# Re: Rational numbers, irrational numbers: each dense in real numbers

*From*: MoeBlee <jazzmobe@xxxxxxxxxxx>*Date*: Mon, 08 Oct 2007 18:38:28 -0700

On Oct 8, 5:58 pm, "Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:

On Oct 6, 9:14 pm, lwal...@xxxxxxxxx wrote:

On Oct 5, 10:41 am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

Good call. Though, it would be interesting to me any progress you make

toward a systemm that upholds "infinite-case pigeonhole" and is

adequate for proving an alternative real analysis

That's still my goal, but of course it won't be easy (otherwise TO,

RF,

etc., would already have accomplished it).

That's an interesting goal, one held by many, who aren't necessarily

cranks,

Right. To work toward a particular alternative mathematical goal is

not itself to be a crank. What is crank is in the manner of operation

and communication regarding such manners.

and I'm not a crank.

You're quintessentially a crank.

Here's quintessentially crank writing:

I think that in the infinite the universal quantifier can be

specialized into forms that reflect whether the transfer principle

applies, and, that might have some meaning.

Consider for example, if there was a set of only all the finite

ordinals, that for each n-set of finite ordinals ({0, 1, ..., n}),

it's a finite ordinal, but for all n-sets of finite ordinals, it's not

a finite ordinal.

As another example, for each finite integer n there exists a value

between 1/n and zero, but for all finite integers n, there doesn't

exist a value between 1/n and 0.

Obviously, sometimes the transfer principle applies.

I think an adequate theory is the null axiom theory because it can be

both complete and consistent. Things exist no matter what we say, so

why demand to proscribe them? I think that the null axiom theory,

which corresponds to a variety of long-held creation stories, has

objects in its universe, and that they're not inscrutable.

Then, in terms of discovering meaningful interactions among these soi-

disant mathematical objects, largely in the sense of what could be

done with them, instead of generation of primary/primitive elements

along the lines of 0, 1, ..., instead it is 0, universe, ....

(Interactions among mathematical objects are discovered moreso than

invented, yet of course methods of expression might be moreso invented

than discovered, in terms of novel mathematics.)

So, then there's the empty set (as a set, null, void, nothing) and the

universal set (everything, being). As sets, they contain other

things, or not, with variously the empty set containing nothing and

universal set containing everything, in a set theory.

The empty set is the universe, then there's everything else,

everything other, everything, in the universe. Or, the universe is

empty, then ....

With some principles along the lines of sufficiency and necessity, the

infinitely many elements uniquify themselves, differentiate, only to

the point yielding a continuum of them as they wouldn't more. The

continuum of elements is recognized as having the properties of a

number-theoretic continuum, and much analysis derives from it.

As mathematicians there are many perfectly reasonable theories like

geometry and number theory. They're great. Since Goedel and the 50's

many would believe that there is no set of all true statements about,

say, the natural integers,

Let me interject your nonsense at this particular point to say: WRONG.

Godel said no such thing.

or, points and lines, yet via a simple

counterargument, true statements about those objects can only be

expressions of the theory, those that aren't inconsistent, otherwise

they would be provable. That's not necessarily to say that according

to Goedel, or rather others as many refer to Goedel, there is no set

of only true statements about, say, the natural integers or points and

lines. Then there wouldn't be a collection of false statements

either. Given all the statements, true and false, Goedel can't

separate them.

Anyways, in terms of infinite sets being irregular, consider the

casual notion that infinity + 1 = infinity. It is presumed in

transfinite ordinal arithmetic that omega + 1 = omega,

I do hate to interrupt again when you've got such a great rhythm

going, but WRONG. In ordinal arithmetic it is NOT the case that w+1 =

w.

while in

transfinite cardinal arithmetic aleph_0 + 1 = aleph_0. So, consider

infinity as an ordinal, and adding another means to include the set

itself, when infinity + 1 = infinity, the infinity already included

itself: infinity is irregular. Consider some countable universe, if

the universe contains itself because it contains everything, then

according to Russell's paradox some least infinite set is irregular,

so all of them are.

In terms of an alternative analysis, it has much to do with geometry,

and geometrical mutations of a sort in the large and small, and

polydimensional points and the space containing them.

So, do you think the above argument holds, about the "transfinite

recursion schema" describing an uncountable set and for each element

of it a distinct rational? If not, why is not the "transfinite

recursion scheme" defined for more than countably many irrationals

unles there are not more than countably many?

Half of the integers are even.

I think I already have indicated the theory, because it's the only one

that could possibly be, the question then is how to make theorems of

it.

The question is how you got so mixed up. Or rather, why in the world

you think that rambling inchorently about mathematics should move

anyone to think anything other than that you're a huge nutcase or a

huge phoney.

MoeBlee

.

**Follow-Ups**:**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*Ross A. Finlayson

**References**:**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*MoeBlee

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*lwalke3

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*MoeBlee

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*lwalke3

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*MoeBlee

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*lwalke3

**Re: Rational numbers, irrational numbers: each dense in real numbers***From:*Ross A. Finlayson

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