Re: discrete mathematics

ed:

> Each rational number is a quotient x/y with y not 0. So
> each rational number is point of our x-y plane.

Proginoskes:

No, it isn't. It's an infinite number of them! i.e., (1,2), (2,4),
(3,6), ...

I make my sentence more precise. Out of the plane we delete all point with common factors in the numerator and the denominator . Then there is an 1-1- function to and fro from the plane and Q, But this step isn't neccesary.

We are talking about Q. Not about which Q numbers are equivalent. We have still to delete common factors.

I know 1/2 is equivalent to 2/4 but they are two different expressions. So what I am telling holds.

ed:

> Is this clear. And Q is sufficient in the sciences, and
> in the computer world.

Proginoskes:

Q is NOT sufficient for the sciences, not even geometry. What is the
length of the diagonal of a square whose side is length 1?

When we have a unit square we have also the expression sqrt (2) Butr what is that. It's a real number. But what is that? Can you tell me that exactly?

Scientists have to measure it with the unit and that means they receive a rational number. I am very sorry for you.


Proginoskes:

About the Actually, if the Banach-Tarski Paradox proved 1 = 2, then the BTP
wouldn't be a paradox.


No in fact they have proved the choice axiom is too optimistic. But many mathematicians don't take that standpoint. So it's for them a paradox.

Do you mean "In discrete" or "Indescrete" (as in not discrete)?

If you only work with finite sets, you don't have to worry about AC.

Yes. I mean discrete. For finite sets you can always do anything in a finite time. That is real recursive as well.

Proginoskes:

3. The 3-body problems deals also with a space
> of Real coordinates. And noone has found a solution.

!?!?!?!?!?

Ed: Does that mean you don't know of it?

> I can show you a paper on the net open for everybody about this subject.

I can show you TWO papers on the net open for everybody.

That is great. About what?


Why am I wasting my time with this?

I agree agree with you

--- Christopher Heckman

P.S. You should co-write a paper with James Harris.

------------------------

Thank for the hint.

Something about the constructing of reals.

The theory tells we can construct them with equivalence classes of sequences of rational numbers. They can converge to a limit. That limit is the real.

So each real is equivalent to an equivalent class of rational sequence.

Some comments on that.

1. We are forgetting the quantum behavior of in the reality measured so often in all kinds of experiments. Look at the photo-electric effect. Alas this is physics.

Have you solved hydrogen fusion. Please bring that news.

2. what is an equivalence class. How can we construct that recursively.

We can make one sequence for instance to pi. And is the class then filed with other sequences. How can we get that. For the funny thing with infinite sequences. You can choose for the first n terms, free numbers. The limit ( not the sum) isn't dependent of the beginning terms. And the nice thing we can make n as large as we want.

So please tell me how I can construct those equivalent classes. Thus I don't accept this construction of the reals. In set theory you need an axiom for it.

3. Set theory start with an empty set. See that as a model make a theory above it with meta- language. That is the subject proof theory. With famous people like Gödel. An there you have to define the notion set. {} So set theory doesn't start out of nothing. The empty set is still a set.

We have to be a little bit precise.

-----------------------------------
Finally:

Author: Torkel Franzen

Why, then, do you post your rambling in sci.math?

Ed because I post about the wide subject mathematics.

But many aren't critical enough. that's my idea.


Ed
.

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