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Topic: Matheology § 038
Replies: 94   Last Post: Jun 19, 2012 12:56 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 038
Posted: Jun 15, 2012 6:36 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 15 Jun., 19:37, PotatoSauce <kiwisqu...@gmail.com> wrote:
> > On Friday, June 15, 2012 12:42:39 PM UTC-4, WM wrote:
> > > Of course there is a limit involved. Otherwise you could not biject
> > > all numbers.

> >
> > Bijection between Natural numbers and the Even Natural numbers.
> >
> > f: N ----> 2N,
> >
> > f(n) = 2n.
> >
> > What limit?
> >

> > > Without limit you cannot include all numbers unless you
> > > find a last one.

> >
> > What "last one"?  Tell me exactly why I need to find a "last one" to define
> > the map
> >
> > f: N ---> 2N
> >
> > f(n) = 2n.
> >

>
> You define nothing else, but a bijection between finite initial
> segments.

That would only be true for those who cannot think.
>
> > >  Do you think there was a last natural number in an
> > > infinite set?

> >
> > 1) Your question makes no sense.

>
> You are wrong. What does not make sense is to talk about "all" natural
> numbers as if there was a last one.

Then why do you keep doing so?

> What does absolutely not make
> sense is finished infinity.

It makes a good deal more sense than WM's matheological mish-mashes.

According to WM, one can never arrive anywhere, because one would have
to complete first half the trip, then half the remaining distance , then
half of that, and so on, but no such infinite process can ever be
allowed to end in WM's matheological world.
> >
> > 2) It has absolutely nothing to do with bijections.
> >

> Look here:
> Every initial segment of the even positive numbers
> (2, 4, ..., 2n) has cardinality n, i.e., less than 2n.
> That can be proved for every finite initial segment and every natural
> number n.
> |{2, 4, ..., 2n}| = n < 2n
> You need the limit in order to breack that rule.

No one even wants to break that rule, except WM.
>
> Unless we go to the limit, there is no chance to have a cardinality
> aleph_0 of a set that contains only finite numbers 2n.

That implies that if we include infinite numbers one CAN have sets of
cardinality aleph_0. But why does WM need the size of a set be in any
way linked to the size of its members?
>
> Regards, WM

--

Date Subject Author
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
6/14/12 Jürgen R.
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Jürgen R.
6/14/12 mueckenh@rz.fh-augsburg.de
6/14/12 Uergil
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6/14/12 Ki Song
6/14/12 Virgil
6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Virgil
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6/15/12 Virgil
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6/15/12 mueckenh@rz.fh-augsburg.de
6/15/12 Ki Song
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6/16/12 Ki Song
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6/18/12 Jürgen R.
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6/18/12 Jürgen R.
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6/17/12 Virgil
6/16/12 Virgil
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