Re: abundance of irrationals!)
- From: Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx>
- Date: Tue, 3 May 2005 12:50:42 -0400
Ed van der Meulen said:
> Tony
>
> You are so easily talking about infinite as if you daily meet it on the streets and everywhere
Is that not interesting? I have been studying infinity for over 25 years now. I
do meet it daily on the streets, and am quite confident that my understandings
are correct. :)
>
> Infinite is not a clear notion in mathematics but in the first place with out an end, in-finte. But using only finite numbers.
Infinite means "without end", and takes several forms. All those forms and
understandings must be in accord.
>
> I know we can call that mathematically "to that limit". But the definition of the limit is that we don't reach it. We can go further and further but we don;t reach it.
So what? Can we not say that the limit of the sum of powers of 1/2 from 1 to oo
is 1? What do you mean we never approach it? Does Achilles never overtake the
tortoise? Balderdash!
>
> Look at the faculty 3! = 2.3 = 6. 4! = 3! x 4 = 24. In pure mathematicc we can define them in the complex plane.
>
> Only not in the negative whole numbers. But we can approach them surely. Only the negative numbers stay untouched. This shows again that limits you don't really reach. Do you know of the faculties on the complex plane?
I have more to learn about the complex plane. Perrrrrhaps that is why I don't
get your point. What is it?
>
> The word limit tells it also we are always on our way but we are never reaching it.
Last I heard a limit was an end, a stopping point.
>
> limit with n to infinity from n. What is that? No, it becomes greater and greater, n is always finite. And no limit really can reach infinity. We define it's the same and that it exist.
Is this like this line of thinking that never reaches its limit, or makes a
point?
>
> DEFINE is not proving it. Where do you find in the realty really an infinity. Infinities we have in the surreal numbers of course with axioms we can do everything.
Between my eyes, and between my hands, and between any two moments in history.
Also infinity is inherent in circles, and in zeroes. Infinity is calulated
using integrals. It depends how narrowly you view the field of infinities.
>
> The reals are not recursively constructed out of the integers. An equivalence class of rational sequences is not recursively to proof. We need also axioms here. Too many axioms for scientists. This belongs to pure mathematics which is most for playing. There are also many mathematical games.
Look, you can play all the games you want. Just don't tell me you have derived
any truth or proof of anything, if you derive your conclusions with shaky logic
based on unjustified axioms and assumptions. Axioms are assumed true in any
model, and within that model can be accepted until contradicting with something
else in that model. But, what if the axioms all contain the same flaw, and
agree, even though they are wrong? Question each axiom. Most are true only
within certain confines.
>
> I have also enjoyed a pure mathematical education targeted to the fundamentals of mathematics. So with the subject proof theory. With people like Gödel. A destroying excellent mathematician. All formal theories are incomplete. And maybe very incomnplete. And this yields also for the purely mathematical theories from the pure mathematicians. Isn't that great. Applied to the works of the same very intelligent group.
Yes, well, I have heard intimations that Godel's work is somewhat based on
Cantor's i some sense. If that's true, then it needs reexamination (whenever I
have time, I suppose).
>
> And we follow also Popper who says falsyfing has to been done. And it's a feast for us to do it. You certainly need your brains for it. The same mathematical brains. And we are becoming in this way more critically as well.
I am not so sure we are. I would like to hope.
>
> So Tony you are right for the pure mathematicians. But for scientists, no -- Infinities don't belong to the reality.
>
> Can you do infinite many things Tony. Are you so powerful?
>
> Irrational means literally they aren't rational. The name shows already it belongs to playing.
>
Thanks for the commentary. You might want to limit your line lengths to 8 or so
characters so one can read without scrolling sideways.
You say math is a game, but no, it is the foundation for science.
Mathematicians like to think their work is independent of any utility, but the
only reason most of the world appreciates math IS for its utility.
Mathematicians seem to think a system is fine as long as it is internally
consistent, but the entire field of mathematics needs to be internally
consistent, which means each subfield needs to be externally consistent with
other subfields. Cardinality is not.
--
Smiles,
Tony
.
- Follow-Ups:
- Re: abundance of irrationals!)
- From: Dave Rusin
- Re: abundance of irrationals!)
- References:
- Re: abundance of irrationals!)
- From: aeo6
- Re: abundance of irrationals!)
- From: Ed van der Meulen
- Re: abundance of irrationals!)
- Prev by Date: Re: Is there a solution?
- Next by Date: Re: Solution for x^x=a ?
- Previous by thread: Re: abundance of irrationals!)
- Next by thread: Re: abundance of irrationals!)
- Index(es):
Relevant Pages
|
Loading
