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supsetneq

Denotes a strict superset relationship where one set properly contains another set, with explicit inequality emphasized.

Overview

Serves as a specialized mathematical relation symbol commonly used in set theory and advanced mathematics to explicitly indicate proper containment between sets.

  • Essential for precise mathematical writing where the distinction between proper and non-proper supersets matters
  • Frequently appears in proofs and formal mathematical statements about set relationships
  • Particularly useful in topology, abstract algebra, and analysis when describing strict hierarchical relationships between sets
  • Often used alongside other set relation symbols to build complex mathematical arguments

Examples

Showing that the set of real numbers is a proper superset of the integers.

R⊋Z\mathbb{R} \supsetneq \mathbb{Z} 
\mathbb{R} \supsetneq \mathbb{Z}

Demonstrating nested proper supersets with number systems.

C⊋R⊋Q⊋Z\mathbb{C} \supsetneq \mathbb{R} \supsetneq \mathbb{Q} \supsetneq \mathbb{Z} 
\mathbb{C} \supsetneq \mathbb{R} \supsetneq \mathbb{Q} \supsetneq \mathbb{Z}

Illustrating proper superset relationship between infinite sets.

{x∈R:x>0}⊋{x∈N:x>0}\{x \in \mathbb{R} : x > 0\} \supsetneq \{x \in \mathbb{N} : x > 0\} 
\{x \in \mathbb{R} : x > 0\} \supsetneq \{x \in \mathbb{N} : x > 0\}