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Numbers may either precede or follow their noun (see Latin word order). Most numbers are invariable and do not change their endings: regnāvit Ancus annōs quattuor et vīgintī (Livy) [1] 'Ancus reigned for 24 years' However, the numbers 1, 2, 3, and 200, 300, etc. change their endings for gender and grammatical case.
The ordinal category are based on ordinal numbers such as the English first, second, third, which specify position of items in a sequence. In Latin and Greek, the ordinal forms are also used for fractions for amounts higher than 2; only the fraction 1 / 2 has special forms.
Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced.
Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers : Finite and infinite numbers used to describe the cardinalities of sets . Infinitesimals : These are smaller than any positive real number, but are nonetheless greater than zero.
The ordinal numbers are difficult to reconstruct due to their significant variation in the daughter languages. The following reconstructions are tentative: [ 20 ] "first" is formed with * pr̥h₃- (related to some adverbs meaning "forth, forward, front" and to the particle * prō "forth", thus originally meaning "foremost" or similar) plus ...
Cantor's work with derived sets and ordinal numbers led to the Cantor-Bendixson theorem. [14] Using successors, limits, and cardinality, Cantor generated an unbounded sequence of ordinal numbers and number classes. [15] The (α + 1)-th number class is the set of ordinals whose predecessors form a set of the same cardinality as the α-th
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