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  1. „Ein Beitrag zur Mannigfaltigkeitslehre”. Journ. für Math. Bd. 84, 1878, pp. 242–258; cf. Math. Ann. Bd. 46, 1895, p. 494. Fundamentally the same method was used by Cantor („Über eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen” (Journ. für Math. Bd. 77, 1874, pp. 258–263) in proving the enumerability of the aggregate of real algebraic numbers. Cantor (see Bernstein, „Untersuchungen aus der Mengenlehre”, Diss. Göttingen, Halle a. S., 1901, p. 49; or, in the reprint, with corrections and additions, in Math. Ann. Bd. 61, 1905, pp. 150–151) has indicated that his theorem can be generalised into one on the multiplication of any Alephs, but he neither gave a proof nor mentioned the difficulty about the «multiplicative axiom» (which can be overcome, in this case).

  2. The meaning of this phrase is that the termu μ,v in the double series (u μ,v ) is theλ th term counted, where\(\lambda = \frac{1}{2}(\mu + v - 1) (\mu + v - 2){ + }\mu \) Cf. Jourdain, ‘On Unique, Non-Repeating, Integer-Functions’, Mess. of Math., May 1901.

  3. „Grundbegriffe der Mengenlehre”, Göttingen 1906, pp. 106–109. On p. 109, Hessenberg stated that Zermelo had also communicated a proof of (6) to him which, since it is essentially different from his own, will be published elsewhere.

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Jourdain, P.E.B. The multiplication of Alephs. Math. Ann. 65, 506–512 (1908). https://doi.org/10.1007/BF01451166

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