Re: Two results of set geometry

On 18 Sep., 17:06, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
WM wrote:
On 17 Sep., 22:50, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
WM wrote:
On 17 Sep., 21:47, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
Do you disagree that, for any rational number, it can be distinguished
from pi, as being either greater or less than pi?
I diagree. The rational number which is made up from the first 10^100
digits of pi and a subsequent 5 cannot be distinguished from pi as
being greaer or less.
Based on what premise? If you already knew the first 10^100 digits of
pi, you couldn't calculate the next digit and tell if it were greater or
less than 5? To whatever accuracy you have attained, you can attain
greater, so that argument flops with me. Sorry.
It is impossible to know the first 10^100 digits of pi because the
universe including your and my brain has less memory space.
Then you could not have a rational number of that accuracy to begin
with, and the question becomes moot, because you don't have the rational
number to compare.

Of course there is no such rational number. Otherwise the question
could be answered. My point is that this question cannot be answered.

You appear to have answered quite clearly, "no".



So, let me try again. Given that you could actually represent some
rational number, do you disagree that you could determine whether it was
greater than or less than pi?

Given you would use all ressources to represent your rational number,
then no ressources would remain to store the digits of pi (and. taken
exactly, no ressources would remain to establish a comparing device
like your brain). The existence of large numbers is not independent of
the choice which should be represented. The possibility to represent
every number we wish, independently of those which already have a
representation, exists only for very small numbers.

You didn't answer the question. Given any particular rational number,
can it be distinguished from pi?


I answered this question. But the answer is very unfamiliar to most.
So they do not immediately comprehend.

If you use all ressources for representing a rational number, then you
cannot compare it to pi because pi then does not and cannot exist. At
best you can use abaout 10^100 bits to represent the first 10^100 bits
of pi and about another 10^100 bits to represent a rational number.
Then, given enough time and stability of the representation and having
available another 10^20 bits for a comparator, you can compare this
number with pi.

Shorter rational numbers (such which require less than 10^100 bits to
represent them) may be compared with same success. Longer rational
numbers (such which require more than 10^100 bits to represent them)
can neither be represented nor compared with pi.





Have you seen my model M7? It makes this all very clear on an easily
understandable basis:

http://groups.google.com/group/sci.math.research/msg/a07444cf340546d5...

All numbers are ideas, but there is a difference between the point on
the real line and the digital representation of it. No completed digital
representation, in any natural base, exists for pi. That doesn't mean
the point doesn't exist on the real line.
It does.
It is.
Try to show it.
Behold! Observe my circle of unit diameter, upon the circumference of
which I have marked a point, right here.

What is the diameter of your pencil? Is it really very sharp?

It is infinitely sharp and accurate, and has marked just a single point.

I don't believe you.

Will that point jump off the line as it approaches?

Mathematics needs physics for representation.
I am not sure Heisenberg needs to be applied to mathematics for it to be
mathematics.
Everything that exists, exists in physics, is limited by physics
including Heisenberg, and underlies the laws of physics in general.
Except theology and matheology.

And the spirit world, of course. Can't forget the psychic universe.

Spirit, as intelligence or "esprit", is physics. It is only that
science has not yet advanced far enough to derive the laws of mind
from those of Newton, Einstein, or Heisenberg.

Regards, WM

.

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