| 单词 | cantor | |||||||||
| 释义 | cantorcan·torC0075700 (kăn′tər)cantor(ˈkæntɔː)can•tor(ˈkæn tər, -tɔr)n. Can•tor(ˈkæn tɔr, ˈkɑn-)n. cantor
cantorcantor[Lat.,=singer], a singer or chanter, especially one who performs the solo chants of a church service. The office of cantor, at first an honorary one, originated in the Jewish synagogues, in which from early times it was the custom to appoint a lay member to represent the congregation in prayer. The notation of the chants was forbidden. In the 6th cent. poetic prayer forms were developed, and with them more complicated modes, or music, thus necessitating professional cantors. In the early Christian church, cantors known as precentors had charge of the musical part of the service. In modern Roman Catholic and Anglican services cantors sing the opening words of hymns and psalms.Cantorin the Catholic Church, a singer; in Protestant churches, a singing teacher, choir conductor, and organist, whose duties also often included the composition of music for the church (for example, J. S. Bach at St. Thomas in Leipzig). In a Jewish synagogue, the main singer, or hazan. cantorCantor(person, mathematics)Cantor devised the diagonal proof of the uncountability of thereal numbers: Given a function, f, from the natural numbers to the real numbers, consider the real number r whose binary expansion isgiven as follows: for each natural number i, r's i-th digit isthe complement of the i-th digit of f(i). Thus, since r and f(i) differ in their i-th digits, r differsfrom 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 thereals is surjective. A further theorem dependent on theaxiom of choice turns this result into the statement thatthe reals are uncountable. This is just a special case of a diagonal proof that afunction 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) andlet U = { x in S: x not in f(x) }. Now, observe that any x inU 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 isin P(S). Therefore, no function from a set to its power-setcan be surjective. Cantor(language)[Athas, Caltech 1987. "Multicomputers: Message PassingConcurrent Computers", W. Athas et al, Computer 21(8):9-24(Aug 1988)]. CantorCan·tor(kan'tŏr),CANTOR
cantor
Synonyms for cantor
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cantor - the musical director of a choir