Re: Weierstrass

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 07/09/04 

Date: Fri, 09 Jul 2004 13:42:19 +0200

Eckard Blumschein <blumschein@et.uni-magdeburg.de> writes:

> David W. Cantrell wrote:
>
>
>> I suspect I do: Eric Weisstein wrote "strangely" because the words "open"
>> and "closed" _seem_, based on their extramathematical meanings, to
>> contradict each other.
>
> Isn't the mathematical meaning: Zero is included as well as
> excluded?

Included and excluded in what? How would that be the meaning?

> This is exactly what I am trying to suggest for any infinitely precise
> real, not just for zero. If a frontier stone of zero dimensions is
> immediately surrounded by infinitely much of very similar stuff, then
> its removal or the opposite does not matter at all. I suspect: Included
> and excluded do contradict in mathematics too, unless they refer to
> something infinitesmal small.

Maybe you should look at fuzzy set theory and see if work done on
fuzzy representations of R satisfy your intuitions. 

-- 
Meaningless movies                                
on the screen behind the band that's blowing       Waterboys,
throwing shapes                                    "My Love is My Rock
Half of the music is on tape                         in the Weary Land"

Relevant Pages

  • Re: Weierstrass
    ... Eckard Blumschein wrote: ... > Isn't the mathematical meaning: Zero is included as well as excluded? ... > and excluded do contradict in mathematics too, ...
    (sci.math)
  • Re: Weierstrass
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    (sci.math)
  • Re: Weierstrass
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