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Meaning of CANTOR

Pronunciation:  'kantur

WordNet Dictionary
  1. [n]  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
  2. [n]  the musical director of a choir

CANTOR is a 6 letter word that starts with C.


 Synonyms: choirmaster, hazan, precentor
 See Also: musician, spiritual leader



Webster's 1913 Dictionary
\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.

Computing Dictionary

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)].

Thesaurus Terms
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