Re: Motion 13 and "<="
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
.
.
.
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).
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.
.
.
.
John
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