Sentence examples for collections of sets from inspiring English sources

Another version of Zorn's Lemma can be given in terms of collections of sets.

It is to be noted that AC1 and CAC for finite collections of sets are both provable (by induction) in the usual set theories.

This argument shows that collections of sets of atoms need not necessarily have choice functions, but it fails to establish the same fact for the "usual" sets of mathematics, for example the set of real numbers.

(Note that by setting for some subsets, fractional partitions using arbitrary collections of sets can be thought of as fractional partitions using the full power set.) Thus, the game having a nonempty core is equivalent to its being balanced.

If ( E i ) i ∈ ℑ, ( F i ) i ∈ ℑ are two finite collections of sets in ( K ( X ), h ), then h ( ⋃ i ∈ ℑ E i, ⋃ i ∈ ℑ F i ) ≤ sup i ∈ ℑ h ( E i, F i ).

(Informally, a closed collection of sets contains a maximal member a set that cannot be contained in any other set in the collection).

A member of S is said to be maximal if it is not a subset of any other member of S. Zorn's lemma is the statement: Any collection of sets closed under unions of chains contains a maximal member.

The collection of sets of wiretap edges is,,,.

This was a wide ranging collection of sets bringing in various franchises from different partners.

where recall that H is the collection of sets of hereditary cardinality less than κ+.

Let Γ∞ be the collection of sets of reals that are universally Baire.