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

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 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: Matheology § 258
Posted: May 3, 2013 12:51 PM

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 .....

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
4/29/13 mueckenh@rz.fh-augsburg.de
4/29/13 Virgil
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
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5/1/13 mueckenh@rz.fh-augsburg.de
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5/1/13 Virgil
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