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In German, it is not and never was ambiguous, so it is not a mistranslation. What the meaning of "Whole number" in English is, is not really relevant, except fo
by auggierose 3y ago
In German, it is not and never was ambiguous, so it is not a mistranslation. What the meaning of "Whole number" in English is, is not really relevant, except for explaining the mistake in the book.
- Someone 3y ago> In German, it is not and never was ambiguous I’m not sure about that ”and never was”. Mathematicians used to have fairly loose definitions for all kinds of things and different fields sometimes have incompatible definitions for a term, so I think it’s not impossible “ganzzahlig” was used ambiguously for ℤ or ℕ (in- or excluding zero) for a while in some corners. When was the phrase “natural number” even invented? The best I can find is https://jeff560.tripod.com/n.html https://jeff560.tripod.com/n.html (via https://mathoverflow.net/questions/379699/origin-of-phrase-natural-number https://mathoverflow.net/questions/379699/origin-of-phrase-n...) which says “Chuquet (1484) used the term progression naturelle for the sequence 1, 2, 3, 4, etc.” There may well have been a time where “ganzzahlig” existed but “Natürliche Zahl” didn’t yet.
- auggierose 3y agoThis comment goes as far back as Euler and 1767: https://news.ycombinator.com/item?id=39917278 https://news.ycombinator.com/item?id=39917278