Re: Existence of reals and observation of them

In article
<60ea60f1-2ae7-47d2-ab3f-3094f58dc409@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Venkat Reddy <vreddyp@xxxxxxxxx> wrote:

On Dec 13, 1:34 am, Virgil <Vir...@xxxxxxx> wrote:
In article
<6d52b3ce-694d-4887-ad7c-83ad535fb...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Venkat Reddy <vred...@xxxxxxxxx> wrote:

No, it won't. It will *approach* that number. It won't *hit*
that number. Ever.

If it doesn't hit that number, then how far off it is? Zero? Then it
has hit the number. Not zero? then we have infinitesimals.

Then Venkat is obviously unable to deal with open intervals.

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.

WRONG! That is only true of closed sets, not open ones. Open sets can
have 0 distance and still have gaps between them.


We still
can place the point becuase it is of zero length.

Your limited mind does not seem to grok that "distance between sets"
means the greatest lower bound of distances between a point of one set
and a point of the other, and such a greatest lower bound does not have
to be achieved by any two such points.

And in the case of (0,1) and (1,2), that GLB is zero even though there
are no x in(0,1) and y in (1,2) with y = x.

You ignorance of analysis is showing.

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)?

You may be doing that but we do things much more sensibly.
.

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