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subsetneqq

Denotes a strict subset relationship where one set is properly contained within another, with an additional emphasis on the inequality.

Overview

Serves as a specialized mathematical notation primarily used in set theory and related mathematical fields to indicate a proper subset relationship with explicit inequality.

  • Commonly used when emphasizing that one set is strictly contained within another set, with at least one element difference.
  • Particularly valuable in formal mathematical proofs where precise set relationships need to be distinguished.
  • Often appears alongside other set theory symbols in academic papers and advanced mathematics textbooks.
  • Preferred over simpler subset symbols when explicit emphasis on proper containment is required.

Examples

Showing a proper subset relationship between number sets.

N⫋Z⫋Q⫋R\mathbb{N} \subsetneqq \mathbb{Z} \subsetneqq \mathbb{Q} \subsetneqq \mathbb{R} 
\mathbb{N} \subsetneqq \mathbb{Z} \subsetneqq \mathbb{Q} \subsetneqq \mathbb{R}

Demonstrating strict subset relationship between two specific sets.

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

Expressing a proper subset relationship in set builder notation.

{x∈R:x>0}⫋{x∈R:x≥0}\{x \in \mathbb{R} : x > 0\} \subsetneqq \{x \in \mathbb{R} : x \geq 0\} 
\{x \in \mathbb{R} : x > 0\} \subsetneqq \{x \in \mathbb{R} : x \geq 0\}