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.
A \varsubsetneq B \implies |A| < |B|Demonstrating nested subset relationships between number sets.
\mathbb{N} \varsubsetneq \mathbb{Z} \varsubsetneq \mathbb{Q} \varsubsetneq \mathbb{R}Expressing a strict subset relationship in set builder notation.
\{x \in \mathbb{R} : x < 0\} \varsubsetneq \{x \in \mathbb{R} : x \leq 0\}