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

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Matheology � 176
Posted: Dec 10, 2012 10:30 AM
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On Mon, 10 Dec 2012 01:23:07 -0800 (PST), WM
<> 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]

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? Most of us don't need to misquote
people to support our conclusions.

>Regards, WM

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