Zsban Ambrus <[EMAIL PROTECTED]> wrote: > On Sat, 1 Jul 2006, Mark D. Niemiec wrote: > > I know there are some functions that have both identities, and in which the > > two are different, but I can't think of any at the moment. > > In fact, there aren't any in the mathematical sense because if x is a > left identity of u and y is a right identity then x u y is equal to both x > and y so they must be equal. This sort of makes my statement irrelevant.
Duh! I should have thought of this! > However, J verbs shouldn't of course be treated functions in the > mathematical sense, so such an anomaly can happen. It probably won't > happen in practice though that you want to use both inverses of such a > function and expect J to find them. Let me show an example. > > u =: (^ + ])"0 This J expression IS a mathematical function in the most basic sense: f(x,y) = x^y + y > This verb has 0 as its left identity (at least if the right argument is > positive) and 1 as its right identity. It is true that 0 is the left identity (0^y + y = 0 + y = y for all y>:0) (In fact, in J, it seems to work for all complex numbers except for non-positive reals: 0 ^ 1 r. 1p1 _ 0 ^ 1 r. 1p1 - 1e_15 0 However, 1 is not the right identity. (x^1 + 1) is 1 larger than x for all x. It is only an identity if x e. _ __ _. -- Mark D. Niemiec <[EMAIL PROTECTED]> ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
