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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 31   Last Post: Oct 3, 2017 3:02 AM

 Messages: [ Previous | Next ]
 netzweltler Posts: 473 From: Germany Registered: 8/6/10
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 2, 2017 8:53 AM

Am Montag, 2. Oktober 2017 13:12:21 UTC+2 schrieb FromTheRafters:
> netzweltler explained on 10/2/2017 :
> > 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.

>
> Why would I need to do that?

If there is no such step, then there is no reason to assume that we reach point 1.

> e raised to the pi times i equals -1 exactly without my needing to
> explain what the ellipses means in the 3.1415... or 2.71828... decimal
> representations. Those representations are of numbers not strictly
> procedures for approximations of numbers.
>
> Were they only meant to be procedures then I could substitute division
> by zero with division by 'e to the pi times i plus one' and avoid ever
> dividing by zero again since pi and e could *only* be approximated. You
> see then that everything in calculus would be an approximation under
> this scenario.
>
> Of course, some people think that this is already the case.

Date Subject Author
9/30/17 mitchrae3323@gmail.com
9/30/17 netzweltler
9/30/17 FromTheRafters
9/30/17 mitchrae3323@gmail.com
10/1/17 netzweltler
10/1/17 mitchrae3323@gmail.com
10/1/17 jsavard@ecn.ab.ca
10/1/17 mitchrae3323@gmail.com
10/2/17 netzweltler
10/2/17 Jim Burns
10/2/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 Me
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/3/17 netzweltler
10/2/17 FromTheRafters
10/2/17 jsavard@ecn.ab.ca
10/2/17 netzweltler