# cantor

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Related to chazan: Hazzanut

## 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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On the other hand, Chazan provides a convincing portrait of how new, unpredictable and in many cases positive changes were made possible through this campaign, ones that resisted both the triumphalism of development narratives and the pessimism of anti-development narratives.
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Socializar en torno a una fogata pudo haber sido un aspecto esencial de los comportamientos que nos distinguen como seres humanos", ha afirmado el arqueologo Michael Chazan, de la Universidad de Toronto, coautor de ese detallado estudio.
The analysis pushes the timing for the human use of fire back by 300,000 years, suggesting that human ancestors as early as Homo erectus may have begun using fire as part of their way of life," said University of Toronto anthropologist Michael Chazan, co-director of the project and director of U of T's Archaeology Centre.
Taglit-Birthright Israel, launched in late 1999, was designed to enhance Jewish identity, love of Israel, and klal Yisrael--a sense of Jewish community--among Diaspora young adults (Saxe & Chazan, 2008).
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Naomi Chazan , former deputy speaker of the Knesset and currently dean of the School of Government and Society at the Academic College of Tel-Aviv-Yaffo, is president of the New Israel Fund.
Naomi Chazan, the President of the New Israel Fund (NIF) gave a talk in Marrickville NSW during her recent Australian tour offering a critique of theC Palestinian Civil Society call for Boycotts Divestments and Sanctions (BDS) against Israel.
Golda Meir, the redoubtable Labour prime minister, never was really reconciled to it and genuine Israeli liberals, figures such as Naomi Chazan, for many years a political scientist specialising in Africa or Shulamit Aloni, always spoke out against it.
Guy Chazan, "A New Route for Natural Gas to Europe," The Wall Street Journal, November 6, 2009, available at <http://online.
Chazan and Ball (1995) noted that only allowing students to discuss their thinking about a problem with one another fails to promote a strong mathematics community.

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