Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 038
Posted:
Jun 17, 2012 1:24 PM
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In article
<fa9c09b3-52cd-4535-a6ed-4cda17950283@cu1g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Jun., 20:28, PotatoSauce <kiwisqu...@gmail.com> wrote:
> > On Saturday, June 16, 2012 12:32:18 PM UTC-4, WM wrote:
> >
> > > Take the set of natural numbers as an example. There exists x concerns
> > > always a finite initial segment.
> >
> > Yet, another meaningless statement.
> >
> > If you mean that x is always a finite number, and that number belongs to a
> > finite initial segment, then you are not saying anything interesting.
To say that each natural is from a finite initial of naturals
immediately suggests the existence of a non-finite initial segment.
>
> It is basic to all mathematics. It is of utmost interest. You only
> have not yet perceived how important it is.
Since there are bits of mathematics not requiring any natural numbers
nothing of the naturals is basic to all mathematics.
> >
> > > There exists no x concerns the
> > > *finite* definition of the set.
> >
> > Here you are mixing up "finite initial segment" of natural numbers with
> > "finite definition."
>
> No.
Yes!
> Think deeper. It is not possible to look at infinitely many
> elements of a set. You can only look at the finite definition of the
> set.
WM can only say what HE cannot see, at least until he can tell us how to
look out through other peoples' eyes.
WM's admitted limitations only limit himself.
> Example:
> From "set of even numbers" you can obtain that 3 is not a member.
> From "2, 4, 6, 8, 10, try to imagine this sequence continued in
> infinity" you cannot conclude on the absence of 3, because you never
> know whether 3 will be the next element, unless you have seen all
> elements. But you never have seen all elements of an infinite set
Thus, according to WM, no finite set of even numbers will allow us to
conclude that 3 is not among a larger set of them, and one must allow
the infinite set of them to draw that trivial conclusion.
AS to often occurs, WM's argument proves his claim to be fasle
>
> From "2, 4, 6, ..." you can conclude that 3 does not belong to the
> set. But "2, 4, 6, ..." is a finite definition.
Of an infinite sequence.
> >
> > Unless you can give me an example of an even number which does not come
> > from a natural number through the map
> >
> > f(n) = 2n,
> >
> > I'm going to continue to say that you are just talking nonsense.
>
> Above you gave a finite definition.
Of an infinite set!
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