Re: infinity

William Hughes wrote:

Kirby Cook wrote:

William Hughes wrote: 

<snip>

looks like we agree.  What I also have is the concept of the
state after all the finite steps. Call this state, state E
Which balls are in the vase at state E.
We do not know, this has to be defined.

I balk at "*all* the finite steps". Easy to say, hard to define. 


You can only define state E by defining what happens at
state E.  This is done below.


Definition 1:

   Let I be the union of the sets of balls added to
   the vase at any finite step.

   Let O be the union of the sets of balls removed from
   the vase at any finite step.

   Then 0 is a subset of I and we define the set of balls
   that is in the vase at state E is the set difference I\O.


	Actually, I - O, right?  And that is not at E (which has yet to be
defined, IMO) but at any given specific step.


I like the notation A\B for set difference rather than A-B, as the
former makes it a bit clearer that the result of a set difference is
a set, but use whatever notation you like. 

Ah.  Yours is OK with me.

And there is
no mistake.  I and O are defined as unions over all finite steps
and I\O (or I-O if you like) is by definition the set of balls
in the vase at state E.

I suspect we've reached an impasse. "...at any finite step" is fine; I'm with you. When you make the leap to "...over all finite steps" without so much as a by-your-leave, you lose me. <shrug> I freely admit it is due to my own lack of undestanding. Sorry.

Kirby
.

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