Cup
Represents the binary operation of disjoint union between sets in mathematical notation.
Overview
Essential in set theory and abstract algebra for denoting the union of disjoint sets, emphasizing that the operands have no elements in common.
- Commonly used in advanced mathematics and theoretical computer science
- Appears frequently in formal proofs and set-theoretic constructions
- Distinguished from regular union by explicitly indicating disjointness
- Particularly useful in category theory and algebraic topology when discussing coproducts
Examples
Binary multiset union operation between sets A and B.
A \Cup B = \{x : x \in A \text{ or } x \in B\}Expressing multiset union in probability theory.
P(X \Cup Y) = P(X) + P(Y) - P(X \cap Y) + P(X \cap Y)_{\text{duplicates}}