Re: Cantor set

From: Andersen <andersen_800@xxxxxxxxxxx>
Date: Mon, 02 Apr 2007 16:48:27 +0200

Dave Seaman wrote:

One way to see this is to notice that 1/3 can be written as
(0.02222...)_3. Any number having a base-3 representation that contains
no 1's is a member of the Cantor set.

This is my problem. Because the Cantor set was indeed defined as the way you defined it in my book. But 1/3 is (0.1)_3 right? So (0.0222...)_3 is some other number. Because of this (apparently faulty reasoning), (0.1)_3 is not in the Cantor set, hence the intervals that should be removed from [0,1] should have their first brackets in the inclusive form.

Where am I wrong? Is it so that (0.1)_3 = (0.02222...)_3 ? If so, then why?
.

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