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Re: Weierstrass
Posted:
Jul 9, 2004 6:28 AM
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jesse@phiwumbda.org (Jesse F. Hughes) wrote:
> Eckard Blumschein <blumschein@et.uni-magdeburg.de> writes:
>
> > Robin Chapman wrote:
> >
> >>>I realized: An empty set is known to be neither open nor closed, of
> >>>course.
> >>
> >>
> >> !
> >
> > http://mathworld.wolfram.com/EmptySet.html
> >
> > Well, they did not write "neither not" but "both" open and closed.
> > Since open and close contradict each other, I was just a bit sloppy.
>
> But the topological notions don't contradict each other at all.
>
> I'm not sure that I'd call your statement above "just a bit sloppy".
> If X and Y are true, then asserting "NOT X and NOT Y" is more than a
> bit sloppy.
>
> > I merely do not understand why they wrote "strangely".
>
> Me either.
I suspect I do: Eric Weisstein wrote "strangely" because the words "open"
and "closed" _seem_, based on their extramathematical meanings, to
contradict each other.
David
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