Re: Existence of reals and observation of them

In article <60ea60f1-2ae7-47d2-ab3f-3094f58dc409@xxxxxxxxxxxxxxxxxxxxxxxxxxx> Venkat Reddy <vreddyp@xxxxxxxxx> writes:
On Dec 13, 1:34 am, Virgil <Vir...@xxxxxxx> wrote:
....
The distance between the open intervals (0, 1) and (1,2) is zero but
they not only have no points in common, there is a point in neither of
them which is between them.

If the distance is zero, it means there is no break or gap. We still
can place the point becuase it is of zero length. So we are talking of
placing a point of non-existent size into a gap of non-existent size
and calling that gap as different from some other zero gap between (0,
1] and [1, 2)?

But those two sets have a point in common, so how can you state that there
is a gap between them? I would think that there is a gap between two
intervals if there is a point to the left of every point in one set and
to the right of every point of the other set, that is not a member of
the two sets.
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