Jan 29, 2016 · The notation $A\sqcup B$ (and phrase "disjoint union") has (at least) two different meanings. The first is the meaning you suggest: a union that happens to be disjoint.

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 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:

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 …

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 …

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 $ (X_ {\alpha})_ {\alpha\in A}$ be an indexed family of nonempty …

Aug 28, 2016 · How do you show that two sets are disjoint? Ask Question Asked 9 years, 5 months ago Modified 9 years, 5 months ago

Oct 21, 2022 · How can I show that two sets are disjoint? Ask Question Asked 3 years, 3 months ago Modified 3 years, 3 months ago