Uergil
Posts:
433
Registered:
6/11/11
|
|
Re: Matheology � 047
Posted:
Jun 24, 2012 4:23 PM
|
|
In article
<d0aef538-a20b-46e7-b81b-36b967c11444@z19g2000vbe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Jun., 22:13, Uergil <Uer...@uer.net> wrote:
> > In article
>
> >
> > Since it is WM's definition of "singleton" which is at issue here, HE
> > should be the one to explain his understanding of the term, not ask
> > others to read his mind!
>
> What is your definition of an uncovered singleton in the set that
> partially is covered by the intervals I_n?
The standard meaning for "singleton" in English mathematics is a set
with one and only one member:
http://en.wikipedia.org/wiki/Singleton_(mathematics)
What you may be wanting to talk about are ISOLATED POINTs in your set of
uncovered irrationals. Such a point must have a neighborhood not
containing any other point of the set in which it is to be considered
isolated.
The Cantor set, for example, does not contain any isolated points.
Your set of uncovered irrationals may contain isolated points, but, as
far as has been proved, might not.
--
"Ignorance is preferable to error, and he is less
remote from the- truth who believes nothing than
he who believes what is wrong.
Thomas Jefferson
|
|
