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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 7 Nov 2024 14:03:23 +0100
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On 07.11.2024 12:18, Jim Burns wrote:
> On 11/7/2024 3:46 AM, WM wrote:

> I want to find out from you (WM)
> what "not in contact with" means.
> 
> For a point
> in the boundary but not in the set,
> is it "not in contact with" the set?
> Is it "in contact with" the set?

It is not in contact with the set. "For every eps" is not a valid 
criterion because eps depends on what you can define, not on what 
exists. The endpoint is in contact with the set.

> 0 is in the boundary of [-1,0) > Is 0 "in contact with" [-1,0) ?

I am not an expert on these things. I would say it is in contact with 
the set because a point of the set is next to it. The closure of a set 
is in contact with the set.

Regards, WM