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Definitions of cantor

the musical director of a choir Scrapingweb Dictionary DB

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

A singer; esp. the leader of a church choir; a precentor. Webster Dictionary DB

A precentor. Nuttall's Standard dictionary of the English language. By Nuttall, P.Austin. Published 1914.

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 ith digit isthe complement of the ith digit of f(i).Thus, since r and f(i) differ in their ith 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 powersetcan be surjective.2. An objectoriented language with finegrainedconcurrency.[Athas, Caltech 1987. "Multicomputers: Message PassingConcurrent Computers", W. Athas et al, Computer 21(8):924(Aug 1988)]. foldoc_fs
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