Re: Infinity can not exist

From: Ish (chaos.org_at_gmail.com)
Date: 07/12/04 

Date: 12 Jul 2004 06:48:49 -0700

"Tracy Yucikas" <tyucikas@nethere.com> wrote in message news:<1089613755.721084@news-1.nethere.net>...
> "Robert J. Kolker" <robert_kolker@hotmail.com> wrote in message
> news:8ESHc.45385$JR4.25009@attbi_s54...
> >
> >
> >
> > Inifinite cardinality of sets is very well defined. A set has infinite
> > cardinality if it can be mapped 1-1 onto a proper subset of it self.
>
> Robert,
>
> if (0,3) is the continuous interval (real numbers) between 0 and 3 without
> the endpoints included and
> [0,3] is the interval between 0 and 3 WITH the endpoints included
>
> is (1,2) a "proper" subset of [0,3] ?
>
> I ask because I don't think a 1-1 mapping exists between
> open interval and closed intervals, tho both seem to possess infiinite
> cardinality
>
Hey tracy,

a 1-1 mapping does exist...infact it is very simple to construct....
between (1,2) and [0,3]..... however the map cannot be
bicontinuous....for then it would imply that the two sets are
homeomorphic..a contradiction.

Sets of same cardinality only need to have a 1-1 mapping between
them.... cxontinuity is not a requirement.

ish

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