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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

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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 1:54 PM
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Am Montag, 2. Oktober 2017 16:15:47 UTC+2 schrieb FromTheRafters:
> on 10/2/2017, netzweltler supposed :
> > 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.

>
> If you assume that it is a stepwise process to approach a number, then
> of course it is a stepwise process to approach a number. I can't argue
> against a stipulation like that from within the system which you insist
> I use, which in turn stipulates that assumption.
>
> The number pi can be represented as a process (actually many equivalent
> ones) like you stipulate, and the 'process' can never be completed
> because of the 'infinite steps' aspect. Nevertheless pi is an exact
> number. Only when you leave out the 'ad infinitum' part does it become
> a only a rational approximation.
>
> Algebraically, different 'infinite stepwise process' forms of pi's
> representation can exactly cancel with other representations, or
> interact with other numbers (like e) *exactly* without any need
> whatsoever to calculate using the 'infinite stepwise processes' you
> seem to be insisting on.
>
> The number pi is already there, you don't have to approach it in
> discreet steps. Same with 0.999... and 1.000... -- they are just
> different representations of the number one.


Yes. pi is already there and we can exactly locate its position on the number line, but you cannot locate a point on the number line representing pi if this point would be the result of a stepwise process - neither a finite process nor an infinite.


Date Subject Author
9/30/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
mitchrae3323@gmail.com
9/30/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
9/30/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
9/30/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
mitchrae3323@gmail.com
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
mitchrae3323@gmail.com
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
jsavard@ecn.ab.ca
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
mitchrae3323@gmail.com
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/1/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
bursejan@gmail.com
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Me
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
bursejan@gmail.com
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
bursejan@gmail.com
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
bursejan@gmail.com
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
jsavard@ecn.ab.ca
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler

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