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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 10:00 AM

Am Donnerstag, 5. Oktober 2017 15:22:35 UTC+2 schrieb Jim Burns:
> On 10/4/2017 3:58 PM, netzweltler wrote:
>

> > While it is true that there is no line on the list
> > 0 |-> write 0.9
> > 1 |-> append another 9
> > 2 |-> append another 9
> > ...
> > that produces other than a finite string, it is true that
> > the complete list produces an infinite string.
> > "We are dealing with infinitely many finite stepwise processes"
> > is true for each line of the list.
> > "we are dealing with an infinite stepwise process" is true
> > for the complete list. We wouldn't get the resulting
> > 0.999... otherwise.

>
> This is backwards. The finite initial segments
> 0.9, 0.99, 0.999, ...
> _do not_ result in the infinite decimal
> 0.999...
>
> We have the infinite decimal _first_ , and then we trim it
> to finite length, operate on the finite decimals in the
> familiar way, and define the unique least upper bound of
> all of the finite sums as the value of the infinite decimal.
>
> _We don't do what you're describing_

Nevertheless, 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.

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
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10/9/17 Jim Burns
10/9/17 netzweltler
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