PROOF INFINITY DOES NOT EXIST! Not even ONE type [Logic]

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From: Don Stockbauer on 10 Jul 2010 17:22

You can save yourself a lot of bother if you just go with the
cybernetic interpretation of infinity:

http://pespmc1.vub.ac.be/INFINITY.html

From: Marshall on 10 Jul 2010 18:25

On Jul 10, 2:22 pm, Don Stockbauer <don.stockba...(a)gmail.com> wrote:
> You can save yourself a lot of bother if you just go with the
> cybernetic interpretation of infinity:
>
> http://pespmc1.vub.ac.be/INFINITY.html

I felt myself getting stupider with each sentence of that
article that I read, so I stopped early. I expect a complete
recovery.

Marshall

From: FredJeffries on 10 Jul 2010 19:22

On Jul 9, 10:17 am, Dan Christensen <Dan_Christen...(a)sympatico.ca>
wrote:
> I can't imagine that you would be able to do very much using
> "finitist" methods. How do they handle such basic concepts as the
> square root of 2?
>

Terence Tao in "A computational perspective on set theory"
http://terrytao.wordpress.com/2010/03/19/a-computational-perspective-on-set-theory/

in which he explores the question "what is the finitary analogue of
statements such as Cantors theorem or the Banach-Tarski paradox?"
summarizes thus:

<quote>
The above discussion suggests that it is possible to retain much of
the essential mathematical content of set theory without the need for
explicitly dealing with large sets (such as uncountable sets), but
there is a significant price to pay in doing so, namely that one has
to deal with sets on a "virtual" or "incomplete" basis, rather than
with the "completed infinities" that one is accustomed to in the
standard modern framework of mathematics. Conceptually, this marks
quite a different approach to mathematical objects, and assertions
about such objects; such assertions are not simply true or false, but
instead require a certain computational cost to be paid before their
truth can be ascertained. This approach makes the mathematical
reasoning process look rather strange compared to how it is usually
presented, but I believe it is still a worthwhile exercise to try to
translate mathematical arguments into this computational framework, as
it illustrates how some parts of mathematics are in some sense "more
infinitary" than others, in that they require a more infinite amount
of computational power in order to model in this fashion. It also
illustrates why we adopt the conveniences of infinite set theory in
the first place; while it is technically possible to do mathematics
without infinite sets, it can be significantly more tedious and
painful to do so.
</quote>

From: Vesa Monisto on 10 Jul 2010 20:01

"Marshall" <marshall.spight(a)gmail.com> wrote:
>
>> On Jul 10, 2:22 pm, Don Stockbauer <don.stockba...(a)gmail.com> wrote:
>> You can save yourself a lot of bother if you just go with the
>> cybernetic interpretation of infinity:
>>
>> http://pespmc1.vub.ac.be/INFINITY.html
>
> I felt myself getting stupider with each sentence of that
> article that I read, so I stopped early. I expect a complete
> recovery.

"To find his stupidity is the first step to get rid of it". ;)
The link Don gave is worth to read!
Curt gave the idea of infinity in the form "10 goto 10".
I gave the idea in Basic; here even in more conventional notation:

Deduction called "mathematical induction":
T_(n+1)_ = T_n_ + 1
Read: "Let the next term T_(n+1)_ be the earlier term T_n_ plus 1
in-finitely = continuously without Exit from the loop".

In Basic:
A = 0
Step: A = A+1 :
Print A : Goto Step
End

Fibonacci sequence:
T_(n+1)_ = T_n_ + T_n-1_
Read: "Let the next term T_(n+1)_ be the sum of two earlier Terms
T_n_ and T_n-1_ in-finitely = continuously without Exit".

In Basic:
A = 0
B = 1 : Print B
Fibo: C = A+B : Print C
A = B
B = C
Goto Fibo
End

Homework: Write the same for fractals "zoomable ad infinitum".

The idea: The programms are giving the stepping potential
(= possibility) for to actualize the stepping process without Exit
(= halting) from stepping. Even the programms are finite (Ending),
the stepping process is infinite (never-ending), i.e., -> impossible.
You can step endlessly, first forward, then shortening steps
for to step at your place, and with negative steps even backwards
..... if you need a re-covery. -- Halting helps, too!

V.M.
(Just 'fun for the road'.)

From: Curt Welch on 10 Jul 2010 20:30

George Greene <greeneg(a)email.unc.edu> wrote:
> On Jul 7, 2:36=A0pm, c...(a)kcwc.com (Curt Welch) wrote:
> > You have to be careful in such debates to understand what "exists"
> > means and how you are using it.
>
> You MEANT to say that ONE has to be careful.

That's exactly right. I have a bad habit of writing "you" when I'm
meaning "one".

> *I* certainly do not have to be any more careful than usual.
> I am already aware of the point you are trying to make here.
> You are in no position to lecture me personally.

Well, this is Usenet. We are both in a fine position to lecture anyone we
damn well feel we want to here! As you have done to me now as well!

> You have to be careful in these debates to understand what "you"
> means, and how you are going to be perceived as using it.

Yes, I do agree!

--
Curt Welch http://CurtWelch.Com/
curt(a)kcwc.com http://NewsReader.Com/