Re: On trits & tetrits...
All,
I agree. I like the concept. It SEEMS like an elegant unification.
On the point of decoration(f,[empty]), I think I want to listen to further discussion and consider further how each alternative would work in code examples.
George
On Apr 9, 2010, at 4:07 PM, Nate Hayes wrote:
> Dan Zuras Intervals wrote:
>> Not quite, Nat.
>>
>> Its kind of the set theoretic equivalent of the
>> fundamental theorem of interval arithmetic.
>>
>> While it is true that assertions on the empty set are
>> vacuously true, we are not gathering assertions.
>>
>> We are mapping the function P(f,x) onto the elements
>> of the set {true, false} FOR ALL x in xx. Thus, the
>> definition:
>>
>> decorationP(f,xx) = { P(f,x) for all x in xx }
>>
>> must have the result {} (the empty set) if there are
>> no elements in xx because it must be true that:
>>
>> decorationP(f,xx) \contained decorationP(f,yy)
>> for all xx \contained yy.
>>
>> In particular, we must have that:
>>
>> decorationP(f,[empty]) \contained
>> decorationP(f,xx) \contained
>> decorationP(f,[entire])
>>
>> for all f & for all xx.
>>
>> Since the empty interval is trivially contained in all
>> intervals we must haved that decoration(f,[empty]) = {}
>> (the empty set).
>>
>> Don't you agree?
>
> As tempting as it may be to draw this conclusion, IMHO it is misleading.
> But I don't mean to be critical, since in regards to all the rest I think your idea is quite elegant and precise way to deal with decorations. I'd be happy to help do a new motion, if you're interested.
> Nate
Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
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