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José Carlos Santos wrote:
> zuhair wrote:
>
> >>> The only representation of 1 is 1.0000......... and to me
> >>> 0.9999........... < 1.
> >> Then you are wrong. If that expression represented a number strictly
> >> smaller than 1, call it x, then (1+x)/2 would be a number strictly
> >> smaller than 1, and strictly larger than x.
> >>
> >> What, pray tell, is the decimal representation of this number?
> >
> > How come I didn't read that post?
> >
> > Anyhow I should answer it.
> >
> > I will change your terminology.
> >
> > Let x = 1- 0.9999..............
>
> That's a rather strange way to answer to Arturo, since he told you to
> call _x_ to 0.9999... and you choose to call _x_ to 1 - 0.9999....
>
> > Now 1+ 0.99999... = 2 -x
> >
> > Now (2 - x)/2 = 2/2 - x/2
> >
> > now x/2= x
>
> How did you get that? But if you think (as I do) that this is a true
> statement, then the conclusion is, of course, that x = 0. Since you
> defined _x_ as 1 - 0.9999..., it follows that 1 = 0.999....
>
> Now, what about answering Arturo's question. If x = 0.9999..., what is
> the decimal representation of (1 + x)/2?
>
> Best regards,
>
> Jose Carlos Santos
I answered Arturo's question.
Let me repeat it again but I will use Arturo's terminology.
x= 0.9999.......
Let y = 1-x
it follows that x= 1-y
Now 1 + x = 1+ 1- y = 2 - y
Now y/2 = y
Then ( 1+x)/ 2 = (2-y)/2 = 1 -( y/2) = 1- y = x = 0.99999...........
You see the same number.
Zuhair
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