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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

Replies: 40   Last Post: Jan 4, 2018 7:37 AM

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 FromTheRafters Posts: 248 Registered: 12/20/15
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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