# countable

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## countable

[′kau̇nt·ə·bəl]
(mathematics)
Either finite or denumerable. Also known as enumerable.

## countable

(mathematics)
A term describing a set which is isomorphic to a subet of the natural numbers. A countable set has "countably many" elements. If the isomorphism is stated explicitly then the set is called "a counted set" or "an enumeration".

Examples of countable sets are any finite set, the natural numbers, integers, and rational numbers. The real numbers and complex numbers are not
References in periodicals archive ?
The solutions, oscillating with the cut-off frequency, appear to be arranged in a new countable set of the fields generated by Eqs.
Existence of a new countable set of the waveguide modes is established.
These perspectives either have been, or could be, used to describe thinking about countable sets (in our case, the set of natural numbers N).
In our review of the literature on visualization, we did not find any investigations on the use of visual image as a mental structure for countable sets.
Another curiosity is that in both places, the theorem as stated - 'ZF plus V = L has an [Omega]-model which contains any given countable set of real numbers' - appears to be [[Sigma].
If f is Putnam's coding of countable sets of reals and s is a countable set of reals, what Putnam has shown is that there is some constructible M and s[prime] [element of] M such that M [satisfies] x = f(s)[s[prime]].
To prove (b) take any countable set A [subset] X and assume that there exists a point x [member of] [bar.
Therefore every countable set is closed in X so if A [subset] X is countable then all subsets of A are closed in X, i.
Then each element of D has null coordinates off of the countable set [[union].
The class A of countable groups admitting an amenable, transitive and faithful action on a countable set is introduced by Glasner and Monod in [2].
Marino said he first came up with the concept for the game while in a discrete mathematics class, studying such concepts as countable sets and finite mathematics, at Worcester State College.
11 of [Ma]), it will be [omega]-homogenous as a countable union of an elementary chain of countable [omega]-homogenous models, it will be countable as a countable union of countable sets and it will have infinite transcendence degree over Q as this already holds for the subset [K.

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