Re: Calculus XOR Probability

In article <MPG.1eadc62482edcd1498ac39@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

Matt Gutting said:
Tony Orlow wrote:
David R Tribble said:
Tony Orlow wrote:
I think if you are talking about a uniform probability distribution
over the
naturals, you may have a point, but I don't think it exactly applies
here.
Let's consider the vase, and we'll add ball 1 at 11:00, ball 2 at
11:30, ball 3
at 11:45, etc, so that all finite natural labeled balls are in the
vase. Now
shake it at 12:00, and again at 12:30, then 12:45, etc. At 1:00,
remove a ball
from the vase. Is there a uniform probability distribution, or are
some of
those naturally-labeled balls more likely than others to be chosen?
Matt Gutting wrote:
I don't see that there's a probability distribution at all. What would
be the
consequences of the existence of a probability distribution on this
set?
If a probability distribution actually exists, then we can answer the
following questions:
1. If n values are chosen, what is their expected average value?
2. If a value x is chosen, what is the probability that the next
chosen value y is greater than x?

I don't see these having any answers, so the conclusion is that there
is no valid probability distribution.



Yes, you're right, over the finite naturals, of course. It seems
impossible to
define what the range or count is, and trying to assume any such thing
leads to
contradiction. Correct. Of course, in the above example, I can't see,
despite
the inability of calculating any such numbers, that any ball has any
different
chance than any other. If there is some set of balls in the vase, then
whatever
size that set is, each ball has the reciprocal of that size as a
probability.

Assuming that one can define a reciprocal for that number, okay. But how
does one compare the probability (say) of drawing one of the first ten
balls
dropped in with the probability of drawing one of the first twenty? Can you
show that the numbers you use there exist?

If we have n balls, the probability of each is 1/n, and so the probability of
the ball being one of the first 10 is 10/n, as opposedto 20/n chance of it
being one of the first 20. If we have n=1:000...000, a megabigulous number,
then the inverse is 1/n, or 0:000...001 probability for each, 0:000...010
that
it be one of the first 10, or 0:000...020 that it be in the first 20.

TO has yet to show that his alleged number system works as number
systems are supposed to work. TO has not shown that his alleged number
system has the properties requires of a ring a ring, much less an
ordered ring.



Now, you want me to prove these numbers exist?

We would like you to produce any system in which these "numbers" CAN
exist. Currently, they are no more substantial than leprechauns or tooth
fairies.



I think if one creates a number system, which is basically a language
where each word represents a quantity, then one can determine what
operations are possible with it. The possibilities are somewhat
limited compared to finite arithmetic, but rational portions of these
quantities can certainly be represented using the connecting
repeating digit strings between limit points. Does that capability
make the system "exist"?

TO's digit strings as described by him cannot exist in any current set
theory. He posits a "string" whose bit positions are ordered inwards
from both ends like the naturals from both ends (down from the up end
and up from the down end) but where each position, except the end ones
has an immediate successor and an immediate predecessor.

In any system in which the Peano axioms hold, such strings are easily
shown to be impossible, and have been shown by many to be impossible.

Thus, they are total fantasies as far as mathematics is concerned.

At least until TO comes up with that long promised but not yet delivered
system in which the impossible becomes possible.
.

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