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| Science Forum Index » Fractals Science Forum » [Fwd: Re: Cantor set question] |
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| Author |
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| Roger Bagula |
 Posted: Wed Dec 08, 2004 11:59 am |
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Guest
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-------- Original Message --------
Subject: Re: Cantor set question
Date: Tue, 07 Dec 2004 22:50:01 +0100
From: Horst Kraemer <h-kraemer@lycos.de>
Newsgroups: sci.math
References: <1102437980.557253.321310@f14g2000cwb.googlegroups.com>
agapito6314@aol.com wrote:
[quote:bd20befb7c]Let P be the Cantor set, k and m any positive integers. How does one
prove that no (open) segment of the form
( (3^k + 1)/3^m , (3^k + 2)/3^m )
has a point in common with P? It appears as if segments of this form
are those middle thirds discarded in the construction of P, but how
does one prove formally?
[/quote:bd20befb7c]
This follows from the fact that the Cantor set is the set of real
numbers which can be written as
oo
2*Sum a_i/3^i
i=1
where a_i is either 0 or 1 for every i.
--
Horst
--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn |
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