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

Replies: 42   Last Post: Oct 9, 2017 11:53 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 3, 2017 3:21 AM

Am Dienstag, 3. Oktober 2017 03:22:11 UTC+2 schrieb Jim Burns:
> On 10/2/2017 2:47 PM, netzweltler wrote:
> > 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 + ... ?

>
> Your '...' is not usable. If we say what we _really_ mean,
> in a manner clear enough to reason about, then the '...'
> disappears. Also, what we are left with are finitely many
> statements of finite length. You will not find infinitely
> many commands in those finitely-many, finite-length
> statements.
>
> We sometimes write the set of natural numbers as
> { 0, 1, 2, 3, ... }
> The '...' is informal. We do not use '...' in our reasoning,
> we use a correct description of what the '...' stands for.
>
> Do you see '...' anywhere in the following?
>
> The set N contains 0, and for every element x in N, its
> successor Sx is in N.
>
> This is true of N but not true of any _proper_ subset of N.
>
> _Therefore_ , if we can prove that B is a subset of N
> which contains 0 and which, for element x of B, contains Sx,
> then B is not a _proper_ subset of N.
>
> B nonetheless is a subset of N, we just said so. The only subset
> of N which B can be is N. Therefore, B = N.
>
> This is finite reasoning about the infinitely many elements
> in N. Note that there is no '...' in it.
>
> I could continue and derive 0.999... = 1 from our definitions,
> and nowhere in that derivation will be '...'. There will not be
> infinitely many commands in it either.
>

> >> 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

> >

Sorry, no. The meaning of "..." is absolutely clear in this context and we both know that there is a decimal place for each n ? N in 0.999...

Date Subject Author
10/2/17 Guest
10/2/17 netzweltler
10/2/17 Jim Burns
10/3/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 bursejan@gmail.com
10/4/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 Jim Burns
10/4/17 netzweltler
10/4/17 Jim Burns
10/4/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 FromTheRafters
10/6/17 netzweltler
10/6/17 Jim Burns
10/7/17 FromTheRafters
10/8/17 FromTheRafters
10/8/17 netzweltler
10/8/17 Jim Burns
10/8/17 netzweltler
10/8/17 Jim Burns
10/9/17 netzweltler
10/9/17 Jim Burns
10/9/17 netzweltler
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