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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: 460
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 3:15 PM
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Am Dienstag, 3. Oktober 2017 14:20:11 UTC+2 schrieb FromTheRafters:
> netzweltler brought next idea :
> > 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
> >>>>>> your meaning, than that is your problem, not ours.

> >>>
> >
> > 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...

>
> But 0.999 repeating is a rational number, no need for repeating
> decimals at all in the naturals. Repeating zeros is okay I guess, but
> why use them in the naturals. In the rationals and reals, repeating
> zeros are called 'terminating' decimal expansions and the trailing
> zeros are elided.


I'm not sure if you got what I meant. Let me rephrase it:

The meaning of "..." is absolutely clear in this context and we both know that there is a nth decimal place for each n ? N in 0.999...



Date Subject Author
10/2/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Guest
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
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
bursejan@gmail.com
10/4/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/3/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/4/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/4/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/4/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/5/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/6/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/6/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/7/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/8/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
FromTheRafters
10/8/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/8/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/8/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/8/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/9/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/9/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/9/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
netzweltler
10/9/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns
10/7/17
Read Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...
Jim Burns

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