On Fri, May 27, 2011 at 5:53 PM, Daniel C. <[email protected]> wrote:
> On Fri, May 27, 2011 at 3:14 PM, Levi Pearson <[email protected]> wrote:
>> Cardinal arithmetic can be used to show not only that the number of
>> points in a real number line is equal to the number of points in any
>> segment of that line, but that this is equal to the number of points
>> on a plane and, indeed, in any finite-dimensional space. These results
>> are highly counterintuitive, because they imply that there exist
>> proper subsets and proper supersets of an infinite set S that have the
>> same size as S, although S contains elements that do not belong to its
>> subsets, and the supersets of S contain elements that are not included
>> in it.
>
> Is it possible to say what you just said in terms of injective,
> surjective, etc. functions? It sounds like this would only apply to
> countably infinite groups, but I may be mistaken about that as well.
>
That wasn't me, that was some Wikipedia editor that I was quoting.
Sorry if that wasn't clear. Cardinal arithmetic is not on my list of
competencies. I started thinking about mapping functions, but I
didn't care enough to spend any more time on the subject of
infinities. :)
--Levi
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