

C[x]⊋R[x]\mathbb{C}[x] \varsupsetneq \mathbb{R}[x] 
\mathbb{C}[x] \varsupsetneq \mathbb{R}[x]