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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 5, 2017 3:12 PM

Am Donnerstag, 5. Oktober 2017 17:59:25 UTC+2 schrieb Jim Burns:
> On 10/5/2017 10:00 AM, netzweltler wrote:
> > Am Donnerstag, 5. Oktober 2017 15:22:35 UTC+2
> > schrieb Jim Burns:

>
> [...]

> >> _We don't do what you're describing_
> >
> > Nevertheless,

>
> "Nevertheless"?
> Do you agree that what you're describing is not what we're doing?
>

> > the process
> > 0 |-> write 0.9
> > 1 |-> append another 9 (to the 0.9 already written)
> > 2 |-> append another 9 (to the 0.99 already written)
> > ...
> > results in 0.999...
> >
> > Whereas the process you specified earlier
> > 0 |-> 0.9
> > 1 |-> 0.99
> > 2 |-> 0.999
> >  ...
> > is nothing else but an infinite list of terminating decimals.

>
> Right. Nothing else but an infinite list of terminating decimals,
> which presents no problem, right?
>
> And we (meaning _we_ whether or not you include yourself)
> assign the value of the least upper bound of that list
> to the non-terminating decimal 0.999...
>
> I'm guessing you don't have a problem with the LUB either,
> _But this is what we do_

We obviously agree that the process you specified earlier
0 |-> 0.9
1 |-> 0.99
2 |-> 0.999
...
is nothing else but an infinite list of terminating decimals.

What you don't want to see is, that the process
0 |-> write 0.9
1 |-> append another 9 (to the 0.9 already written)
2 |-> append another 9 (to the 0.99 already written)
...
results in 0.999...

Maybe you cannot see that I am not writing a new number in a new line at each step - as in your process. I am appending the 9s in the same line. So I am not creating an infinite list of terminating decimals. I am creating a single non-terminating decimal. The append operations are representing addition operations - infinitely many addition operations.

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
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10/3/17 netzweltler
10/3/17 Jim Burns
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10/4/17 netzweltler
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