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- Successor_ordinal abstract "In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal. Every ordinal other than 0 is either a successor ordinal or a limit ordinal.Using von Neumann's ordinal numbers (the standard model of the ordinals used in set theory), the successor S(α) of an ordinal number α is given by the formulaSince the ordering on the ordinal numbers α < β if and only if α ∈ β, it is immediate that there is no ordinal number between α and S(α), and it is also clear that α < S(α). The successor operation can be used to define ordinal addition rigorously via transfinite recursion as follows:and for a limit ordinal λIn particular, S(α) = α + 1. Multiplication and exponentiation are defined similarly.The successor points and zero are the isolated points of the class of ordinal numbers, with respect to the order topology.".
- Successor_ordinal wikiPageID "375256".
- Successor_ordinal wikiPageRevisionID "582655838".
- Successor_ordinal hasPhotoCollection Successor_ordinal.
- Successor_ordinal subject Category:Ordinal_numbers.
- Successor_ordinal type Abstraction100002137.
- Successor_ordinal type DefiniteQuantity113576101.
- Successor_ordinal type Measure100033615.
- Successor_ordinal type Number113582013.
- Successor_ordinal type OrdinalNumber113597280.
- Successor_ordinal type OrdinalNumbers.
- Successor_ordinal comment "In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal.".
- Successor_ordinal label "Nachfolger (Mathematik)".
- Successor_ordinal label "Następnik liczby porządkowej".
- Successor_ordinal label "Ordinal successeur".
- Successor_ordinal label "Successor ordinal".
- Successor_ordinal label "后继序数".
- Successor_ordinal sameAs Izolovaný_ordinál.
- Successor_ordinal sameAs Nachfolger_(Mathematik).
- Successor_ordinal sameAs Ordinal_successeur.
- Successor_ordinal sameAs 따름서수.
- Successor_ordinal sameAs Następnik_liczby_porządkowej.
- Successor_ordinal sameAs m.020ylh.
- Successor_ordinal sameAs Q1191286.
- Successor_ordinal sameAs Q1191286.
- Successor_ordinal sameAs Successor_ordinal.
- Successor_ordinal wasDerivedFrom Successor_ordinal?oldid=582655838.
- Successor_ordinal isPrimaryTopicOf Successor_ordinal.