# Denumerable Set

## denumerable set

[də′nüm·rə·bəl ′set]
(mathematics)
A set which may be put in one-to-one correspondence with the positive integers. Also known as countably infinite set.

## Denumerable Set

(or countably infinite set), an infinite set whose elements can be indexed by the natural numbers—that is, a one-to-one correspondence can be established between the set of all natural numbers. As G. Cantor demonstrated, the set of all rational numbers and even the set of all algebraic numbers are denumerable, but the set of all real numbers is nondenumerable. Every infinite set contains a denumerable subset. The union of a finite or denumerable set of denumerable sets is also a denumerable set.

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If for any complete preference subset of E, there is denumerable set {[x.sub.n]} [subset] M such that if x [member of] M, x [not equal to] sup M, there is [mathematical expression not reproducible], then E is said to be pseudo separable in incomplete preference.
It is a state space that can be a limited and denumerable set or a nonempty set.
(1) For any [sigma] > 0, there exist the denumerable set of positive eigenvalues [[chi].sub.i]([sigma]), where i = 1, 2, ..., of a finite multiplicity with only cumulative point at infinity.
Si'lnikov, "A case of the existence of a denumerable set of periodic motions," Soviet Mathematics, Doklady, vol.
Given a denumerable set S and an infinite denumerable class C of overlapping directed circuits (or directed cycles) with distinct points (except for the terminals) in S such that all the points of S can be reached from one another following paths of circuit edges; that is, for each two distinct points i and j of S there exists a finite sequence [c.sub.1], ...
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the denumerable set which achieves that maximum [v.sub.1](N([OMEGA])), i,e;
Let G acting on a denumerable set E and R be a relational structure such that AutR = [bar.G].
To develop this argument, Putnam first introduces the denumerable set MAG of all knowable physical magnitudes, and then OP, the set of values of the members of MAG at each of denumerably many spacetime points.
It is clear that the model M (the family M) includes absolutely denumerable sets. We consider the family M as the interpretation of the signature symbol "S " and will show that any axiom of ZFK is either true in the model M or it does not deny the existence of such a model.
The number of elements in one of these denumerable sets is called the cardinal number, or cardinality.

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