cap

Represents the intersection operation between sets in mathematical notation, showing elements common to both sets.

Overview

Essential in set theory and mathematical logic for expressing the common elements between two or more sets. Widely used across various mathematical disciplines:

Fundamental in discrete mathematics and computer science for describing overlapping data sets
Common in probability theory when describing intersecting events
Appears frequently in abstract algebra and topology for describing overlapping subgroups or spaces
Often paired with other set operations like union (\cup) in mathematical proofs and theorems

Examples

Finding the intersection of two sets A and B.

A \cap B = \{x : x \in A \text{ and } x \in B\}

A \cap B = \{x : x \in A \text{ and } x \in B\}

Intersection of multiple sets in probability theory.

P(A \cap B \cap C) = 0.15

P(A \cap B \cap C) = 0.15

Multiple set intersections in number theory.

\mathbb{N} \cap \mathbb{Z} \cap \mathbb{Q} = \mathbb{N}

\mathbb{N} \cap \mathbb{Z} \cap \mathbb{Q} = \mathbb{N}