| 释义 |
denumerable, a. Math.|dɪˈnjuːmərəb(ə)l|
[f. denumerate v. + -able. Cf. G. abzählbar, Fr. dénombrable.]
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 a.
C. S. Peirce used the term in a different sense.
[1893C. S. Peirce Coll. Papers (1933) IV. i. iv. 91 The dinumerable [sic] is to the innumerable as logarithmic infinity is to ordinary infinity. ]1902A. N. Whitehead in Amer. Jrnl. Math. XXIV. 367 Imagination is very misleading, since it presents to us special aggregates which are denumerable. 1903B. 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― Hum. Knowl. iv. x. 345 Each atom may contain any one of a certain discrete denumerable series of amounts of energy. 1960S. Körner Philos. of Math. iii. 63 The class of all rational numbers and the wider class of all (complex) algebraic numbers..are denumerable. 1964E. Bach Introd. Transformational Gram. vii. 151 The ‘smallest’ kind of infinite set is a set which is denumerable or countable. 1968Language XLIV. 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. 1968P. A. P. Moran Introd. Probability Theory v. 218 It therefore has at most a denumerable number of discontinuities.
Hence deˈnumerably adv.
[1893C. S. Peirce Coll. Papers (1933) IV. i. iv. 91 The innumerable is not only dinumerably [sic] more than the dinumerable but is innumerably more. ]1932M. 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. 1964E. Bach Introd. Transformational Gram. vii. 153 The rules will specify the possible and denumerably infinite distributions for each of the forms of the language. |