Re: Epistemology 201: The Science of Science

From: aeo6 (aeo6_at_cornell.edu)
Date: 02/15/05 

Date: Tue, 15 Feb 2005 13:17:50 -0500

robert j. kolker said:
>
>
> Allan C Cybulskie wrote:
> >
> > The problem, as I see it, is that it is clear that every single point in the
> > range (0,1) is ALSO in the range (0,2), plus all the points you can get by
> > generating them from (0,1). So how can there NOT be more elements in the
> > range (0,2)? It really does seem like just a word game to me; you get stuck
> > claiming that they are both "infinite" and then give that more significance
> > than it deserves.
>
> Pay attention. Two sets A, B, have the same number of elements if and
> only if there is a one to one function from A onto B. That is the
> definition of equal cardinality.
>
> Bob Kolker
>
So now cardinality is the same as the number of elements..... Didn't you
say they were two different things? Make up your mind. If set A is a
proper superset of set B, then A has all the elements of B and MORE - a
greater number. You admitted that there are more reals between 0 and 1
than between 0 and 2, but then you say they have the same cardinality,
so they have the same number. This flip flopping is the problem I am
addressing. It's illogical. 

-- 
Smiles,
Tony

Relevant Pages