Re: Interval in a continuum is a fractal
- From: mike3 <mike4ty4@xxxxxxxxx>
- Date: Sat, 1 Dec 2007 12:19:30 -0800 (PST)
On Nov 30, 7:20 am, Randy Poe <poespam-t...@xxxxxxxxx> wrote:
On Nov 29, 10:07 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:
This is another perspective to explain things when I say you can't
break the conituum interval into points.
An interval in continuum such as time span is bounded by two time
instants, which are modeled as real numbers in mathematics. The
interval also has a non-zero extent or magnitude or span which is
modeled by the "measure" in mathematics.
Any statement that is even remotely related to "such an interval is
made up of certain things", has to deal with division process of such
interval. Simply defining that such interval is made of time instants
is like saying I just said, and you can't question. We need to attempt
a division process to see if it is right.
Such a division process on an interval results in smaller intervals
which has the same properties of the original interval - having bounds
of same type, and having a non-zero measure of extent which is also
same type. This can be continued for ever but the intervals or parts
do not cease to hold the properties of the whole, which qualifies the
partitions as fractals.
Fractals do not collapse to zero extent. It is just forced by our
arrogance at not recognizing the nature and it symmetry. Nature has no
jumps. If the measure has to collapse to zero, there needs to be a
reason such as hitting the "largest number" of divisions.
This is the crux of what I meant in all my recent posts and threads.
Although a lot of what you wrote is nonsense, there
is one central idea that is essentially correct:
no matter how small an interval of the reals you
choose, [a,b] has the same cardinality as [0,1]
and as [-oo,oo]. That is, there exists a bijection
between each of these sets.
Informally, and I want to emphasize this is not
a rigorous statement, there are "just as many"
points in [0.500001, 0.500002] as in [0,1].
But you always make an unnecessary leap, a conclusion
which is not justified by any axiom, any assumption,
anything other than your own beliefs. The
biggest one here is that "if you can't get to
single points by division, then there aren't
any single points there." Or something like
that.
But the requirement that "if a line contains
single points, you must be able to get there by
division" is a Venkat Reddy axiom, not an actual
one.
You tend to have a blind eye to the axioms you
add to the real numbers. The rest of us can clearly
see that it is the addition of YOUR axioms that
creates the contradictions, and since we don't work
with YOUR axioms we don't have the problems you
perceive.
- Randy
And of course we don't work with his axioms BECAUSE
they create contradictions.
.
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