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From: Archimedes Plutonium on 24 Jan 2010 14:30


David R Tribble wrote:
> Archimedes Plutonium wrote:
> >> The Peano Axioms are flawed and inconsistent because
> >> they require a Successor Axiom which builds this set
> >> {0, 1, 2, 3, 4, 5, 6, . . . . , 9999....9999}
> >
>
> David R Tribble wrote:
> >> Unfortunately, you have never demonstrated how this can
> >> be so. Specifically, you've never explained what happens
> >> in the ". . . ." ellipses following the '6'.
> >
>
> Archimedes Plutonium wrote:
> > Your [juvenile insult] mind has accepted 1 + 1 + 1+ . . . + 1 diverging to
> > infinity so that means it is not a finite-number, yet simultaneously
> > your juvenile mind thinks {0, 1, 2, 3, . . . . } are all finite numbers.
> > How come you hold such simultaneous contradictory beliefs?
>
> What contradiction?
>
> 1 = 1
> 2 = 1 + 1
> 3 = 1 + 1 + 1
> ...
> n = 1 + 1 + 1 + ... + 1 (n times)
>

Your "n" is wrong for you use the three-dot ellipsis saying it is
infinite
yet you say it is "n times". So that is contradictory, but you
probably
never perceived that contradiction.

If you had studied Series you would know that "n times" looks like
this

n = 1 + 1 + 1+ . . +1_n

Notice the two-dot ellipsis.

The above is

infinity = 1 + 1 + ...+ 1

> Every number in the set {0, 1, 2, 3, ...} is the sum of a fixed
> number of '1' terms. Thus every number in the set is a finite
> sum.

So your saying Peano Axioms go to "n" and not to infinity.

It would help you if you ever defined finite from infinite with
a precision definition. Something you have been unable to do
in all your postings. And why have you been unable? Because
all of mathematics has never precisely defined finite.


>
> At no point in the set is there ever a number or sum of an
> unending number of '1' terms. Yet the sum 1+1+1+... is a sum
> of unending terms, therefore it does not exist in the set.
> Furthermore, it cannot be a finite number, otherwise it would
> be a member of the set.
>

Again, you are saying the Peano axioms go to "n" and never to
infinity.


> So where is the contradiction?

So where have you provided any truthful information, other then your
gaggle
of false beliefs. You have never provided enough truthful information
to warrant
a conversation with you. I get tired of having to correct every
sentence of yours.
This does not make for a dialogue or conversation.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
From: David R Tribble on 24 Jan 2010 14:49
Archimedes Plutonium wrote:
>> Your [juvenile insult] mind has accepted 1 + 1 + 1+ . . . + 1 diverging to
>> infinity so that means it is not a finite-number, yet simultaneously
>> your juvenile mind thinks {0, 1, 2, 3, . . . . } are all finite numbers.
>> How come you hold such simultaneous contradictory beliefs?
>

David R Tribble wrote:
>> What contradiction?
>>
>> 1 = 1
>> 2 = 1 + 1
>> 3 = 1 + 1 + 1
>> ...
>> n = 1 + 1 + 1 + ... + 1 (n times)
>>
>> Every number in the set {0, 1, 2, 3, ...} is the sum of a fixed
>> number of '1' terms. Thus every number in the set is a finite
>> sum.
>

Archimedes Plutonium wrote:
> So your [sic] saying Peano Axioms go to "n" and not to infinity.

Um, I'm saying that the set of natural numbers contains only
natural numbers, and does not contain any infinite numbers.

For any given natual number n which is in the set, its
successor S(n) = n+1 is also in the set.

From that we can conclude several things:
that the set contains only natural numbers;
that every successor of a natural number is also a natural number;
that there is no "last" or "largest" natural number, because such
a thing would not have a successor and so it could not be a
natural number.
And so on.


> It would help you if you ever defined finite from infinite with
> a precision definition. Something you have been unable to do
> in all your postings. And why have you been unable? Because
> all of mathematics has never precisely defined finite.

Non sequitur. You say I can't define "finite" because all of
mathematics has never defined it. If that's true, then by the
same logic, you can't define it, either.


David R Tribble wrote:
>> At no point in the set is there ever a number or sum of an
>> unending number of '1' terms. Yet the sum 1+1+1+... is a sum
>> of unending terms, therefore it does not exist in the set.
>> Furthermore, it cannot be a finite number, otherwise it would
>> be a member of the set.
>

Archimedes Plutonium wrote:
> Again, you are saying the Peano axioms go to "n" and never to
> infinity.

If you mean the Peano set is not an infinite set, then, no,
because the Peano set is indeed infinite.

If you mean that the Peano set does not contain any infinite
numbers, then, yes.

Since you apparently believe the opposite is true, and since
it is not very obvious how the Peano axioms produce such a
thing as an "infinite number", then it is incumbent upon you to
demonstrate how they do, in fact, result in a member of the
natural numbers that is unlike all the other naturals, i.e., not
finite.

If you simply mean that there are naturals larger than 10^500
(your definition of an "infinite number"), then yes, obviously,
that's true. If you mean something else, then you'll have to
show that can be.


David R Tribble wrote:
>> So where is the contradiction?
>

Archimedes Plutonium wrote:
> So where have you provided any truthful information, other then your
> gaggle
> of false beliefs. You have never provided enough truthful information
> to warrant
> a conversation with you. I get tired of having to correct every
> sentence of yours.
> This does not make for a dialogue or conversation.

Well, that certainly makes it easier for you to not provide any
meaningful answers to our questions, doesn't it?
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