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Re: Motion 13 and "<="

Ralph Baker Kearfott wrote:

On 5/4/2010 02:38, John Pryce wrote:

Nate, Dan, P1788

On 4 May 2010, at 07:32, Nate Hayes wrote:

Nate Hayes wrote:

John Pryce wrote:

Dan&  P1788


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1.
"aa lessEqual bb" is defined, following Vincent, as
   (all b in bb)(exist a in aa) a<= b
   and
   (all a in aa)(exist b in bb) a<= b



This clashes with my intuitive idea of \a <= \b.
In particular (and correct me if I am confused here),
the above allows a possible overlap overlap.
In contrast, in my
own implementations and my use in codes and software,
I have used \a <= \b in the "certainly less than
or equal" sense (terminology proposed by Walster).
In Motion 13 speak, this relation has become "precedes-or-touches", i.e., the definition of the relation remains the same as Walster's "certainly less than or equal," but the name and symbol of the relation has changed. 

Nate






Above:

[   a  ]
    [    b   ]    ==> \a <= b evaluates to "true"


Certainly less than or equal:

[   a  ]
           [    b   ]    : The only way \a <= b evaluates to "true"

Furthermore, this (certainly less than or equal)
interpretation appears to be that given in INTLAB
version 6, and INTLAB  is probably the most
wide-spread "existing practice:"


a = infsup(1,3)

intval a =
[    1.0000,    3.0000]

b = infsup(2,4)

intval b =
[    2.0000,    4.0000]

c = infsup(3,4)

intval c =
[    3.0000,    4.0000]

a <= b

ans =
     0

a <= c

ans =
     1




Are there further comments?

Baker


Hence
   empty lessEqual any gives
   (all b in any)(false)  and  (true)
   =  (false)  and  (true)
   =  false.

   any lessEqual empty gives false, similarly.

   empty lessEqual empty gives
   (true)  and  (true)
   =  true.


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John