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Re: Could you recommend CD/DVD writer program?



On Friday October 16 2009 10:56:29 am Boyd Stephen Smith Jr. wrote:
> On Friday 16 October 2009 11:03:13 Matthew Moore wrote:
> > On Friday October 16 2009 9:11:05 am Lee Winter wrote:
> > > And you are adding to it in order to shorten it?
> >
> > This thread is much like any infinite set. Adding a finite number of
> > elements to it does not change it's size.
> 
> By size do you mean cardinality or ordinality?

The size of a set is a cardinal number. Generally, when you talk about the 
"size" of a set, you are referring to it's cardinality.

> You can take a set of (infinite) ordinality aleph-naught and add single new
> element that is greater than all the others (generally denoted "1*") and
>  get a new set of the same cardinality but an ordinality of aleph-naught +
>  1.

I suppose that you are thinking of the "length of the thread" as the length of 
the maximal ascending (or descending) ordered chain (here a<b if and only if b 
is a reply to a). I admit that I interpreted "this thread has to stop!" as 
"this thread must stop having additional members added to it!" and not "this 
thread must have a finite maximal chain!".

MM


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