Re: Calculus XOR Probability

In article <MPG.1ed290581a4f392198acd4@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

cbrown@xxxxxxxxxxxxxxxxx said:
Tony Orlow wrote:

For the last time, no. If the limit of the staircase is anything
different from the diagonal, which it is, then there is no
contradiction.

There is no mathematically valid model in which the limit of the
sequence of staircase functions is anything but the diagonal function.

If TO wished to claim otherwise, then he must create and present to us
the entire system in which he claims his allegations hold, as they do
not hold in any current system.

Well, do you agree that /if/ the limit of the staircase is /not/
"anything different from" the diagonal, then there /is/ a
contradiction?

Of course. If there were not distinguishing characteristics between
the diagonal and the staircase in the limit, or some other
explanation for the discrepancy, then I would have to admit that you
may have a real counterexample to refute the validity of infinite
induction.

And in standard mathematics there are no such distinguishing
characteristics. I have, in fact, given a specific and concrete example
of the staircases as parametric functions of the diagonal distance whose
limit is the diagonal itself.


However, the differences I pointed out not only serve as a
probable cause of the discrepenancy, but lead to an exact
quantitifcation of what the dsicrepancy is.

Except that they provably do to hold in any standard mathematics, and TO
has not produced any other system in which they do hold.




But I have /defined/ the limit of the staircases and the diagonal
as /sets/ which are identical.

Sets of points, which do not lend themselves to additive measure.

They are sets which have well defined arc lengths in the only sense that
any set of points is allowed to have an arc length in standard
mathematics. Where is TO's definition of the 'arc length of a set of
points' which is self-consistent.


Well, obviously, now I have to define a measurable limit definition
for sets of "points", on top of everything else. Fine, it's on my
list.

Until it is done, TO is wrong.



And that's what I mean when I say, your knowledge of what
constitutes a mathematical argument is sorely lacking; particularly
your knowledge of what a mathematical definition is.

Uh huh. When I point out exactly why the measure fails, including how
the error is calculated, I don't know anything about making a
mathemtical argument. But, when you use a definition of limit which
doesn't lend itself to linear measure, and then blame the fact that
the measure of the limit isn't correct on infinity, for vague
reasons, that's a mathematical argument? Where do YOU think the error
ratio of sqrt(2) comes from? Infinity?

Everyone following these posts except TO knows where it comes from. The
error comes directly from TO's insistence on his false "principle of
infinite induction".


That's a very sound
mathematical argument, if ever I heard one.
.

Relevant Pages

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