Re: Do we have implicit semi-infinites...?
On 14 Mar 2012 at 10:22, Dan Zuras Intervals wrote:
To: stds-1788@xxxxxxxxxxxxxxxxx
Copies to: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
From: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
Send reply to: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
Subject: Do we have implicit semi-infinites...?
Date sent: Wed, 14 Mar 2012 10:22:51 -0700
> Folks,
>
> I have been contemplating that split function we discussed
> earlier. In so far as is possible, I would like to write
> it independent of the underlying interval form. In effect,
> not caring whether one uses explicit (inf-sup or [a,b] form)
> or implicit (mid-rad or <m,r> form).
>
> But I am running up against the differences in the set of
> intervals these two forms can represent. Specifically, I
> need to know something about how (or whether) implicit forms
> will represet semi-infinite intervals.
>
> How does one (or can one) represent a semi-infinite interval
> of the explicit form [a,+inf] as an implicit <m,r>?
>
> Can one represent Entire? Perhaps as <0,+inf>?
>
> Can one use r = +inf at all?
>
> Can one represent Empty? Say <0,-inf>?
>
> Can one use r < 0 at all?
>
> Or have these things been decided yet?
>
> Anything you can tell me...
>
> Thanks,
>
> Dan
Good questions!
As I said before, if an interval in mid-rad form is such
that, say rad >= 1/2 |mid|, then according to common
sense, such an interval is meaningless and useless.
(Instead of 1/2 any other convenient fp constant between,
say, 1/10 and 1/2 can be used.)
This is because mid-rad numbers are used to model
approximate numbers and the latter are useless when
the error (rad) is too large or the mid-point is of unknown
sign. Hence, infinite mid-rad intervals and mid-rad intervals
containing zero are practically useless.
Negative radii correspond to improper (Kaucher) intervals.
If Kaucher intervals are used, then a meaningful
condition becomes, say | rad | < 1/2 |mid |.
IMO if |rad| >= 1/2 |mid|, then used should be
notified that there is somethng wrong with his/her
computations.
Hence, the following tasks:
1) what precisely test to choose;
2) how to perform the test, and
3) how to notify the user.
S Markov