The disjoint union of two sets and is a binary operator that combines all distinct elements of a pair of given sets, while retaining the original set membership as a distinguishing characteristic of the union set. For sets, the notation is commonly used for the disjoint union (Prasolov 2006, p. xii). The notation is also used, with the dot emphasizing that the union is disjoint (Mohamad and Rara 2023).

The notation denotes the same operation. One concrete construction that keeps the copies of any common elements distinct is

where is a Cartesian product. For example, the disjoint union of sets and can be computed by finding

so

See also

Graph Disjoint Union, Graph Union, Union, Unsorted Union

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References

Armstrong, M. A. Basic Topology, rev. ed. New York: Springer-Verlag, 1997.Mohamad, J. S. and Rara, H. M. "1-Movable Resolving Hop Domination in Graphs." Eur. J. Pure Appl. Math. 16, 418-429, 2023. https://doi.org/10.29020/nybg.ejpam.v16i1.4671.Prasolov, V. V. Elements of Combinatorial and Differential Topology. Providence, RI: Amer. Math. Soc., p. xii, 2006.

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Disjoint Union

Cite this as:

Weisstein, Eric W. "Disjoint Union." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DisjointUnion.html

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