| slovo | definícia |
cantor
(mass) | cantor
- kantor |
cantor
(encz) | cantor,kantor n: Zdeněk Brož |
Cantor
(gcide) | Cantor \Can"tor\, n. [L., a singer, fr. caner to sing.]
A singer; esp. the leader of a church choir; a precentor.
[1913 Webster]
The cantor of the church intones the Te Deum. --Milman.
[1913 Webster] |
cantor
(wn) | cantor
n 1: the musical director of a choir [syn: choirmaster,
precentor, cantor]
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: cantor, hazan] |
cantor
(foldoc) | 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)
|
| | podobné slovo | definícia |
cantor
(mass) | cantor
- kantor |
cantor
(encz) | cantor,kantor n: Zdeněk Brož |
cantors
(encz) | cantors,kantoři Jiří Šmoldas |
schola cantorum
(encz) | schola cantorum, n: |
Cantoral
(gcide) | Cantoral \Can"tor*al\, a.
Of or belonging to a cantor.
[1913 Webster]
Cantoral staff, the official staff or baton of a cantor or
precentor, with which time is marked for the singers.
[1913 Webster] |
Cantoral staff
(gcide) | Cantoral \Can"tor*al\, a.
Of or belonging to a cantor.
[1913 Webster]
Cantoral staff, the official staff or baton of a cantor or
precentor, with which time is marked for the singers.
[1913 Webster] |
Cantoris
(gcide) | Cantoris \Can*to"ris\, a. [L., lit., of the cantor, gen. of
cantor.]
Of or pertaining to a cantor; as, the cantoris side of a
choir; a cantoris stall. --Shipley.
[1913 Webster] Cantrap |
cantor
(wn) | cantor
n 1: the musical director of a choir [syn: choirmaster,
precentor, cantor]
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: cantor, hazan] |
schola cantorum
(wn) | schola cantorum
n 1: a school that is part of a cathedral or monastery where
boys with singing ability can receive a general education
[syn: choir school, schola cantorum] |
cantor
(foldoc) | 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)
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