bigcap

Represents a large intersection operation between multiple sets or mathematical collections.

Overview

Essential in set theory and mathematical logic for expressing the intersection of multiple sets simultaneously, particularly when dealing with families of sets or sequences of intersections.

Commonly used in advanced algebra and topology to denote the intersection of an arbitrary collection of sets
Appears frequently in formal mathematical proofs and theoretical computer science
Often paired with subscripts to indicate the range or index of sets being intersected
Serves as a larger, more prominent version of the standard intersection symbol for better visibility in displayed equations

Examples

Intersection of multiple sets A₁ through An.

\bigcap_{i=1}^{n} A_i = A_1 \cap A_2 \cap \cdots \cap A_n

\bigcap_{i=1}^{n} A_i = A_1 \cap A_2 \cap \cdots \cap A_n

Intersection of probability events in a sample space.

P\left(\bigcap_{k=1}^{n} E_k\right) \leq \min_{k} P(E_k)

P\left(\bigcap_{k=1}^{n} E_k\right) \leq \min_{k} P(E_k)

Common elements in a family of vector spaces.

V = \bigcap_{i=1}^{m} V_i \subseteq W

V = \bigcap_{i=1}^{m} V_i \subseteq W