TeXipedia

uplus

Represents a multiset union operation in set theory and mathematical notation.

Overview

Primarily used in advanced mathematics and computer science when working with multisets (bags) where duplicate elements matter. Unlike standard union, this operation preserves multiplicity of elements.

  • Common in formal specifications and algorithm analysis
  • Essential for describing operations where element repetition is significant
  • Appears frequently in discrete mathematics and database theory when combining collections that maintain duplicate counts

Examples

Multiset union operation between sets A and B.

A⊎B={1,1,2,3}⊎{1,2,2,4}={1,1,1,2,2,2,3,4}A \uplus B = \{1,1,2,3\} \uplus \{1,2,2,4\} = \{1,1,1,2,2,2,3,4\} 
A \uplus B = \{1,1,2,3\} \uplus \{1,2,2,4\} = \{1,1,1,2,2,2,3,4\}

Expressing the decomposition of a set into disjoint subsets.

S=A⊎B⊎CS = A \uplus B \uplus C 
S = A \uplus B \uplus C