
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted:
Oct 3, 2017 8:32 PM


Well its the mean value between 0.999... and 1.0. Look if we have a and b, the mean value is (a+b)/2:
a b (a+b)/2 0.9 1.0 0.95 0.99 1.00 0.995 0.999 1.000 0.9995 0.9999 1.0000 0.99995 Etc..
If 0.999... <> 1, then also 0.999... <> 0.999...9995 and then also 0.999...9995 <> 1.
And so on, as soon 0.999... <> 1, there are miriad other numbers inbetween.
My suggestion: Don't do this nonsense, just interpret 0.999... as limit. Then you can also interpret
0.999..9995 as limit, namely this charming limit, the following summands summed up to finity:
0.5 0.45 0.045 0.0045 ...
Guess what is the result?
1/2+sum_i=1^n (45/10^(i+1)) = 1/2 + (1  10^(n))/2
lim n>oo 1/2 + (1  10^(n))/2 = 1
Am Mittwoch, 4. Oktober 2017 02:24:32 UTC+2 schrieb burs...@gmail.com: > So whats this Gabriel number: > > lim n>oo 0.999...9995 = ? > \n/ > > Am Mittwoch, 4. Oktober 2017 02:08:09 UTC+2 schrieb burs...@gmail.com: > > So if 0.999... <> 1, do we have: > > > > 0.999... < 1 > > > > Or rather? > > > > 0.999... > 1 > > > > Am Mittwoch, 4. Oktober 2017 01:40:31 UTC+2 schrieb John Gabriel: > > > > nonsense. Right. But this was clear from the beginning. > > > > > > Yes. Of course S = Lim S is nonsense. So why do you still believe in it?

