Word:

# Cantor

Can´tor
 n. 1 A singer; esp. the leader of a church choir; a precentor.The cantor of the church intones the Te Deum.- Milman.
 Noun 1 cantor - the musical director of a choirSynonyms: choirmaster, precentor 2 cantor - the official of a synagogue who conducts the liturgical part of the service and sings or chants the prayers intended to be performed as solosSynonyms: hazan
 1 (person, mathematics) Cantor - 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 (language) Cantor - 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)].
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