The notation A ⊔ B A ⊔ B (and phrase "disjoint union") has (at least) two different meanings. The first is the meaning you suggest: a union that happens to be disjoint.

Jun 24, 2017 · The term disjoint refers to a collection of subsets, it means that its subsets are disjoint. The term pairwise disjoint refers to a familly of collections of subsets. It not only means that any two …

Mar 9, 2019 · Typically, pairwise disjoint means that no two sets in the collection have a member in common. The answer to your first question is no, in fact each pair of distinct subsets has a common …

Mar 8, 2019 · A "disjoint union" is a union of pairwise disjoint sets; one does not say "pairwise disjoint union". To corroborate my point of view, here is a citation from Halmos: Pairs of sets with an empty …

Feb 4, 2021 · The term disjoint may serve as a shortcut either for pairwise disjoint or collectionwise disjoint depending on the used convention (but obviously not both at the same time).

Mar 7, 2018 · With that definition, disjoint sets are necessarily mutually exclusive, but mutually exclusive events aren't necessarily disjoint. Consider points in the square with each coordinate uniformly …

Nov 13, 2020 · I am confused here that whether distint and disjoint sets mean the same? I have to find the intersection of two sets. It could be empty set if these two sets are disjoint. And it could be any …

Apr 22, 2015 · What is mutually disjoint sets? I know it has something to do with subsets but I don't know for sure.

Clearly, collection of open intervals is a base for the standard topology. Hence any open set in $\mathbb {R}$ can be written as countable union of open intervals. If any two of exploited open intervals …

Sep 24, 2018 · The following is the definition of disjoint union spaces in John Lee's "Introduction to Topological Manifolds": Let (Xα)α ∈ A be an indexed family of nonempty topological spaces.