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.