denumerableadj.
/dɪˈnjuːmərəb(ə)l/ Mathematics.
Of a set: infinite but countable; capable of being put into a one-to-one correspondence with the set of finite integers or natural numbers; also more widely, either finite or countably infinite; enumerable adj.C. S. Peirce used the term in a different sense.
ΘΚΠ
the world > relative properties > number > enumeration, reckoning, or calculation > [adjective] > numerable or reckonable > denumerable
denumerable1902
countable1906
1893 C. S. Peirce Coll. Papers (1933) IV. i. iv. 91 The dinumerable [sic] is to the innumerable as logarithmic infinity is to ordinary infinity.]
1902 A. N. Whitehead in Amer. Jrnl. Math. 24 367 Imagination is very misleading, since it presents to us special aggregates which are denumerable.
1903 B. Russell Princ. Math. xxxvi. 296 A series of this type..is denumerable, that is, by taking its terms in a suitable order..we can give them a one–one correspondence with the finite integers.
1948 B. Russell Human Knowl. iv. x. 345 Each atom may contain any one of a certain discrete denumerable series of amounts of energy.
1960 S. Körner Philos. of Math. iii. 63 The class of all rational numbers and the wider class of all (complex) algebraic numbers..are denumerable.
1964 E. Bach Introd. Transformational Gram. vii. 151 The ‘smallest’ kind of infinite set is a set which is denumerable or countable.
1968 Language 44 571 The set of all sets of integers is non~denumerable; the set of all Turing machines is denumerable; each recursively enumerable set corresponds to a Turing machine; therefore there are sets of integers which are not recursively enumerable.
1968 P. A. P. Moran Introd. Probability Theory v. 218 It therefore has at most a denumerable number of discontinuities.
Derivatives
deˈnumerably adv.
ΘΚΠ
the world > relative properties > number > enumeration, reckoning, or calculation > [adverb] > denumerably
countably1906
denumerably1932
1893 C. S. Peirce Coll. Papers (1933) IV. i. iv. 91 The innumerable is not only dinumerably [sic] more than the dinumerable but is innumerably more.]
1932 M. H. Stone Linear Transformations in Hilbert Space i. 20 Special notations for sets of elements constructed from a finite or denumerably infinite collection..of closed linear manifolds will be found..helpful.
1964 E. Bach Introd. Transformational Gram. vii. 153 The rules will specify the possible and denumerably infinite distributions for each of the forms of the language.
This entry has not yet been fully updated (first published 1972; most recently modified version published online June 2018).
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adj.1902