Re: no comments?

From: The Ghost In The Machine (ewill_at_sirius.athghost7038suus.net)
Date: 10/09/04 

Date: Sat, 09 Oct 2004 02:00:46 GMT

In sci.math, Keckman
<keckman@welho.com>
 wrote
on Thu, 07 Oct 2004 20:40:45 +0300
<opsfigp7go3uk9lu@cs81133.pp.htv.fi>:
> Your conversation about is Cantor's proof this or that
> is meaningless if somebody comes and tell/prove you there
> is error in structure and language called mathematichs before
> that.
>
> And where is that error? Here
>
> From these:
>
> Peano's Axiom
> 3. zero is not the successor of a number.
> 5. (induction axiom.) If a set S of numbers contains
> zero and also the successor of every number in S,
> then every number is in S.
>
> ...it has been made conclusion that N is infinite, but it is wrong.

N cannot be infinite in any practical sense (the Universe
would die the heat death first), but, given any finite and
supposedly complete set of natural numbers K and a *lot*
of time, I can take the maximum element of K (the natural
numbers have a natural ordering), find its successor,
and then prove that it's not in K (it's bigger than all
elements in K, after all). Whoops, K wasn't complete,
was it? So N has no maximum element.

In order to proceed one must define "infinite" properly, but it's
clear that N is not finite, either. (There are at least two
infinities: card(N) and card(R).)

>
> The right word should be limitless. And this is really not just semantic.
> If set is limitless it has as many items as ever, but allways finite
> number of them. Same as Paxiomn=n+1 keeps the bigness of number allways
> finite,
> so is the amount of numbers.

So N is finite but limitless? An interesting notion. I suppose
one could construct a mapping from N to R (n => 1 - 1/n would work,
preserving ordering) but I've no idea what you're getting at here.

>
> And this is not just semantic, because i can prove that there is a
> contradiction
> in saying that set N is infinite what comes to numbers amount, but only
> limitless
> what comes to bigness of number.

This paragraph makes no sense.

>
> Now lets try once again. Set N is said to be infinite. Infinete is said to
> be
> bigger than any number in N.
>
> Let's mark every item in N by label so that 1->1, 2->2,...,n->n,... How
> many
> labels? Answer: Infinite, because N is said to be infinite. What is the
> "biggest
> number"? Should be infinite because there is one label for every number
> and one
> number for every label, but all n in N are finite. cotradiction. There is
> not
> enough labels in N so that there could be infinite amount of numbers in N.
> Only
> limitless but not infinite. Or other way aroun: there is not enough
> numbers in N
> so that there could be infinite amount of labels in N. Only limitless but
> not
> infinite.

Your logic is goofy. For starters, you're assuming that there *is*
a biggest number, which is the true contradiction. Therefore, N has
no biggest number.

Since all finite sets which are (proper) subsets of a well-ordered
universal set N have a maximum element (the details are left to the
reader but one implementation is one iteration of a bubble-sort-like
algorithm), N is not finite.

>
> About proveing: If you got eyes you should see it here:

What I see is total confusion on your part. You need to clarify
your thinking, IMO. 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.

Relevant Pages

  • no comments?
    ... ...it has been made conclusion that N is infinite, ... The right word should be limitless. ... so is the amount of numbers. ... enough labels in N so that there could be infinite amount of numbers in N. ...
    (sci.math)
  • Re: no comments?
    ... Keckman wrote: ... The right word should be limitless. ... If set is limitless it has as many items as ever, but allways finite ... Set N is said to be infinite. ...
    (sci.math)
  • Re: no comments?
    ... If the set has a finite number of elements, it is not limitless. ... A set if finite quantities can be infinite. ... > enough labels in N so that there could be infinite amount of numbers in ... > so that there could be infinite amount of labels in N. Only limitless ...
    (sci.math)
  • Re: infinity
    ... I get suspicious at attempts to relate the finite to the infinite, or at casual transits from one to the other, as appears to happen when time passes from that path being followed by the defined sequence to noon, and the number of balls is said to pass from a number without limit to a perfectly finite and ordinary zero. ... And that is supposed to be accomplished by subtracting only one ball at a time from that limitless number, albeit a limitless number of times, and somehow bypassing the sequence 3,2,1,0 in reaching zero. ... And, finally, the arguement seems to be that commutivity in an infinite sum makes it ignorable. ...
    (sci.math)
  • Re: Zenkins paper on Cantor
    ... ...it has been made conclusion that N is infinite, ... The right word should be limitless. ... so is the amount of numbers. ... A few sentence about proveing. ...
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