Re: Is continuum completely filled up?


"Robert Maas, see http://tinyurl.com/uh3t"; <rem642b@xxxxxxxxx> wrote in
message news:REM-2006dec30-001@xxxxxxxxxxxx
From: "ooo" <fara...@xxxxxxxxx>
If real line is filled with points and each point is
distinguished,then each point has difference from every other
points.

Yes, however the difference from a given point to various other
points can be arbitrarily small (close to zero).
Between a given point and any other point on one side of it, there
are lots and lots of other points.
Then all reals cannot be listed (I don't now apropreate words,but I don't
mean reals is numbered, but rather cannot complehend. )
If there are nowhere to be listed all reals in anyform,where they exist ,on
real line? But we cannot take up all of them as a form we can deal with from
there.
But there is no single place that is between a given point and all
other points on one side of it.

Therfore real line has void.

Nope. Anywhere between real points you think there's a void, in
fact there's at least one real point in there to refute your void.

It gets more interesting if you talk about voids between sets of
real points instead of between two singleton real points. Given any
two sets, where all the points of one are strictly less than all
the points of the second set, there is at least one real point
"between" the two sets in the sense that it is either:
- The very greatest element of the set of lesser points.
- The very least element of the set of greater points.
- Strictly between the two sets.
Abobe explanation is similler to a case that berween any two reals ,there
exist at least one real ,even though not so much .
Please cosider follouing question I intended to posr another place.
These arguments ,including Cantor's diagonal, mention up to countable
case,and assume that these argument hold for infinite numbers objects.
These arguments sometimes lead to confusion.
In the question of vase and ball, argument is
cardinarity of all added balls and that of removed balles is equevalent,
hence at noon number of ball is 0 on the vase regardless process before
then.
Is it not the same with that cardinality of all naturas is equevalent with
that of even numbers, so that naturals minus even numbers = 0.
Why can it be ?

Regards OT











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