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more about cantor
## cantor |

3 definitions found From Webster's Revised Unabridged Dictionary (1913) [web1913]: Cantor \Can"tor\, n. [L., a singer, fr caner to sing.] A singer; esp. the leader of a church choir; a precentor. The cantor of the church intones the Te Deum. --Milman. From WordNet r 1.6 [wn]: cantor n 1: the musical director of a choir [syn: {choirmaster}, {precentor}] 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 [syn: {hazan}] From The Free On-line Dictionary of Computing (13 Mar 01) [foldoc]: Cantor 1.A mathematician. 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. An {object-oriented language} with fine-grained {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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