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Topic: Is continuum completely filled up?
Replies: 610   Last Post: Jun 9, 2012 10:57 AM

 Messages: [ Previous | Next ]
 ooo Posts: 167 Registered: 10/20/06
Re: Is continuum completely filled up?
Posted: Jan 5, 2007 11:14 AM

A point on a line is a boundery that seperate it into two parts at that
point.
As we assume that a point has measure 0,it does'nt affect to the substance
in ordinary sence.
But in set theory, it is considered as a part of substance.
Therefore we can take out this boundery ,and leave void.
We can point out a point, but cannot remove it, that is my view about a
line.
Objects that discreet points are removed from compact set are important
concept in real analysis and are very useful. For example, open set,dense
set...
The treatment to remove a point may be translated the treatment to ignore
this point.
The treatment that I want to inhibit is to build objects which are
constracted from members which looks like being connected intimately in the
condition being seperated from each other like Vitali set.
My wish is to leave real analysis intact as far as possible ,and avoid these
odd objects.

Regards OT

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1/1/07 ooo
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