Re: Motion 31 draft text V04.4, extra notes
On 2012-04-05 15:35:18 -0500, Nate Hayes wrote:
> Vincent Lefevere wrote:
> >I agree. But there will be no "overflown" intervals at Level 2.
> >AFAIK, the Level 2 choice for the midpoint on unbounded intervals
> >has been done for practical reasons, not because of some notion
> >of "overflown" intervals (if this is what you meant).
>
> Nope. That's not what I meant.
>
> What I meant is that at Level 1 there is no definition of midpoint for
> unbounded intervals. So why include unbounded intervals in the Level 1
> model?
because the midpoint is not the only function. For instance:
1 / [0,1] = [1,+oo]
at Level 1 and Level 2 (+ some decorations).
> Especially when a similar treatment at Level 2 of "overflown"
> intervals can provide the same practical benefits? IMO the Level 1
> model is then cleaner and simpler.
I disagree: without unbounded intervals, you wouldn't have a closed
arithmetic (except by introducing some form of NaI, but it wouldn't
even be part of the set theory, and problems you could find with
unbounded intervals would occur with NaI anyway).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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