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

On 11/7/2024 3:46 AM, WM wrote:

On 06.11.2024 21:20, Jim Burns wrote:

On 11/6/2024 2:50 PM, WM wrote:

From every positive point we know that
it is not 0 and
not in contact with (-oo, 0].
Same for every point not in an interval.

>
Is 0 "not in contact with" [-1,0) ⊆ ℝ

>
0 is not a positive point.

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?
Point x′ is in the boundary of set S
iff
each interval [x,x″] such that
x′ is in its interior, x < x′ <  x″,
holds points in S and points not.in S
For S = [-1,0) and x = 0
each [x,x″] such that x < 0 < x″
holds points in [-1,0) and points not.in [-1,0)
0 is in the boundary of [-1,0)
Is 0 "in contact with" [-1,0) ?