Re: Could you recommend CD/DVD writer program?
On Friday October 16 2009 10:39:23 am you wrote:
> > This thread is much like any infinite set. Adding a finite number of
> > elements to it does not change it's size.
> Good point. But I think there's a reasonable quibble about the
> difference between unbounded and infinite (in the cantorian sense).
In order to define boundedness, you require some kind of ambient space in which
to embed your set. If your ambient space is a nonmetrizable infinite
topological space, you may be right, depending on the topology. Cantor,
however, worked with densely ordered metrizable spaces. These spaces have a
measure, called the generalized Lebesgue measure. With regard to this measure,
the size of a finite number of elements is 0. Hence adding a finite number of
elements to ANY subset of a "cantorian" space does not change its "size" (i.e.