Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: Motion 31 draft text V04.4, extra notes

Nate, P-1788,

I'd like to point out that Motion 5, which passed 43 to 8,
makes operations on unbounded intervals explicit.  The semantics
are that the endpoints, i.e. -\infty and +\infty, are not
actual numbers, but symbols used to describe an unbounded
set of real numbers.  (As such, in some ways they are like
numbers in the set, but in others, they are not.)  These
semantics were pinned down in Motion 3, which passed 48 to 6.

If someone strongly disagrees with this, we can revisit the
issue.  However, as acting chair, I'd like to discourage
such churning, since we are already going to run into an
extension of the working group's term, and I understand a
second extension may be more difficult to obtain.  (That is,
I'm a bit worried about finishing the document before IEEE gives
up on us.)

Best regards,

Baker

On 04/11/2012 11:47 AM, Nate Hayes wrote:

Nate Hayes wrote:

>>When restricted to bounded intervals, the Level 1 arithmetic is
>>closed and cancellative for addition, subtraction, multiplication
>>and division with 0 not in the denominator.
>
>This is not the definition of a closed arithmetic. If you can get
>an interval as a result, say [0,1], you mustn't remove it from the
>possible inputs of an operation.

At Level 2 its not.


Do you mean that you have an operation at Level 2 with no
corresponding operation at Level 1? This doesn't make sense.

Sure it does.
It all depends on the underlying axioms and definitions.


BTW, in the current P1788 model, the midpoint operation is a prefect example of this because it is not defined at Level 1!

Nate




--

---------------------------------------------------------------
Ralph Baker Kearfott,   rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------