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Topic:
If you claim 0.999... is a rational number, then you must find p/q such that 0.999... = p/q. 12/26/2017
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Last Post:
Jan 4, 2018 7:37 AM




Re: If you claim 0.999... is a rational number, then you must find p/q such that 0.999... = p/q. 12/26/2017
Posted:
Dec 31, 2017 9:23 AM


WM wrote on 12/31/2017 : > Am Sonntag, 31. Dezember 2017 11:00:37 UTC+1 schrieb Zelos Malum: >>> Yes. Nobody has denied that. But since oo is no natural number you have not >>> a sum over terms with natural indices but the limit. >> >> Again, oo is a shorthand for the limit and the infinite sum is defiend as >> the limit. > > I agree. But the infinite sum, whether or not defined as the limit, *is* not > a limit.
True, it is not a limit. It is the limit of the sequence of partial sums not the infinite sum. The place you are headed, not the (partial)progress you have made toward it.
> A sum is the addition of summands  and that is rational for every > summand added. The adding does never stop, and the rational character of the > result does never stop.
It is the rational character of the *partial* sums that doesn't stop.
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