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Re: [HM] The word "Anzahl" (number)
Posted:
Jan 27, 2004 10:12 AM
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On Jan 19, 2004, at 5:57 AM, Peter Flor wrote:
> Actually, for a mathematician "Anzahl" could always correctly be
> translated by "cardinality".
Cantor did not use it that way: rather he used it to refer to counting
number, so that in the case of infinite sets, the anzahl depends on
the particular well-ordering. Hallett (Cantorian Set Theory and
Limitations of Size) translated it as ``enumeral'', but then , as I
recall and in any case I think wrongly, identified the anzahlen with
the ordinal numbers and there with Cantor's transfinite numbers. Cantor
used the term ``power' in his early work for cardinality. Many other
writers in the same period seem to have used anzahl for counting
number.
Frege on the other hand did use it for cardinal number.
Best regards,
Bill Tait
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