Re: Is continuum completely filled up?

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.
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.
.

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