Re: Is continuum completely filled up?
- From: Lester Zick <dontbother@xxxxxxxxxxx>
- Date: Fri, 29 Dec 2006 12:09:20 -0700
On 28 Dec 2006 21:49:13 GMT, richard@xxxxxxxxxxxxxxx (Richard Tobin)
wrote:
In article <en10lj$ka1$1@xxxxxxxxxxxxxxxxx>, ooo <farawfu@xxxxxxxxx> wrote:
If real line is filled with points and each point is
distinguished,then each point has difference from every other points.
Therfore real line has void.
Can you prove that? Why does the fact that every point is a finite
distance from every other point mean that there are gaps?
Because distanse between two points is finite (that is not necesarily
realnumber), we can take point at a potition of their middle.
What makes you think the distance is not necessarily a real number?
The distance between two points on the real line is their difference,
which is certainly a real. So the point in the middle is also a real
number.
What real line? There is no real line in formal terms. Transcendentals
such as pi are defined on circular arcs and not on non circular lines.
~v~~
.
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