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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 ]
 FromTheRafters Posts: 248 Registered: 12/20/15
Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted: Oct 2, 2017 10:15 AM

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.

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