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Definitions of cantor

  1. the musical director of a choir Scrapingweb Dictionary DB
  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 Scrapingweb Dictionary DB
  3. A singer; esp. the leader of a church choir; a precentor. Webster Dictionary DB
  4. A precentor. Nuttall's Standard dictionary of the English language. By Nuttall, P.Austin. Published 1914.
  5. 1. A mathematician.Cantor devised the diagonal proof of the uncountability of thereal numbers:Given a function, f, from the natural numbers to the realnumbers, 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.2. An object-oriented language with fine-grainedconcurrency.[Athas, Caltech 1987. "Multicomputers: Message PassingConcurrent Computers", W. Athas et al, Computer 21(8):9-24(Aug 1988)]. foldoc_fs

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