论无理数

On the Irrationals

将完全k方数的概念由N推广到R^+,从而,得到一个很有用的引理,由之推出一系列有关无理数的命题.此外,关于2^(1/2)~(2^(1/2)),2^(1/2)~(2^(1/2))及α~β(α为≠0,1的代数数,而β乃不为有理数的代数数)的无理性的简单证明,也分别在此地给出.

The writer generalizes the notion of perfect k-power number from N to R^＋ , and by means of it obtains a very useful lemma out from which a series of propositions concerning the irrationals are drawn. Furthermore, simple proofs about the irrationality respectively of √2^√2, 2^√2 and α^β （α being an algebraic number≠0, 1, whilst β,an algebraic number not to be rational） are here given.