denumerable

For the case of denumerable state space we put in place of .

Hence, there is a countable, or denumerable, infinity of computer programs.

(This will take a denumerable infinity of steps.)

This set is denumerable.

Any infinite set that can be placed in one-to-one correspondence with the natural numbers is said to be "countable" or "denumerable".

The set of real arithmetical numbers is denumerable, dense and order-isomorphic to the set of rational numbers.

Sweden's twenty-seven-year-old media-acclaimed 'prodigy' of astrophysics tries once more to predict his pattern in a way that will make them denumerable.

In particular, there exists a model of ZF in which there exists an infinite set with no denumerable subset.

Therefore, in order to avoid ambiguity, one may use the term finitely enumerable or denumerable to denote one of the corresponding types of distinguished countable enumerations.

He called these cardinal numbers transfinite cardinal numbers, and defined all sets having a one-to-one correspondence with N to be denumerable (countably infinite) sets.

R. Vaught, "Denumerable models of complete theories", Infinitistic Methods (Proc.

In this paper he characterizes the countable ("denumerable") structures which can be made into models of a theory by adding interpretations of the extra predicates used in defining the theory.

He used this concept to define finite and infinite sets, subdividing the latter into denumerable (or countably infinite) sets and uncountable sets (nondenumerable infinite sets).

The axiom of countable choice or axiom of denumerable choice, denoted AC, is an axiom of set theory (a special case of the axiom of choice).

His address was published in the Conference Proceedings (The Theory of Models, North-Holland Publishing Co., 1965) as "On the denumerable models of theories with extra predicates", pp 376-389.

Cantor defined countable sets (or denumerable sets) as sets which can be put into a 1-to-1 correspondence with the natural numbers, and proved that the rational numbers are denumerable.

The syntax of a first-order theory can describe only a denumerable number of sets; hence, only denumerably many sets may be eliminated in this fashion, but this limitation is not binding for the sort of mathematics contemplated here.

Unlike Tarski's approach, however, Kripke's lets "truth" be the union of all of these definition-stages; after a denumerable infinity of steps the language reaches a "fixed point" such that using Kripke's method to expand the truth-predicate does not change the language any further.

By making the assumption that bodies are finite Dumbleton was able to conjecture that contraction or expansion, as in cases of condensation or rarefaction, does not eliminate any parts of a body; rather, a "denumerable number of parts" always exists (Glick, p. 518).

He also proved that the set of all ordered pairs of natural numbers is denumerable (which implies that the set of all rational numbers is denumerable), and later proved that the set of all algebraic numbers is also denumerable.