On 10 April 2011 23:48, Viktor Cerovski <[email protected]> wrote: >> To start off, the Dictionary entry only says that identities like >> the cited one are extended to certain cases. It does not say >> whether that particular identity holds. And of course, for most >> values of u and y, the identity does *not* hold. It is not a >> general identity. >> > I agree.
Then we should also agree that we cannot use the said identitiy to draw conclusions about what u/y does when 1=#y -- as you initially stated. >> For the particular case of one-item y, witness: >> .................. > Your complaint here is presumably that the last two values > are not equal. My answer to this, in short, is that they > cannot be equal in the case of Minus. Here is why: > .... Of course they cannot, and I did not expect them to be. I was just showing an example why the `identity' is not actually one, except in very special circumstances, and that therefore you cannot derive u/y's result at 1=#y from that `identity'. More generally, the `identity' would not hold for functions that are not (algebraically) associative or do not possess a neutral value. Even for associative functions with neutral values, it will still not hold when 1=#y and y is of inappropriate type for u -- the r.h.s. then is an incorrect expression, while the l.h.s. (u/y) apparently is assumed correct. > Well yeah, sure, the "identity" does not hold because each side > of the identity cannot be evaluated. Actually, the r.h.s. fails, while the l.h.s. doesn't -- which, as I said, once more renders the identity useless as a means to draw conclusions about / in general. > .................................. > I hope the above clarifies it a bit. The problem is not that I do not understand why and how the `identity' is broken. I do understand that very well (I am a mathematician by education). The problem that I see is with the definition and the actual operation of / -- the former appears to be insufficient w.r.t. details, the latter is complicated and has anomalies. That's all -- just an observation -- I don't really suffer because of it :) ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
