Sentence examples for countable collection from inspiring English sources

Let ({ G_{k}, k=1,2,ldots}) be at most countable collection of unbounded open subsets of ((0, infty)).

Skolem's Paradox arises when we notice that the standard axioms of set theory can themselves be formulated as (countable) collection of first-order sentences.

He proved that if a countable collection of first-order sentences has an infinite model, then it has a model whose domain is only countable.

The union of a countable collection of algebraic varieties in (mathbb {P}^n) is a convergence set in (mathbb {P}^n).

The union of a countable collection of closed complete pluripolar sets in (mathbb {P}^n) is a convergence set in (mathbb {P}^n).

The union of a countable collection of analytic varieties in (mathbb {C}^n) is an affine convergence set in (mathbb {C}^n).

In other words, for every A, B ∈ Σ, A ∩B ∈ Σ and X − A ∈ Σ, where X − A denotes the set of all elements of X that are not in A. An algebra Σ of subsets of X is a σ-algebra if and only Σ contains every countable union of countable collections of its elements.

We use this result to define the Doplicher-Roberts cross product of a unital C*-algebra A with centre Cl by a semigroup of (not necessarily unital) endomorphisms Δ generated by a countable orthogonal collection P={ρi, i ∈ N} fulfilling natural conditions.

We also remark that a collection of countable families of uniformly totally quasi-ϕ-asymptotically nonexpansive multi-valued nonself maps is a subcollection of a collection of countable families of totally quasi-ϕ-asymptotically nonexpansive multi-valued nonself maps.

Furthermore, while at all levels < ω1, the collection of predicates is countable, the collection of predicates at level ω1 is of cardinality ω1.

The number of times everything is divided in two is said to be 'countably infinite': there is a countable infinity of things in a collection if they can be labeled by the numbers 1, 2, 3, … without remainder on either side.