cantor

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cantor

[Lat.,=singer], a singer or chanter, especially one who performs the solo chants of a church service. The office of cantor, at first an honorary one, originated in the Jewish synagogues, in which from early times it was the custom to appoint a lay member to represent the congregation in prayer. The notation of the chants was forbidden. In the 6th cent. poetic prayer forms were developed, and with them more complicated modes, or music, thus necessitating professional cantors. In the early Christian church, cantors known as precentors had charge of the musical part of the service. In modern Roman Catholic and Anglican services cantors sing the opening words of hymns and psalms.

Cantor

 

in the Catholic Church, a singer; in Protestant churches, a singing teacher, choir conductor, and organist, whose duties also often included the composition of music for the church (for example, J. S. Bach at St. Thomas in Leipzig). In a Jewish synagogue, the main singer, or hazan.

cantor

1. Judaism a man employed to lead synagogue services, esp to traditional modes and melodies
2. Christianity the leader of the singing in a church choir

Cantor

(person, 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, 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.

Cantor

(language)
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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Founded in 2003 by Cantor Benny Rogosnitzky and Charlie Bernhaut, Cantors World is dedicated to reviving interest worldwide in traditional cantorial music.
For the first time, celebrated liturgical virtuoso Cantor Yitzchak Meir Helfgot will perform at New York's Metropolitan Opera.
Rabbi Steven Tucker, left, and Cantor Jason van Leeuwen light one candle to symbolize Saturday's special benefit concert for the Jewish Federation Victims of Terror Fund at Temple Ramat Zion in Northridge.
Traditionally, since Old Testament days when the chanting became part of the Jewish religious ceremony, cantors have learned the art from their elders.
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Herschel Fox, cantor at the Ventura Boulevard synagogue, said the four have mastered a musical art form that is unique to the religious and cultural heritage of the Jewish faith, and incorporates a great deal of improvisation and vocal flourishes.
There's not one full-time Orthodox cantor in the San Fernando Valley," Fox said, noting that the area - together with the Antelope, Santa Clarita, Conejo and Simi valleys - is home to roughly 217,000 Jews.