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In axiomatic set theory, a function ''f'' : Ord → Ord is called normal (or a normal function) iff it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: # For every limit ordinal γ (i.e. γ is neither zero nor a successor), ''f''(γ) = sup . # For all ordinals α < β, ''f''(α) < ''f''(β). == Examples == A simple normal function is given by ''f''(α) = 1 + α (see ordinal arithmetic). But ''f''(α) = α + 1 is ''not'' normal. If β is a fixed ordinal, then the functions ''f''(α) = β + α, ''f''(α) = β × α (for β ≥ 1), and ''f''(α) = βα (for β ≥ 2) are all normal. More important examples of normal functions are given by the aleph numbers which connect ordinal and cardinal numbers, and by the beth numbers . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Normal function」の詳細全文を読む スポンサード リンク
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