Re: Request for Review/Tutorage of Amateur Proofs

On Wed, 5 Mar 2008 18:31:31 -0800 (PST), MoeBlee <jazzmobe@xxxxxxxxxxx>
wrote:


I guess there's a proof of a theorem that for x, a non-empty chain of
subsets, x has a non-empty intersection as long as 0 is not in x.

Nope.


Do you have that proof available?

Hardly.

Let x = {{0,1,2,3,...}, {1,2,3,...}, {2,3,4,...}, {3,4,5,...}, ...} u
{{-1,0,1,2,3,...}, {-2, -1,0,1,2,3,...}, {-3, -2, -1,0,1,2,3,...}, ...}.

Then x is a non-empty chain of subsets:

.... c= {3,4,5,...} c= {2,3,4,...} c= {1,2,3,...} c= {0,1,2,3,...} c=
{-1,0,1,2,3,...} c= {-2, -1,0,1,2,3,...} c= {-3, -2, -1,0,1,2,3,...} c=
....

0 is not in x. But the intersection of x is empty.


F.

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