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Topic: Matheology § 176
Replies: 10   Last Post: Dec 11, 2012 12:33 AM

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mueckenh@rz.fh-augsburg.de

Posts: 14,952
Registered: 1/29/05
Re: Matheology § 176
Posted: Dec 10, 2012 10:49 AM
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On 10 Dez., 16:30, David C. Ullrich <ullr...@math.okstate.edu> wrote:
> On Mon, 10 Dec 2012 01:23:07 -0800 (PST), WM
>
>
>
>
>
> <mueck...@rz.fh-augsburg.de> wrote:
>

> >Matheology 176
>
> >Here's a paradox of infinity noticed by Galileo in 1638. It seems that
> >the even numbers are as numerous as the evens and the odds put
> >together. Why? Because they can be put into one-to-one correspondence.
> >The evens and odds put together are called the natural numbers. The
> >first even number and the first natural number can be paired; the
> >second even and the second natural can be paired, and so on. When two
> >finite sets can be put into one-to-one correspondence in this way,
> >they always have the same number of members.

>
> >Supporting this conclusion from another direction is our intuition
> >that "infinity is infinity", or that all infinite sets are the same
> >size. If we can speak of infinite sets as having some number of
> >members, then this intuition tells us that all infinite sets have the
> >same number of members.

>
> >Galileo's paradox is paradoxical because this intuitive view that the
> >two sets are the same size violates another intuition which is just as
> >strong {{and as justified! If it is possible to put two sets A and B
> >in bijection but also to put A in bijection with a proper subset of B
> >and to put B in bijection with a proper subset of A, then it is insane
> >to judge the first bijection as more valid than the others and to talk
> >about equinumerousity of A and B.}}

>
> >[Peter Suber: "Infinite Reflections", St. John's Review, XLIV, 2
> >(1998) 1-59]
> >http://www.earlham.edu/~peters/writing/infinity.htm#galileo

>
> You know this is simply dishonest. The part above inside the
> {{}} is not part of what Suber wrote, and isn't even a summary
> of anything in that article. Giving a quote and _modifying_
> it this way, without making it clear that what you added
> was added by you, is simply lying.
>
> Why do you do that?


The parts in {{}} always give my comments, as the regular readers know
and as you have easily recognized too. It is not difficult to see, and
I chose it because practically no author uses this kind of marking. My
comments are necessary to put everything in right perspective.

Regards, WM



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