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About: Normal function     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:OrdinalNumber113597280, within Data Space : dbpedia.org associated with source document(s)

Type: yago:WikicatOrdinalNumbersyago:Abstraction100002137yago:DefiniteQuantity113576101yago:Measure100033615yago:Number113582013yago:OrdinalNumber113597280 New Facet based on Instances of this Class

In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if and only if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: 1. * For every limit ordinal γ (i.e. γ is neither zero nor a successor), it is the case that f(γ) = sup {f(ν) : ν < γ}. 2. * For all ordinals α < β, it is the case that f(α) < f(β).