able to be counted.
(of a set) having a finite number of elements.
(of a set) having elements that form a one-to-one correspondence with the natural numbers; denumerable; enumerable.

1400–50; late Middle English. See count1, -able

countability, countableness, noun
countably, adverb Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
countable (ˈkaʊntəbəl)
1.  capable of being counted
2.  maths, logic able to be counted using the natural numbers; finite or denumerable
3.  linguistics denoting a count noun

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Computing Dictionary

countable definition

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 [proof?].

The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
The net monthly income is the countable income before taxes less countable
Uncurrent coins are coins that are worn yet recognizable as to genuineness and
  denomination, and are machine countable.
Both earned and unearned incomes, less mandatory deductions, are countable with
  few exceptions.
However, you may be able to get conditional payments if you agree to sell some
  of your countable resources resources.
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