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For example, the cofinality of ω 2 is ω, because the sequence ω·m (where m ranges over the natural numbers) tends to ω 2; but, more generally, any countable limit ordinal has cofinality ω. An uncountable limit ordinal may have either cofinality ω as does ω ω {\displaystyle \omega _{\omega }} or an uncountable cofinality.
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.
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 ...
In written languages, an ordinal indicator is a character, or group of characters, following a numeral denoting that it is an ordinal number, rather than a cardinal number. Historically these letters were "elevated terminals", that is to say the last few letters of the full word denoting the ordinal form of the number displayed as a superscript .
In other words, every ordinal number α can be uniquely written as + + +, where k is a natural number, and … are ordinal numbers. Another variation of the Cantor normal form is the "base δ expansion", where ω is replaced by any ordinal δ > 1 , and the numbers c i are nonzero ordinals less than δ .
Every ordinal number is either zero, a successor ordinal, or a limit ordinal. For example, the smallest limit ordinal is ω, the smallest ordinal greater than every natural number. This 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 ...
For example, characters are ordinal because we can call 'A' the first character, 'B' the second, etc. The term is often used in programming for variables that can take one of a finite (often small) number of values.
Pages in category "Ordinal numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...