TeXipedia

varsubsetneq

Denotes a strict subset relationship with a variant styling, emphasizing proper containment between mathematical sets.

Overview

Serves as a stylistic variant of the strict subset symbol, commonly used in set theory and mathematical logic to indicate that one set is properly contained within another set, with distinct visual emphasis.

  • Essential in advanced mathematics for expressing precise set relationships
  • Often preferred in formal proofs and academic papers for its clearer visual distinction
  • Particularly useful when multiple subset relations need to be visually distinguished in the same document
  • Frequently appears in topology, abstract algebra, and analysis contexts where strict set containment needs emphasis

Examples

Showing a proper subset relationship between sets where one set is strictly smaller than another.

AB    A<BA \varsubsetneq B \implies |A| < |B|
A \varsubsetneq B \implies |A| < |B|

Demonstrating nested subset relationships between number sets.

NZQR\mathbb{N} \varsubsetneq \mathbb{Z} \varsubsetneq \mathbb{Q} \varsubsetneq \mathbb{R}
\mathbb{N} \varsubsetneq \mathbb{Z} \varsubsetneq \mathbb{Q} \varsubsetneq \mathbb{R}

Expressing a strict subset relationship in set builder notation.

{xR:x<0}{xR:x0}\{x \in \mathbb{R} : x < 0\} \varsubsetneq \{x \in \mathbb{R} : x \leq 0\}
\{x \in \mathbb{R} : x < 0\} \varsubsetneq \{x \in \mathbb{R} : x \leq 0\}