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

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Scott Berg

Posts: 2,027
Registered: 12/12/04
Re: Matheology � 176
Posted: Dec 10, 2012 11:48 AM
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"WM" <mueckenh@rz.fh-augsburg.de> wrote in message
> 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.

they may be right to you, but wrong to most, and dishonest too.

> Regards, WM

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