Language:
Free Online Dictionary|3Dict

cantor

Source : Webster's Revised Unabridged Dictionary (1913)

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.

Source : WordNet®

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}]

Source : Free On-Line Dictionary of Computing

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)
Sort by alphabet : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z