Von Neumann Cardinal Assignment
22,99 €
inkl. MwSt.

Versandfertig in über 4 Wochen
payback
11 °P sammeln
  • Broschiertes Buch

High Quality Content by WIKIPEDIA articles! The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers. That such an ordinal exists and is unique is guaranteed by the fact that U is well-orderable and that the class of ordinals is well-ordered, using the axiom of replacement. With the full axiom of choice, every set is well-orderable, so every set has a cardinal; we order the cardinals using the inherited ordering from the ordinal numbers. This is readily found to coincide with the ordering via leq_c. This is a well-ordering of cardinal numbers. Each ordinal has an…mehr

Andere Kunden interessierten sich auch für
Produktbeschreibung
High Quality Content by WIKIPEDIA articles! The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers. That such an ordinal exists and is unique is guaranteed by the fact that U is well-orderable and that the class of ordinals is well-ordered, using the axiom of replacement. With the full axiom of choice, every set is well-orderable, so every set has a cardinal; we order the cardinals using the inherited ordering from the ordinal numbers. This is readily found to coincide with the ordering via leq_c. This is a well-ordering of cardinal numbers. Each ordinal has an associated cardinal, its cardinality, obtained by simply forgetting the order. Any well-ordered set having that ordinal as its order type has the same cardinality. The smallest ordinal having a given cardinal as its cardinality is called the initial ordinal of that cardinal. Every finite ordinal (natural number) is initial, but most infinite ordinals are not initial. The axiom of choice is equivalent to the statement that every set can be well-ordered, i.e. that every cardinal has an initial ordinal.