Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/7/2024 8:03 AM, WM wrote:

On 07.11.2024 12:18, Jim Burns 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.

That's what I thought you meant.
If, otherwise,
"not in contact with" meant "not in",
the easier, clearer way to say that is "not in".
Thank you for clarifying.
----
⎛ The boundary of a set S holds
⎜ those points x′ such that
⎜ each interval [x,x″] with
⎜ x′ in its interior, x < x′ <  x″,
⎝ holds points in S and points not.in S