Re: This Month's Thought on Fermat's Last Theorem: 1
From: Keckman (keckman_at_welho.com)
Date: 10/04/04
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Date: Mon, 04 Oct 2004 18:45:12 +0300
On 4 Oct 2004 07:42:01 -0700, Randy Poe <poespam-trap@yahoo.com> wrote:
> Keckman <keckman@welho.com> wrote in message
>> Take any 6 natural numbers you want and put them to set.
>> What must be the biggest natural number in that set?
>
> There is no limit on what the biggest natural number in
> that set must be
But there is limit on what is the biggest at least.
> , since you let me pick any 6.
My point was that the set has biggest number that is at least 6.
And you agree. Now think further...Have a set where is 9999^999^M
(where M is something big finite any number) natural numbers
There must be number that is at least 9999^999^M.
Allthough that doest't matter how big because everything is relative.
I can allways multiply by two not to the infinity because that not exist.
> If you choose {n1, n2, n3, n4, n5, n6}, I can always
> find a different set {2*n1, 2*n2, 2*n3, 2*n4, 2*n4,
> 2*n5, 2*n6} which has a larger maximal element.
Of course. You seems to agree. But that was not my point. My point was
contrast: take any m number from set N, then what must be the biggest
atleast? Answer M.
>> Naturals are not like qeue that's items goes smaller and smaller. "They
>> all takes us much place".
>>
>> n+1 - n = 1
>>
>> If that's queue's length is supposed to be oo then there is item oo.
> Anyway, this statement:
>> If that's queue's length is supposed to be oo then there is item oo.
>
> is simply wrong. You keep saying it, but it's not true.
> That's what you're trying to PROVE, and you "prove" it
> by saying it over and over.
And you keep saying that PAxioms says that there is infinete amount of
natural numbers. Just count them. Starting from 1,2,3... How the hell can
that
infinite number somewhay step to be infinite? And you say it doesn't. But
remember you count them when you enumerate them. So the same as the value
is
allways finite so is the number of numbers.
> You reason thus:
> If I have a list {1,... } of "length oo", the maximal
> element is oo. If I have oo different natural numbers,
> the largest must be at least oo.
>
> -------------------------------------
>
> That third does not follow "by induction" from the first
> two. The problem is that the list of all natural
> number, {1, ...} doesn't have a maximal element.
I agree. There is no maximal element. But that doesn't
mean that there are infinite amount.
> It
> is true that if there was one, M with the property
> that M was greater than or equal to any natural
> number, then M would have to be infinite.
I have made mistake when i spoke here something about maximal element.
There isn't (allthough N is finite).
Because everything is relative somehow we locked to the first step
when trying to list every natural number. We can allways multiply it 2.
But that doesn't mean that the amount of numbers or their bigness
should be infinite. Contrast: just that that we are allways in step 1
in counting them means that both are allways finite.
> There is no requirement that all sets have to have
> a largest element. That's what's throwing you. You
> think "N is a set, it has a largest element, that
> element must be oo, so oo is in N."
I don't think that. It is you who think that N is a set
that has oo element. I think N is a set that has how many
ītems we ever ever want and that can allways be multiplied
by 1,2,3...but still it is allways finite. Allthough
it doesn't have the biggest item.
> The second phrase
> "it has a largest element" is just not true. No such
> axiom.
I agree.
And btw. There is either axiom that the amount of naturals is infinite.
You should have to prove it. You have used to think that form PA3: n->n+1
follows
that the amount is infinite, but that is not true. No matter how many
times you
multiply the amounts of some set by 2 it can allways be multplyed by two
and it
stays at the first step forever. And is finite. The concept we use are
wrong but
they are all we have. Set of natural numbers is always finite allthough it
doesn't
have biggest item. We can allways add more or multiply by three, but we
still hang
on the first step.
Only god could know what infinity is. But i think there is no such a thing
for him
either. Nothing is infinity. Everything is finite allthough it can allways
grow
twice bigger, which can allways grow twice bigger (but not infinite many
times)
and it is still finite in a first step to heaven (course it can allways be
multiplied
by two).
-- Petri Keckman
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