Ordinals - ορισμός. Τι είναι το Ordinals
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Τι (ποιος) είναι Ordinals - ορισμός

INFINITE ORDINAL NUMBER CLASS
Limit ordinals

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).

Βικιπαίδεια

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.