Re: Epistemology 201: The Science of Science

stephen_at_nomail.com
Date: 03/09/05 

Date: 9 Mar 2005 01:57:11 GMT

In sci.math Tony Orlow (aeo6) <aeo6@cornell.edu> wrote:
: Allan C Cybulskie said:
:>
:> <stephen@nomail.com> wrote in message
:> news:d09vvs$2dm3$1@msunews.cl.msu.edu...
:> > In sci.math Allan C Cybulskie <allan.c.cybulskie@yahoo.ca> wrote:
:> > : I don't want to reply to all the posts right now, but really need to
:> reply
:> > : to this part of this here ...
:> >
:> > : Here is the definition (also helpfully left above) that you gave for
:> "proper
:> > : subset":
:> >
:> > :>>If A is a proper subset of B than B contains
:> > :> :> EXACTLY THE SAME elements as A plus some more
:> >
:> > : If that is the definition of proper subset, then what it says is that B
:> must
:> > : have a larger number of elements than A since it has exactly the same
:> > : elements (thus, the same number of elements) as A PLUS SOME MORE, as you
:> > : said. Yes, it says nothing about bijection but note that for the
:> infinite
:> > : sets we have been talking about the bijection approach says that a
:> proper
:> > : subset has the same number of elements as the superset. THAT is a
:> > : contradiction between the two definitions.
:> >
:> > No it is not. The answer to "the number of elements" is a number.
:> > I already showed you several examples of numbers where x+a=x, even
:> > when a is non zero. There is no contradiction.
:>
:> And I dealt with that by pointing out the mathematical trick that it relies
:> on. For example, here's another claim of the same sort:
:>
:> infinity + 1 = infinity + 2 is in fact a balanced equation. But if I try to
:> subtract out the infinities on both sides, I get 1 = 2, which is clearly
:> ludicrous. The reason this is a trick is that we call this a balanced
:> equation because infinity + 1 and infinity + 2 both get treated like
:> infinity, but then we try to get rid of the infinity which is the only thing
:> that made them balanced we end up with a balanced equation.
:>
:> Your argument was exactly like that. You rely on infinity + anything
:> remaining infinity, but that does not mean that the relative number of
:> elements cannot be said to be larger based on the definition of the set
:> itself.
:>
:>
:>
:>
: I agree fully. The added 1 is insignificant in terms of the relative
: increase to infinity, but is a unit of increase nonetheless. To say
: infinity+1=infinity is essentially useless. One member is the difference
: between the infinite sets of natural and counting numbers, and is
: significant enough to warrant a separate name for the set.

Apparently your position has changed since a month ago.

http://groups-beta.google.com/group/comp.ai.philosophy/msg/27aab7dc782bfae3?dmode=source
        "Infinity+1 is (1+0)*infinity. Like the zero is nothing compared
     to the one, the one is nothing compared to the infinity. It is
     therefore impossible to distinguish between infinity and infinity+1."

Stephen

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