On Tue, Apr 12, 2011 at 4:39 PM, Boyko Bantchev <[email protected]> wrote: >> The dictionary says that u/y inserts u between the items of y. For the >> case where 1=#y there is only one item of y and so there is no place >> to insert u, so u is inserted nowhere. > > How does it follow from nowhere-inserting u that u/y returns y as > it is? How does it follow that it returns anything to do with y?
In the general case, it does not return y as it is. Instead, it returns the only item in y. Only when y is rank 0 can u/y return y as it is. > Or anything at all? It doesn't follow. Nothing in the definition > leads to such a conclusion. The definition is underspecified. > Returning an empty or identity value or even an error is as complying > with such a definition as returning y. This can only be true if you have ignored large parts of the dictionary. For example: +/ is sum. The sum of a single item list should be obvious. I already gave you a dictionary url that covers that., > (Note: whether any of these interpretations is meaningful and useful for > any specific purpose is irrelevant here: we are discussing what is deducible > from /'s definition, that's all.) If by /'s definition you mean just that one page, ignoring all of the rest of the dictionary, and anything that a person might use to find the definitions of the words and symbols used? Yeah, ok, that would not define anything at all. But I see no reason to care about that kind of focus. > Besides, consider the following hypothesis. Let us pretend that the DoJ > didn't define u/y for an empty y. Then, if it were true that from the absence > of the possibility to apply u you could still infer /'s behaviour, you should > be able to tell what that behaviour would be. So, could you tell what > would u/$0 have to return then, and why? I do not understand this question. > For me, common sense means that the verb in the sentence > `applies the dyad u between the items of y' > should indeed be understood as `applies' (not including `sometimes it > doesn't'), and precisely `between'. Assuming what happens when there > is no `between' is not a formal consequence of the sentence. > >> http://algebra.math.ust.hk/determinant/01_geometry/lecture1.shtml > > I fail to see the relevance of this text to the discussion on /'s definition. I posted that in a followup -- the determinant of a 1 by 1 matrix is the single number in that matrix. But that was not really necessary. Any use of that definition for determinant is going to be using -/ on single item lists. And larger matrices require the long right scope that J uses. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
