meaning of cantor

1. A singer; esp. the leader of a church choir; a precentor.
2. Cantor 1. mathematics> 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, rs i-th digit is the complement of the i-th digit of fi. Thus, since r and fi 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, PS and let U = x in S: x not in fx . Now, observe that any x in U is not in fx, so U != fx; and any x not in U is in fx, so U != fx: whence U is not in fx : x in S . But U is in PS. 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 218:9-24 Aug 1988].
3. 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

Related Words

cantor | cantoral | cantoris |

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