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In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any , we have The class of additively indecomposable ordinals (aka ''gamma numbers'') is sometimes denoted From the continuity of addition in its right argument, we get that if and α is additively indecomposable, then Obviously , since No finite ordinal other than is in Also, , since the sum of two finite ordinals is still finite. More generally, every infinite cardinal is in is closed and unbounded, so the enumerating function of is normal. In fact, The derivative (which enumerates fixed points of ''f''H) is written Ordinals of this form (that is, fixed points of ) are called ''epsilon numbers''. The number is therefore the first fixed point of the sequence == Multiplicatively indecomposable == A similar notion can be defined for multiplication. The multiplicatively indecomposable ordinals (aka ''delta numbers'') are those of the form for any ordinal α. Every epsilon number is multiplicatively indecomposable; and every multiplicatively indecomposable ordinal is additively indecomposable. The delta numbers are the same as the prime ordinals that are limits. 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「additively indecomposable ordinal」の詳細全文を読む スポンサード リンク
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