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

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 W. Dale Hall Posts: 68 Registered: 2/11/05
Re: Matheology §019
Posted: Jun 2, 2012 3:41 PM

WM wrote:
> On 2 Jun., 16:28, "dilettante"<n...@nonono.no> wrote:
>> "WM"<mueck...@rz.fh-augsburg.de> wrote in message
>>
>>
>> He's back to thinking that a totally disconnected set must be discrete. He
>> thinks that a point in the complement would have to have intervals of the
>> covering "next to it", one on each side. This is not surprising.

>
> If there is an uncovered irratitonal x that is not discrete, i.e.,
> completely isolated *by rationals or by covered irrationals* (other
> isolators are not available), then there is, by definition, another
> uncovered irrational connected with x. Contradiction.
>
> Regards, WM

There is a difference between discrete and disconnected, your
terminological objections notwithstanding. The rational numbers
themselves form a set of points that is disconnected. They are
far from discrete, for within any neighborhood of any rational
number x there exist, as you know, other rational numbers.

The definition of being non-discrete for a set (that is, not
satisfying the definition of discrete: every point of the discrete
set D has a neighborhood that excludes all other points of D)
does not entail (i.e., the phrase *by definition* does not apply)
the existence of a connected neighborhood of any of its points.
Again, the set of rational numbers serves as an example: given
any two distinct rational numbers, there is no connected set
consisting of rational numbers only that contains both. As you
know, between any two distinct rational numbers, there exist
irrationals.

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