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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: 8,155 Registered: 7/9/08
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 5, 2017 2:22 PM

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.

Dan