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cantor 音標拼音: [k'æntɚ] n. 合唱指揮家,領唱者 合唱指揮家,領唱者 cantor n 1: the musical director of a choir [synonym: {choirmaster}, {precentor}, {cantor}] 2: the official of a synagogue who conducts the liturgical part of the service and sings or chants the prayers intended to be performed as solos [synonym: {cantor}, {hazan}] Cantor \Can"tor\, n. [L., a singer, fr. caner to sing.] A singer; esp. the leader of a church choir; a precentor. [1913 Webster] The cantor of the church intones the Te Deum. --Milman. [1913 Webster] 64 Moby Thesaurus words for "cantor": Heldentenor, Levite, Meistersinger, alto, aria singer, baal kore, baritenor, baritone, bass, basso, basso buffo, basso cantante, basso profundo, blues singer, canary, cantatrice, caroler, chanter, chantress, chief rabbi, choir chaplain, choirmaster, choral director, chorister, coloratura soprano, comic bass, contralto, countertenor, crooner, deep bass, diva, dramatic soprano, heroic tenor, high priest, hymner, improvisator, kohen, lead singer, lieder singer, melodist, mezzo-soprano, minister of music, opera singer, precentor, priest, prima donna, psalm singer, rabbi, rabbin, rock-and-roll singer, scribe, singer, singstress, songbird, songster, songstress, soprano, tenor, torch singer, vocalist, vocalizer, voice, warbler, yodeler 1.
Cantor devised the diagonal proof of the uncountability of the {real numbers}: Given a function, f, from the {natural numbers} to the {real numbers}, consider the real number r whose binary expansion is given as follows: for each natural number i, r's i-th digit is the complement of the i-th digit of f(i). Thus, since r and f(i) differ in their i-th digits, r differs from any value taken by f. Therefore, f is not {surjective} (there are values of its result type which it cannot return). Consequently, no function from the natural numbers to the reals is surjective. A further theorem dependent on the {axiom of choice} turns this result into the statement that the reals are uncountable. This is just a special case of a diagonal proof that a function from a set to its {power set} cannot be surjective: Let f be a function from a set S to its power set, P(S) and let U = { x in S: x not in f(x) }. Now, observe that any x in U is not in f(x), so U != f(x); and any x not in U is in f(x), so U != f(x): whence U is not in { f(x) : x in S }. But U is in P(S). Therefore, no function from a set to its power-set can be surjective. 2. {concurrency}. [Athas, Caltech 1987. "Multicomputers: Message Passing Concurrent Computers", W. Athas et al, Computer 21(8):9-24 (Aug 1988)]. (1997-03-14)
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