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Topic: Re: Matheology §019
Replies: 88   Last Post: Jun 6, 2012 10:59 PM

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 Jürgen R. Posts: 60 Registered: 7/5/11
Re: Matheology §019
Posted: Jun 2, 2012 11:25 AM

"Jürgen R." <jurgenr@arcor.de> schrieb im Newsbeitrag
news:4fca2f12\$0\$6552\$9b4e6d93@newsspool4.arcor-online.net...
>
>
> "WM" <mueckenh@rz.fh-augsburg.de> schrieb im Newsbeitrag

>> On 2 Jun., 15:06, Jürgen R. <jurg...@arcor.de> wrote:
>>> "WM" <mueck...@rz.fh-augsburg.de> schrieb im
>>>
>>>
>>>
>>>
>>>

>>> > On 2 Jun., 14:41, Jürgen R. <jurg...@arcor.de> wrote:
>>>
>>> >> One error is the belief that the complement of
>>> >> the union of closed sets must be open.
>>> >> Another error is the belief that if a set isn't open then
>>> >> it must be closed.

>>>
>>> > I do not require open or closed sets. Take any set that you believe to
>>> > exist.

>>>
>>> > If there is an irrational number in the complement (may it belong to
>>> > a
>>> > disconnected set or to a karfunkel set), then it lies between two
>>> > intervals I_n, because a number on the real axis cannot be scattered
>>> > over many places such that it includes an interval like brackets.
>>> > Numbers are not electrons, agreed?

>>>
>>> > Now assume such a number between two intervals. Then these intervals
>>> > have endpoints (whether they belong to the intervals or to the
>>> > complement is of no interest). But it is clear that there is no
>>> > rational between these endpoints.

>>>
>>> Wrong. Let x be your point of the complement. Then there are intervals
>>> [a,b] and [c,d] in your original sequence {I_n} such that b < x < c;
>>> in fact there are infinitely many such intervals.

>>
>> Haha, good joke. Look, the intervals that I use belong to mathematics,
>> not to matheology. They exist. An irrational number x that is not
>> covered by an interval and exists too, must lie between two intervals
>> such that there is no rational number between x and the upper end of
>> the first interval and the lower end of the second interval. No?

>
> No, indeed. If x is any point in the complement and [a,b] any one
> of the intervals of the form
> [r - 1/(sqrt(2)*10^n), r + 1/(sqrt(2)*10^n)]
> and a < b < x then the are infinitely many other such
> intervals between b and x. There is no largest such interval.

... and no rightmost such interval.
>
> This has been pointed out to you innumerable times by me
> and by others.

>>
>> Regards, WM

>

Date Subject Author
6/1/12 Guest
6/1/12 Guest
6/1/12 W. Dale Hall
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Jürgen R.
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Jürgen R.
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Jürgen R.
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Jürgen R.
6/2/12 Jürgen R.
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Jürgen R.
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Uergil
6/3/12 Jürgen R.
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Uergil
6/2/12 Uergil
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Uergil
6/2/12 Uergil
6/2/12 Uergil
6/2/12 Uergil
6/2/12 W. Dale Hall
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 W. Dale Hall
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 dilettante
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Uergil
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Uergil
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 W. Dale Hall
6/2/12 mueckenh@rz.fh-augsburg.de
6/2/12 Uergil
6/3/12 Uergil
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Jürgen R.
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Jürgen R.
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Jürgen R.
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Jürgen R.
6/3/12 dilettante
6/3/12 Uergil
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Uergil
6/3/12 dilettante
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 Uergil
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 Uergil
6/4/12 dilettante
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 Uergil
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 dilettante
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 dilettante
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 dilettante
6/4/12 mueckenh@rz.fh-augsburg.de
6/4/12 Uergil
6/5/12 mueckenh@rz.fh-augsburg.de
6/5/12 Uergil
6/4/12 Uergil
6/4/12 Uergil
6/4/12 Uergil
6/6/12 Michael Press
6/3/12 Uergil
6/3/12 LudovicoVan
6/3/12 Uergil
6/3/12 Uergil
6/3/12 Uergil
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Uergil
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Uergil
6/2/12 Uergil
6/3/12 mueckenh@rz.fh-augsburg.de
6/3/12 Uergil
6/2/12 Uergil
6/1/12 Uergil