TeXipedia

biguplus

Represents a multiset union operation with a plus sign, commonly used in mathematical set theory and algebra.

Overview

Serves as a specialized mathematical operator for combining multisets, particularly useful in advanced algebra and theoretical computer science.

  • Essential in contexts where elements can appear multiple times in sets
  • Common in formal specifications and discrete mathematics
  • Often appears in papers and texts dealing with bag semantics or multiset theory
  • Frequently used alongside other big operators like bigcup and bigcap for comprehensive set operations

Examples

Disjoint union of sets indexed from 1 to n

i=1nAi=A1A2An\biguplus_{i=1}^n A_i = A_1 \uplus A_2 \uplus \cdots \uplus A_n
\biguplus_{i=1}^n A_i = A_1 \uplus A_2 \uplus \cdots \uplus A_n

Computing multiset union over a family of multisets

M=k=13{1,1,2}k={1,1,1,1,1,1,2,2,2}M = \biguplus_{k=1}^3 \{1,1,2\}_k = \{1,1,1,1,1,1,2,2,2\}
M = \biguplus_{k=1}^3 \{1,1,2\}_k = \{1,1,1,1,1,1,2,2,2\}

Disjoint union of vector spaces

V=i=1mViV = \biguplus_{i=1}^m V_i
V = \biguplus_{i=1}^m V_i