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Topic: Finally the discussion is over: S = Lim S is a bad definition.
Replies: 3   Last Post: Oct 5, 2017 2:28 PM

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 Dan Christensen Posts: 7,671 Registered: 7/9/08
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 5, 2017 2:28 PM

On Thursday, October 5, 2017 at 2:22:40 PM UTC-4, Dan Christensen wrote:
> On Thursday, October 5, 2017 at 1:22:37 PM UTC-4, John Gabriel wrote:
>

> > >
> > > 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.

> >
> > Yes, S = Lim S. Clear as water.
> >

>
> Wrong again, Troll Boy. That should be:
>
> S = Lim(n-->oo): S_n
>
> where S_n = 1 - 1/10^n (the nth partial sum)
>
> S_1 = 0.9
> S_2 = 0.99
> S_3 = 0.999
>
> and so on.

Or equivalently, S_n = Sum(k=1,n): 9/10^k

>
> Dan
>