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Что (кто) такое ordinals - определение
INFINITE ORDINAL NUMBER CLASS
Limit ordinals
Найдено результатов: 46
Ordinal
WIKIMEDIA DISAMBIGUATION PAGE
Ordinals; Ordinally; Ordinal (disambiguation)
·noun A book containing the rubrics of the Mass.
II. Ordinal ·noun A word or number denoting order or succession.
III. Ordinal ·adj Of or pertaining to an Order.
IV. Ordinal ·adj Indicating order or succession; as, the ordinal numbers, first, second, third, ·etc.
V. Ordinal ·noun The book of forms for making, ordaining, and consecrating bishops, priests, and deacons.
ordinal
WIKIMEDIA DISAMBIGUATION PAGE
Ordinals; Ordinally; Ordinal (disambiguation)
<mathematics> An isomorphism class of well-ordered sets.
(1995-03-10)
ordinal
WIKIMEDIA DISAMBIGUATION PAGE
Ordinals; Ordinally; Ordinal (disambiguation)
¦ noun
1. short for ordinal number.
2. Christian Church, historical a service book, especially one with the forms of service used at ordinations.
¦ adjective
1. relating to order in a series.
2. Biology relating to a taxonomic order.
Origin
ME: the noun from med. L. ordinale; the adjective from late L. ordinalis 'relating to order', from L. ordo, ordin- (see order).
Edwardine Ordinals
![Elizabeth I was required to strike a ''[[via media]]'' between Reformation and Catholic impulses.](https://commons.wikimedia.org/wiki/Special:FilePath/Elizabeth-I-Allegorical-Po.jpg?width=200 "Elizabeth I was required to strike a ''[[via media]]'' between Reformation and Catholic impulses.")
.jpg?width=200 "Pope Leo XIII declared Anglican orders \"absolutely null and utterly void\" in 1896 (''Apostolicae curae'').")
![illuminated]] Roman Pontifical](https://commons.wikimedia.org/wiki/Special:FilePath/Pontificale cracoviense (64094977).jpg?width=200 "illuminated]] Roman Pontifical")
TWO 16TH-CENTURY CHURCH OF ENGLAND LITURGICAL BOOKS
Edwardine Ordinal; 1550 ordinal; 1552 ordinal; Edwardian ordinals; Anglican ordinal
The Edwardine Ordinals [may also be used (though this latter spelling typically refers to Edward VII]). Ordinal itself is an [[anachronism with regards to the Edwardine Ordinals, as the word was not first applied to such texts until the 17th century.
Even and odd ordinals
Even ordinal; Odd and even ordinals; Odd ordinal
In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers. They are useful in some transfinite induction proofs.
Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ.
Nonrecursive ordinal
THE ORDER TYPE OF THE SET OF ALL RECURSIVE ORDINALS
Church-Kleene ordinal; Church ordinal; Kleene ordinal; Church–Kleene ordinal; Unrecursive ordinals; Nonrecursive ordinals
In mathematics, particularly set theory, non-recursive ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using ordinal collapsing functions.
Ordinal arithmetic
DESCRIBES THE THREE USUAL OPERATIONS ON ORDINAL NUMBERS: ADDITION, MULTIPLICATION, AND EXPONENTIATION
Cantor normal form; Ordinal addition; Ordinal exponentiation; Ordinal multiplication; Arithmetic of ordinals; Product of ordinals; Transfinite arithmetic; Hessenberg sum; Natural sum of ordinals; Natural product of ordinals; Prime ordinal; Hessenberg product; Cantor normal form theorem; Natural operation (ordinal arithmetic)
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion.
ordinal number
ORDER TYPE OF A WELL-ORDERED SET
Ordinal numbers; Von Neumann ordinal; Ordinal Number; Ordinal (mathematics); Transfinite ordinal number; Transfinite ordinal numbers; Finite ordinal number; Ordinal number (finite); Transfinite sequence; Ω (ordinal number); Ordinal number (mathematics); O (ordinal number); Ordinal number (set theory); Least infinite ordinal; Second number class; First number class; Omega (set theory); Ω+1; First infinite ordinal; First infinite ordinal number; Countable ordinals; Countable ordinal; Von Neumann definition of ordinals; Von Neumann encoding; Number class; Omega (ordinal); Von Neumann ordinals
¦ noun a number defining a thing's position in a series, such as 'first' or 'second'.
ordinal number
ORDER TYPE OF A WELL-ORDERED SET
Ordinal numbers; Von Neumann ordinal; Ordinal Number; Ordinal (mathematics); Transfinite ordinal number; Transfinite ordinal numbers; Finite ordinal number; Ordinal number (finite); Transfinite sequence; Ω (ordinal number); Ordinal number (mathematics); O (ordinal number); Ordinal number (set theory); Least infinite ordinal; Second number class; First number class; Omega (set theory); Ω+1; First infinite ordinal; First infinite ordinal number; Countable ordinals; Countable ordinal; Von Neumann definition of ordinals; Von Neumann encoding; Number class; Omega (ordinal); Von Neumann ordinals
(ordinal numbers)
An ordinal number or an ordinal is a word such as 'first', 'third', and 'tenth' that tells you where a particular thing occurs in a sequence of things. Compare cardinal number
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N-COUNT
Википедия
Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ. Every ordinal number is either zero, or a successor ordinal, or a limit ordinal.
For example, ω, the smallest ordinal greater than every natural number is a limit ordinal because for any smaller ordinal (i.e., for any natural number) n we can find another natural number larger than it (e.g. n+1), but still less than ω.
Using the von Neumann definition of ordinals, every ordinal is the well-ordered set of all smaller ordinals. The union of a nonempty set of ordinals that has no greatest element is then always a limit ordinal. Using von Neumann cardinal assignment, every infinite cardinal number is also a limit ordinal.
