doublecap
Represents the double intersection operation, commonly used in set theory to find the intersection of multiple sets.
Overview
Essential for advanced set theory and mathematical logic where multiple set intersections need to be denoted compactly. This notation appears frequently in:
- Abstract algebra for intersections of algebraic structures
- Topology when describing intersections of multiple topological spaces
- Computer science, particularly in database theory and formal specifications
- Mathematical proofs requiring the intersection of multiple sets or families of sets
Often preferred over repeated use of single intersection symbols when dealing with three or more sets, providing a more elegant and space-efficient notation.
Examples
Intersection of three sets A, B, and C using the double intersection symbol.
A \doublecap B \doublecap C = \{x : x \in A \land x \in B \land x \in C\}Multiple intersection in probability theory showing the intersection of independent events.
P(E_1 \doublecap E_2 \doublecap E_3) = P(E_1)P(E_2)P(E_3)Set theory expression showing nested intersections with the double intersection operator.
(X \doublecap Y) \subseteq (X \doublecap Z) \implies Y \subseteq Z