Date: Oct 2, 2017 2:47 PM
Author: netzweltler
Subject: Re: It is a very bad idea and nothing less than stupid to define 1/3<br> = 0.333...

Am Montag, 2. Oktober 2017 20:35:56 UTC+2 schrieb Jim Burns:
> On 10/2/2017 1:58 PM, netzweltler wrote:
> > Am Montag, 2. Oktober 2017 17:59:21 UTC+2 schrieb Jim Burns:
> >> On 10/1/2017 3:22 AM, netzweltler wrote:
>
> >>> Do you agree that 0.999... means infinitely many commands
> >>> Add 0.9 + 0.09
> >>> Add 0.99 + 0.009
> >>> Add 0.999 + 0.0009
> >>> ...?

> >>
> >> 0.999... does not mean infinitely many commands.

> >
> > But that's exactly what it means.

>
> That's not the standard meaning.


So, you disagree that

0.999... = 0.9 + 0.09 + 0.009 + ... ?

> You give it some other meaning, and then you find a problem
> with the meaning you gave it. Supposing I wanted to sort out
> what that other meaning was, and how to make sense of it, my
> attention to your meaning would not affect the standard meaning.
>
> I am not a math historian, but the impression I have
> is that great care was taken in choosing the standard meaning
> in order to avoid problems like the ones you are finding.
>
> You have the ability to create and then wallow in whatever
> problems you choose. No one is able to take that power away
> from you. But you can't "choose" by an act of your will to
> make your created problem relevant to what everyone else
> is doing. You are not the boss of us.
>

> > Infinitely many commands. Infinitely many additions.
> > Infinitely many steps trying to reach a point on the number line.
> >

> >> There is a set of results of certain finite sums, a set of
> >> numbers. We can informally write that set as
> >> { 0.9, 0.99, 0.999, ... }
> >> That is an infinite set, but we can give it a finite description.
> >>
> >> (Our finite description won't use '...'. The meaning of
> >> '...' depends upon it being obvious. If we are discussing
> >> what '...' means, it must not be obvious, so we ought to
> >> avoid using '...')
> >>
> >> There is number which is the unique least upper bound of that set.
> >> The least upper bound is a finite description of that number.
> >>
> >> 0.999... means "the least upper bound of the set
> >> { 0.9, 0.99, 0.999, ... }".
> >> That number can be show to be 1, by reasoning in a finite manner
> >> from these finite descriptions of what we mean.
> >>
> >> If you give 0.999... some meaning other than what we mean,
> >> and then it turns out there are problems of some sort with
> >> your meaning, than that is your problem, not ours.