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Что (кто) такое Church integer - определение
REPRESENTATION OF THE NATURAL NUMBERS AS HIGHER-ORDER FUNCTIONS
Church numeral; Church number; Church boolean; Church booleans; Church numerals; Church integer; Church numbers
Найдено результатов: 6528
Church integer
<theory> A representation of integers as functions invented by
Alonzo Church, inventor of lambda-calculus. The integer N
is represented as a higher-order function which applies a
given function N times to a given expression. In the {pure
lambda-calculus} there are no constants but numbers can be
represented by Church integers.
A Haskell function to return a given Church integer could be
written:
church n = c
where
c f x = if n == 0 then x else c' f (f x)
where
c' = church (n-1)
A function to turn a Church integer into an ordinary integer:
unchurch c = c (+1) 0
See also von Neumann integer.
(1994-11-29)
Church encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation.
Almost integer
![[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name="MathWorld"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Almost integer in triangle.svg?width=200 "[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name=\"MathWorld\"/>")
ANY NUMBER THAT IS NOT AN INTEGER BUT IS VERY CLOSE TO ONE
Near integer; Near-integer
In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers are considered interesting when they arise in some context in which they are unexpected.
Integer
![negative]] integers are shown in blue and negative integers in red.](https://commons.wikimedia.org/wiki/Special:FilePath/Number-line.svg?width=200 "negative]] integers are shown in blue and negative integers in red.")
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.
integer
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
n.
Whole number.
integer
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
(integers)
In mathematics, an integer is an exact whole number such as 1, 7, or 24 as opposed to a number with fractions or decimals. (TECHNICAL)
N-COUNT
integer
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
<mathematics> (Or "whole number") One of the finite numbers
in the infinite set
..., -3, -2, -1, 0, 1, 2, 3, ...
An inductive definition of an integer is a number that is
either zero or an integer plus or minus one. An integer is a
number with no fractional part. If written as a fixed-point
number, the part after the decimal (or other base) point will
be zero.
A natural number is a non-negative integer.
(2002-04-07)
Integer
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
·noun A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
integer
NUMBER THAT CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT
IntegerNumbers; Integers; Integer number; Signed Numbers; Rational integer; ℤ; Interger; Integer value; Negative integer; Set of integers; Zahlen; Integar; Intergar; Construction of the integers; Integer-valued; Z (set); Integer numbers; Ring of rational integers; Intger
['?nt?d??]
¦ noun
1. a whole number.
2. a thing complete in itself.
Origin
C16: from L., 'intact, whole', from in- (expressing negation) + the root of tangere 'to touch'; cf. entire.
Gaussian integer
COMPLEX NUMBER WHOSE REAL AND IMAGINARY PARTS ARE BOTH INTEGERS
Gauss prime; Gaussian prime; Gaussian integers; Gaussian prime number; Complex integers; Complex integer; Gaussian ring; Gaussian primes
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as .
Википедия
Church encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way.
Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function.
