Re: Delusions and occasional bleak truth

On Nov 28, 8:58 am, mike3 <mike4...@xxxxxxxxx> wrote:
On Nov 26, 8:34 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:

Today's Calvin & Hobbes comic has this final statement from Calvin:
"Isn't it sad how people grip on their lives is so precarious that
they'll embrace any preposterous delusion rather than face an
occasioanl truth". Though Calvin was wrong in the context of the
comic, this seems to be true with us to some extent.

I would say any branch of mathematics (topology etc) which desires to
model physical continuum and depends on the notion of "open and closed
intervals of continuum" needs clean up. Because by allowing those open
and close notions, we are modeling only descretum by assuming that it
is possible to strip off zero extent boundaries from their regions.

And "b" does not make a discretuum... how????

It does not. Because it still represents a small piece of continuum,
from which the finite and infinite extents can spring back to life. In
contrast, when you modeled continuum with points of zero extent, you
just killed it, because it each piece now has non-existent (zero)
extent.


Forget about all the "extents" and other geometric
concepts and just concentrate on the sets. Why
cannot one take elements out of those sets? Why
can't I puncture the complex plane, take zero
out of it, deny zero membership in it?

You can't forget "extent" when you talk about "puncturing" something.
It depends on what are your members of the plane. If the members are
points, you are right, you can puncture it by removing zero. However,
that modeling with points is only an approximation. If your model is
correct, the removal of a member should alter the extent/measure of
original interval, or change its bounds.

However, you are still in the "set" mindset, and thinking that since
zero is no longer a member of the original set, things should be
different now. unfortunately, I'm not talking about sets. Its your
modeling issue. Not my problem.


Why we can't strip off boundaries? because you can't subtract dogs
from kilometers. Regions are of one dimension higher than their
boundaries.

*Sets* do not have "dimension". That's what is being
discussed here, *sets*.

That's not exactly what is being discussed here. Sets are part of this
discussion, but it is only your part. Read any of my several posts
here. I never use sets in describing my concepts except to discuss
your answers in your own language. "Attempt to model physical
contimuum using mathematical interval". Thats what is being discussed
here. And even in that, "interval" is your part, that is being
questioned against.

Indeed with some sets dimension is
totally undefined!

See, that should ring a bell, just as several other contradictions.

But that does not mean we cannot
add or remove elements. Sets only have dimension
when you define it.

If someone says a = x - 0 but x and a are different, then wouldn't you
cry foul and write essays on how bad that guy is? Removal of bounds
from an interval and then calling that interval a diffrent thing is
equivalent to this.


How would you define the dimension of the set

{ roadrunner, Easter bunny }

Again, try to identify who is agianst what. I'm not for fixing your
sets. I'm not for fixing self equality of infinity. I'm not for
destroying whole civilization.

I just need your mathematical models not to detroy the "measure" (and
whole existence) by building it with zero extent bricks.

- venkat


?

I can't. But even then I can still take "Easter bunny"
out of the set and be left with { roadrunner }, which
is no less of a set.

You can't subtract dogs from kilometers, but you can
take elements out of sets.

.

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