subseteqq
Denotes a subset relationship where one set is either equal to or contained within another, with an additional line for emphasis.
Overview
Serves as a specialized mathematical symbol primarily used in set theory and related mathematical proofs to indicate subset relationships with additional emphasis.
- Common in formal mathematical writing where precise set relationships need to be distinguished
- Often used alongside similar symbols like \subseteq and \subset to show different levels of inclusion
- Particularly useful in advanced algebra, topology, and analysis where detailed set relationships are crucial
- The double line underneath adds emphasis and helps distinguish this from the regular subset or subset-or-equal symbols
Examples
Showing a subset relationship between number sets.
\mathbb{N} \subseteqq \mathbb{Z} \subseteqq \mathbb{Q} \subseteqq \mathbb{R}Defining a proper subset relationship in set theory.
A \subseteqq B \implies |A| \leq |B|Expressing nested vector spaces.
V_1 \subseteqq V_2 \subseteqq V_3 \subseteqq \mathbb{R}^n