Date: Dec 1, 2012 4:24 PM Author: ross.finlayson@gmail.com Subject: Re: Cantor's first proof in DETAILS On Dec 1, 8:49 am, FredJeffries <fredjeffr...@gmail.com> wrote:

> On Nov 30, 8:42 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>

> wrote:

>

>

>

> > No, I only have a Bachelor's of Science degree (in mathematics thank

> > you and I know computer science). The guy who wrote a dissertation to

> > convince soi-disant set theorists that half the integers are even has

> > a Ph.D. from M.I.T. He got it for writing a dissertation in set

> > theory that half of the integers are even.

>

> I have no time for nor interest in your faux post-modern gibberish. I

> only wish to point our that Fred Katz's dissertation did NOT show that

> "half the integers are even". The interesting thing about the paper

> was that he was unable to determine whether There are "the same

> number" of even natural numbers as odd or whether there is one more

> even than odd.

>

> http://arxiv.org/abs/math/0106100

>

> See also Matthew W Parker "Set Size and the Part-Whole Principle"

> and references therein where he demonstrates that methods like Katz's

> "must be either very weak and narrow or largely arbitrary and

> misleading":http://philpapers.org/rec/PARSSA-3

Well great, sure then that goes back to our discussion of whether

"exactly half the integers are even" or in as to whether "give or take

one element, of the infinitely many, exactly half of the integers are

even, and given an arbitrary method of selecting an integer with no

prior expectations, it is as or more reasonable than any other course

that the estimate is that half of those selected would be even."

Simply, half of the integers are even.

It would seem there would be more use of the modern concrete

mathematics, in number theory and in asymptotics, to constructively

build the part-whole principle than to aver that it's Euclid's and not

explored in recent history.

Parker: "And while the _exploration_ of [...] theories of size is

certainly enlightening, one of the things it ultimately reveals is how

limited [...] sizes themselves are by their unavoidable arbitrariness.

This is not to say they are useless altogether; as noted they may well

have special applications to probability and number theory. However,

anyone who has hoped for a revolutionary new [...] theory of set size

with breadth and informativeness approaching what we would expect from

a notion of _how many_ will ultimately be disappointed."

Concrete mathematics has applications of this simply today, and indeed

ready applications abound. Finite combinatorics is complete, and:

unbounded.

"One might object that language always involves haphazard

stipulations, but this is

mainly in the choice of symbols used. Where the concepts expressed are

also somewhat arbitrary (like the culinary distinction between fruits

and vegetables, for example), this again limits their usefulness and

scientific interest."

Then, Parker goes about describing that sets, as their elements are

plotted on their supersets with regular structure as they are

constructed, have simple translations where the "same" elements have

different sizes as a collection, but those aren't exactly the "same"

elements, _in the context of their being in the overall context_. For

example, shifting or translating the integers from the origin one

right, leaves not the same set of integers, for what they are objects,

defining the set by its elements.

"So unless we want the size of a set to depend on its particular

position (even while holding the relative positions of the elements

fixed), or perhaps on the bare haecceities of its elements (if there

are such things), we should like ATI to hold. And for Euclidean sizes

it can?t."

It can't. So, Schnirelmann and number theory give us that half of the

integers are even, and Katz' result is that proper subsets are

demonstrably smaller than their supersets, _in all their supersets_,

in modern theory, fine. Thank you for clearing up that his direct

statement is to that effect, and that the even integers soundly have a

size less than that of all the integers, in the integers, follows from

further development. Here, it supports that no other rational number,

than one half, best describes how many of the integers are even.

Thanks, Fred.

I promoted that notion, proper subsets are lesser than their subsets,

and was roundly derided, until I pointed them to Katz' Ph.D, from

M.I.T. Now also I'll direct them to Euclid.

Were they wrong before, or after? Or, were they just ignorant? Were

they arguing the point, or the poster? Did they learn, or were they

taught? Are just fools, or just fooled? Does it matter anyways

because there's no use for transfinite cardinals? (And measure theory

is plainly countable and defined by our rules of the integral calculus

in the fundamental theorems of calculus, standardly.)

Then, with regards to the text, that's clear and rather plain, it's

readable, you get gibberish. Read what you read, this is a

statement. And that's technical, and correct.

So, whatever you read of it, here's some more.

Thank you, that's good reading and I enjoy it.

http://arxiv.org/abs/math/0106100

http://philpapers.org/rec/PARSSA-3

And then yes thank you I generally respect all and have a high respect

for Jeffries.

So, particle and wave: point?

Regards,

Ross Finlayson