Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Matheology § 176
Replies:
10
Last Post:
Dec 11, 2012 12:33 AM




Re: Matheology § 176
Posted:
Dec 10, 2012 10:49 AM


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.
Regards, WM



