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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
Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...
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.
1.3 Ordinal numerals + -ārius. 1.4 Plūrāle tantum numerals. 1.5 Distributive numerals. ... Except for the numbers 1, 3, and 4 and their compounds, ...
The ordinal catgegory 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.
If β = ω λ m + ω μ n + smaller terms, then β = (ω μ n + smaller terms)(ω λ−μ + 1)m is a product of a smaller ordinal and a prime and a natural number m. Repeating this and factorizing the natural numbers into primes gives the prime factorization of β. So the factorization of the Cantor normal form ordinal ω α 1 n 1 + ⋯ + ω α ...
The standard definition of ordinal exponentiation with base α is: =, =, when has an immediate predecessor . = {< <}, whenever is a limit ordinal. From this definition, it follows that for any fixed ordinal α > 1, the mapping is a normal function, so it has arbitrarily large fixed points by the fixed-point lemma for normal functions.
Cardinal versus ordinal numbers Cardinal Ordinal zero: 0 ground??? one: 1 first: 1st two: 2 second: 2nd three: 3 third: 3rd four: 4 fourth: 4th five: 5 fifth: 5th six
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