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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

 Messages: [ Previous | Next ]
 Jim Burns Posts: 831 Registered: 9/26/15
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 5, 2017 8:54 PM

On 10/5/2017 3:12 PM, netzweltler wrote:
> 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?

*NETZWELTLER*
DO YOU AGREE THAT WHAT YOU'RE DOING
IS NOT WHAT WE'RE DOING?

I think you do agree.
This a pretty fundamental requirement:
When you criticize what someone is doing,
criticize _what they are doing_ and not something else.

>>> 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.

It think it is also obvious that you have no problem with
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

Suppose, for the sake of argument, that _everything_ that
you have said about what *you* mean by 0.999... is true.
Why does it matter, if it doesn't apply to what *we* mean
by 0.999... ?

*You* give a meaning to 0.999... that involves infinitely
many addition operations, and then *you* find a problem with
the meaning that *you* gave 0.999... -- a meaning which is
*NOT* the meaning *we* give to 0.999... So what?

I mean, fine. Whatever. Let me grant, for the sake of argument,
_every error_ that you point out about what *you* mean is
in fact an error. Whoopsie! We'll just have to fix that right
now: We "now" evaluate infinite decimals in a way that avoids
infinite multiplications, whatever they may be. End of problem.
_There is no problem_

Let me remind you what we're talking about:

<Burns<netzweltler>>

> Do you agree that 0.999... means infinitely many
> commands
> ...?

0.999... does not mean infinitely many commands.

</Burns<netzweltler>>

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
10/9/17 Jim Burns
10/7/17 Jim Burns