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Topic: Matheology � 258
Replies: 104   Last Post: May 5, 2013 2:26 PM

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 gus gassmann Posts: 60 Registered: 7/26/12
Re: Matheology § 258
Posted: May 3, 2013 3:30 PM

On 03/05/2013 1:51 PM, Dan wrote:
> On May 3, 6:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>> On 3 Mai, 08:45, Dan <dan.ms.ch...@gmail.com> wrote:
>>

>>> 1/9 = 0.1111 ..... (infinity ones) it's ALSO a valid continuous
>>> magnitude .

>>
>> It is a limit, but it has no decimal representation.
>>
>> If it had a decimal representation, then it would be in the following
>> list which contains all decimal representations with the digit 1
>> having a finite index.
>>
>> 0.1
>> 0.11
>> 0.111
>> ...
>>
>> Or can you determine a finite index which is not occupied by a 1?
>>
>> Being infinite is a valid mathematical notion, but it is not a means
>> to distinguish decimal representations. If there is a sequence of 1
>> larger than all sequences of the list (not only larger than every),
>> then let me know the difference by naming the indices. Otherwise stop
>> asserting unmathematical properties.
>>
>> Regards, WM

>
> Every real number ,in decimal representation , is an infinite
> sequence . But those on your list are followed by an infinity of
> zeroes :
> 0.1 .............
> 0.110000000 .....
> 0.111000000 .....

To avoid these artificial distinctions, it would be best to use the
infinite representations
0.099999...
0.109999...
0.110999...

> that we choose not to write , for convenience .If we are to understand
> the real numbers correctly , we must take this sequence as formally
> complete . Just as the natural numbers are complete, for every natural
> number n in existence , make a choice between
> 0 ,1 .... 9 . This choice will be the nth digit of your chosen real
> number . Because you can make a choice for 1 , a choice for 2, a
> choice for 3 , .... the completion of your choice process, the
> 'summation' of your choices , is the real number you choose . :
>
> r = 0.3 -> 0.31 -> 0.314 -> 0.3141 -> 0.31415 -> ....... =
> pi /10
>
> Each real number in your list is followed implicitly by an infinite
> amount of zeroes , just as the antidiagonal is followed explicitly by
> an infinite amount of ones .
>
> 0.10000000..... differs from
> 0.11111111..... =1/9 at the second digit .
>
> 0.11000000..... differs from
> 0.11111111..... = 1/9 at the third digit .
>
> 0.11100000..... differs from
> 0.11111111..... = 1/9 at the fourth digit .
>
> Real numbers (like pi , or e , or 1/9 ) have their decimal
> representation formally complete in actual infinity .
> Natural numbers decimal representation ranges only in potential
> infinity .
> If you don't like it, stick to natural numbers.
> That you can't write the full decimal representation of 1/9 doesn't
> change its existence . It has a lot of digits . And every . Single.One
> of them. Is 1 . You're saying black hole singularities (actual
> infinity) don't exist because we can't test them in the lab.
> It's effects DO exist (potential infinity) , the bending of light,
> because we can observe those . But "God" forbid we do an indirect
> derivation and maybe, just maybe , realize that the Universe is
> bigger that the inside of our mammalian heads .
>

Date Subject Author
4/29/13 Virgil
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