Re: Calculus XOR Probability

In article <MPG.1e9c59ef7a16482d98abde@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

MoeBlee said:
Tony Orlow wrote:
And what allows you to conclude that this ordinal is the size
of the set, especially when it is not any definite sort of a
number?

I didn't use "size of set".

Look above. See my question? You answered it with the following
nonsense, as if that referred to the size of the set. So, my
question is relevant, and your inability to see the relevance
isn't my issue.

Your question was what allows one to define the size of a set in
such a way.
Tony: "Consider N is the length of the real line in unit intervals,
and the number of naturals."

Matt: "What allows you to conclude that the real line has a definable
length?"

Tony: "It is an axiomatic statement in my system

TO does not yet have a *system*.
When TO has published a *system* including *all* of his basic axioms and
definitions, only then will he be able to claim a system.



that there is a unit
infinity N, which is the length of the real line, and therefore the
number of unit intervals, or naturals, on the real line, as well as
being the number of nipotent infinitesimal reals in the unit
interval. What drives me to this declaration, which is perfectly
allowed in an axiomatic system, is that it works with the Inverse
Function Rule

TO has yet to define an inverse function rule that is not
self-contradictory.



which works perfectly well for finite and infinite
mappings

As defined, it does not work at all. With some modifications it might be
made workable for certain bijections, but TO wants it to work elsewhere.



to the point of eradicating the Continuum Hypothesis and a
number of other unanswerable questions in your system, in the context
of this system. If we can agree that there is a real number line,
then I can simply call its length N.

We do not agree that the real line as a whole HAS a length. Any
*bounded* interval of reals can be said to have a length, but not the
whole.

I am not arguing with the mechanics of your cardinalities. They're
carved in stone. I simply mean to point out that they fall short in
some respects regarding what we might wish to expect from something
we regard as the "size" of a set.

Unless TO can offer something better consistent with the present systems
of set theory, which he has not done, cardinality is as good as it gets.



In my mind, it is most fundamental
that this measure we call "size" always change with the addition or
removal of elements, if it is to be considered at all precise.

This from someone who claims that infinitesimal changes are undetectable
on a macroscopic scale and that inequalities can become equalities under
suitable changes of scale!

Finite changes become infinitesimal when viewed on an infinite scale,
says TO, at least when TO wants it to be that way, then TO turns around
and says it ain't so when he doesn't want it to be that way.


You're claiming that set theory fails to provide a definite number?
Is that right? Then whether 'definite number' is part of your
system or not,f or us to evaluate whether set theory fails to
provide what you seem to be asking about (definite number), we have
to know what you mean by 'definite number'.

I mean a number that denotes some number of some sort of units.
Something you can perfom arithmetic on. Something that when you add
to it or subtract from it, it changes. Something that has SOME
relation to quantity as we know it. You know, that sort of a thing. A
NUMBER.


In that respect only finite numbers have any relation to quantity as we
know it. No one can actually experience infinite quantities. In fact no
one directly experiences any but a very small range of finite
quantities. Even very large or very small finite quantities are
experienced only indirectly.



No. First you have to define 'real line', and 'length of' and
then prove that there exists a uniuqe object that satisties the
description 'the length of the real line'.

Yes, and thathas to be built up from primitives, and I'm working
on that, in the rare moments when I have time to think. Tonight I
get a bit of a break. we'll see what I can accomplish with that
time.

Then until you come up with something, you're unreasonable to think
that people should see your notions as anything at all, let alone
embodying basic truths upon which mathematics is to be axiomatized.

Perhaps. In the meantime, it's sort of fun to discuss and defend, and
if it succeeds, in the end it will make a good story, or maybe even a
movie. Yeah, Well Ordering the Reals II: Night of the H-riffics. Whom
would you like to play your part? I was thinking maybe James Earl
Jones..... ;-)

Jerry Lewis would be more to type.
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... > Tony Orlow wrote: ... > reals, so it can't possibly denumerate all of the uncountable reals. ... infinite bitstring to represent in that system, ... will require bit strings of infinite length. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... of infinite sets could be applied to infinite sets of points, ... the reals in (0,1] or those in (0,2], and be able to draw conclusions ... TO's definition is either wrong (if his unit intervals are to have ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Since there is always another real between any two reals, ... infinite number of reals in the unit interval. ... The number of points in the interval grows without bound as the number of subdivisions grow without bound. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Show us your definition of "infinite length". ... last of a set of contiguous unit intervals with a 1-1 correspondence to ... as the unit intervals are in 1-1 correspondence with the reals in ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Since there is always another real between any two reals, ... infinite number of reals in the unit interval. ... the number of subdivisions grow without bound. ...
    (sci.math)