R&S HUI wrote: >> I would suggest the following rewording: >> >> "A function which is not 1-1 is restricted to a principal domain. The >> limits on principal values of arcsine and arccos may be obtained as >> follows..." > > This is not correct either. For example, > 11 o. y , which computes the imaginary part of y, > is not 1-1 but is not restricted to a principal > domain. (11 o. y works for any complex number y.) > What is restricted is that the inverse is an inverse > only for a significant subdomain. So _11 o. y is the > inverse of 11 o. y for the set of imaginary numbers, > complex numbers with real part 0. >
We are getting at the same thing: I am just in favor of wording that would make things clearer, especially given some of the confusion voiced in the forum. I understand that 11 o. y works for any complex number y, and that it is restricted to the principal domain of the imaginary numbers (so that the restricted function is 1-1) in order to be inverted. My concerns are - A function has to be 1-1 to be invertible: the condition of being monotone is misleading. While any monotone function is 1-1, there are functions which are 1-1 but not monotone. - I do not think "significant subdomain" captures the point, while "principal domain" (or a "principal values" applied to the inverse) does. - The principal domain refers to the original function, not the inverse. In the Dictionary page for o., it is the principal values of arcsin and arccos, or the principal domains of sin and cos, but not the limits on the real domains of arcsin and arccos that are being described (the latter have domain [_1,1]). Any rewording that conveys this would help. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
