Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Messages: [ Previous | Next ]
 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: Matheology § 258
Posted: May 1, 2013 5:31 PM

On May 1, 11:18 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 1 Mai, 18:27, Dan <dan.ms.ch...@gmail.com> wrote:
>

> > They have similar formulas,but behave in different ways .
> > You would be correct in affirming that  b_inf = 1/9 is not part of the
> > list .

>
> Of course. It is not part of the list, because it cannot be written as
> decimal number. Proof: All decimal numbers that can be written in this
> form *are already in the list*. And there is no reason why 1/9 should
> be missing, if it could be a decimal fraction.
>

> > If it were part of the list , then a_inf would be a well-behaved
> > natural number , but it isn't .

>
> It is neither well behaved nor a natural number. The sequence 0.111...
> does not exist other than by a finite name or formula.
>

> > Limits only work properly with real numbers, not natural numbers .
>
> Yes, that is true. But (and please read this very attentively!):
> Cantor's argument requires the existence of the complete sequence
> 0.111.... in digits:
>
> You can see this easily here:
>
> The list
>
> 0.0
> 0.1
> 0.11
> 0.111
> ...
>
> when replacing 0 by 1 has an anti-diagonal, the FIS of which are
> always in the next line. So the anti-diagonal is not different from
> all lines, unless it has an infinite sequence of 1's. But, as we just
> saw, this is impossible.
>
> Regards, WM

I see no significant difference between referring to a mathematical
object by a formula and referring to it by 'writing it down' .
Writing it down , when possible , is just another formula for it.
"1296" , and "36 * 36" , are both references to the same object ,
and neither of them is "more true of a name" for the object than the
other .

Just like "1296" is "36 * 36" , and we can substitute one for another
in mathematical expressions , and maintain their truth ,
so is "1/9" the same as "0. the infinite sequence of 1's" . That we
cannot truly write down the name of the second expression is of no
relevance. The most important point is that 'names for the same
object , whether finite or infinite, are fully interchangeable'

Since
"0. the infinite sequence of 1's" is the same as "1/9" then

"The third digit of 0. the infinite sequence of 1's" is the same as
"The third digit of 1/9" is the same as "1" .

Same object . Different names .Since we treat all possible names of
the object the same , whether it be "a formula for the object" , or an
"enumeration of its digits" , we never run into problems. And in every
name for an object we can recover every other name, if we so wish .

"1+3" = " 2+2" = "3+1" = "8-4" = "2*2" = "4" = "00 ..... 04"

"A rose by any other name would smell as sweet"

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
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 JT
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Ed Prochak
5/2/13 Virgil
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 dan.ms.chaos@gmail.com
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Virgil
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 Virgil
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 ross.finlayson@gmail.com
5/5/13 LudovicoVan
5/5/13 fom
5/5/13 ross.finlayson@gmail.com
5/5/13 ross.finlayson@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 dan.ms.chaos@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 fom
5/4/13 Virgil
5/4/13 ross.finlayson@gmail.com
5/4/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/4/13 trj
5/4/13 Virgil
5/3/13 Virgil
5/3/13 Virgil
5/3/13 fom
5/3/13 dan.ms.chaos@gmail.com
5/3/13 fom
5/3/13 gus gassmann
5/3/13 Virgil
5/2/13 Virgil
5/1/13 Virgil
5/1/13 JT
5/1/13 Virgil
5/1/13 JT
5/1/13 Bergholt Stuttley Johnson
5/1/13 rt servo
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
4/30/13 Virgil
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
4/29/13 ross.finlayson@gmail.com
4/29/13 Virgil