netzweltler
Posts:
473
From:
Germany
Registered:
8/6/10
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Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Posted:
Oct 2, 2017 2:45 AM
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Am Sonntag, 1. Oktober 2017 17:45:39 UTC+2 schrieb FromTheRafters:
> netzweltler formulated the question :
> > Am Sonntag, 1. Oktober 2017 15:20:16 UTC+2 schrieb FromTheRafters:
> >> After serious thinking netzweltler wrote :
> >>> Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
> >>>>
> >>>> It seems counterintuitive when a number is viewed (or represented) as
> >>>> an infinite unending 'process' of achieving better and better
> >>>> approximations, and that we can never actually reach the destination
> >>>> number. In my view, this sequence and/or infinite sum is a
> >>>> representation of the destination number "as if" we could have gotten
> >>>> there by that process.
> >>> If the process doesn't get us there then we don't get there. Where do you
> >>> get your "as if" from?
> >>
> >> If you had sufficient time, then you would get there.
> > Show how time is involved in our process.
>
> If you have to add a next number (like one quarter) to a previous
> result of adding such previous numbers (like one plus one half) then
> you have introduced time. Thee is a 'previous' calculation needed as
> input to the next calculation. The idea that you 'never' get there (to
> two) introduces time also. I'm with you, I don't think time has any
> place in this.
>
> >>>> IOW "*After* infinitely many 'better'
> >>>> approximations" we reach the destination number *exactly* even if we
> >>>> cannot 'pinpoint' that number on the number line.
> >>> Please define "*After* infinitely many 'better' approximations". All we've
> >>> got is infinitely many approximations - each approximation telling us that
> >>> we get closer to 1 but don't reach 1. There is no *after* specified in
> >>> this process.
> >>
> >> There is also no "time" mentioned, so why is there an assumption of a
> >> process which takes time to complete? It is already completed (pi
> >> exists as a number despite our inability to pinpoint it on the number
> >> line by using an infinite alternating sum or any of the other infinite
> >> processes) we just can't pinpoint it because we exist in a time
> >> constrained universe with processes which take time to complete.
> > If you insist on introducing time to our process, try this:
>
> You misunderstand me. I'm not insisting that, in fact I insist the
> opposite. I take the infinite sequence or series representation to be
> just that, a represenation of a number -- not a process at all. This
> avoids the idea that time is a constraint against a number being exact.
>
> When it come to application, then you may have to consider the
> indicated process and get as close an approximation as you desire. The
> representations 0.999... and the infinite series or the sequences
> related to it, are all just different representations of the number
> one, just as our current representation are all representations of the
> number two. Time has nothing at all to do with it, hence there is no
> 'almost, but not quite there' to worry about.
Correct. Time is of no concern. So, let me modify the list:
t = 0: write 0.9
t = 0.9: append another 9
t = 0.99: append another 9
...
to
1. write 0.9
2. append another 9
3. append another 9
...
Do you still agree that this is a _complete_ list of all the actions needed to write 0.999... (already present - in no time)? It is a list of additions as well. All the additions it takes to sum up to 0.999...
Again the question:
If your claim is, that we reach point 1, you need to show which step on this list of infinitely many steps accomplishes that.
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