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Re: Matheology � 176
Posted:
Dec 10, 2012 11:48 AM


"WM" <mueckenh@rz.fhaugsburg.de> wrote in message news:1a842415d2784aaebea8e688bc5b856e@x10g2000yqx.googlegroups.com... > 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.fhaugsburg.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 onetoone 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 onetoone 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) 159] >> >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



