Re: Discussion paper: what are the level 2 datums?
> Date: Sat, 09 Oct 2010 12:41:42 +0200
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> CC: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: Discussion paper: what are the level 2 datums?
>
> John Pryce wrote:
> >
> > . . .
>
> 3. Concerning the values of the other decoration trits, I think that
> this is part of a general observation that not all combinations of trit
> values make sense. Indeed, assuming the four trits
> v=valid, d=-defined, c=continuous, b=bounded
> (which are the indispensible ones) and the possible values
> + (True), - (False), and 0 (no claim),
> only 10 combinations of trits are computationally relevant and should
> be allowed:
>
> v d c b | #cases
> - 0 0 0 | 1
> + - 0 0 | 1
> + 0 0 0- | 2
> + + +0 +0- | 6
>
> (In particular, v is never 0 and c is never -.)
>
> . . .
>
> Arnold Neumaier
I'll let people with more experience argue about
which cases make sense & which don't.
But this observation brings two things to mind.
First, if there are only a small number of valid
cases, can we not reduce the collection of
decorations to an enumeration type of those cases?
Say, 4 bits when all is said & done?
Maybe that's a level 3 observation but its worth
putting in an informative note.
And second, isn't the signum() function decorated
with ++-+ in any interval containing zero in its
interior?
By signum() I mean the common definition:
signum(x) = (x<0)?-1.0:(x>0)?1.0:0.0;
That is, a function which is valid, defined, &
bounded but not continuous at zero.
Still, 11 is less than 16. :-)
Dan