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  2. Ordered Bell number - Wikipedia

    en.wikipedia.org/wiki/Ordered_Bell_number

    In contrast, when items are ordered or ranked in a way that does not allow ties (such as occurs with the ordering of cards in a deck of cards, or batting orders among baseball players), the number of orderings for items is a factorial number!, [27] which is significantly smaller than the corresponding ordered Bell number.

  3. Ordinal numeral - Wikipedia

    en.wikipedia.org/wiki/Ordinal_numeral

    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 ...

  4. Order (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Order_(mathematics)

    Lexicographical order, an ordering method on sequences analogous to alphabetical order on words; List of order topics, list of order theory topics; Order theory, study of various binary relations known as orders; Order topology, a topology of total order for totally ordered sets; Ordinal numbers, numbers assigned to sets based on their set ...

  5. Order type - Wikipedia

    en.wikipedia.org/wiki/Order_type

    Every well-ordered set is order-equivalent to exactly one ordinal number, by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. Order types thus often take the form of arithmetic expressions of ordinals.

  6. Ordinal number - Wikipedia

    en.wikipedia.org/wiki/Ordinal_number

    Cantor called the set of finite ordinals the first number class. The second number class is the set of ordinals whose predecessors form a countably infinite set. The set of all α having countably many predecessors—that is, the set of countable ordinals—is the union of these two number classes. Cantor proved that the cardinality of the ...

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  8. Ordinal notation - Wikipedia

    en.wikipedia.org/wiki/Ordinal_notation

    If a Gödel numbering is fixed, then the subset relation on the ordinals induces an ordering on well-formed formulae which in turn induces a well-ordering on the subset of natural numbers. A recursive ordinal notation must satisfy the following two additional properties: the subset of natural numbers is a recursive set

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