منابع مشابه
Some New Properties of Transfinite Ordinals
1 Presented to the Society, December 27, 1939. The author is indebted to Professor W. A. Hurwitz for his indispensable advice in the preparation of this paper. 2 W. Sierpinski, Leçons sur les Nombres Transfinis, Paris, 1928, p. 202; hereafter referred to as Sierpinski (I). The theorem was first stated for ordinals of the first and second ordinal class by G. Cantor, Beitrdge zur Begründung der t...
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Riemann’s theorems on the rearrangement of absolutely convergent and conditionally convergent series of real numbers are analysed within Bishop-style constructive mathematics. The constructive proof that every rearrangement of an absolutely convergent series has the same sum is relatively straightforward; but the proof that a conditionally convergent series can be rearranged to converge to what...
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This paper deals mainly with generalizations of results in nitary combinatorics to innnite ordinals. It is well-known that for nite ordinals P << is the number of 2-element subsets of an-element set. It is shown here that for any well-ordered set of arbitrary innnite order type , P << is the ordinal of the set M of 2-element subsets where M is ordered in some natural way. This result is then ex...
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Normal and composition series of groups enumerated by ordinal numbers are studied. The Jordan-Hölder theorem for them is proved.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1977
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270002342x