In article <T.Mooreemail@example.com> T.Moore@massey.ac.nz (Terry Moore) writes: > In article <DzJv9L.DLI@cwi.nl>, firstname.lastname@example.org (Dik T. Winter) wrote: > > And you ought to have > > given definitions etc. in Tleko mathematics because now we have no idea > > what you are talking about. > > He did. With z = x+iy, I think he defined > df(z)/dz = lim(f((x+h)+i(y+k))-f(x+iy))/(h+ik)) if y >= 0. > For y < 0 he changed the sign of the k in the denominator.
It is my impression that he changed definition along the way. Initially his position was (I think) that df(z)/dz = lim(f((x+h)+i(y+k))-f(x+iy))/(h+sign(x*y).ik)) viz. his remarks that z was analytical in the first and third quadrant and z* was analytical in the second and fourth quadrant, and not analytical elsewhere. His current position appears to be that sign(x*y) is to be replaced by sign((f(z)-f(x))*(z-x)) or something involving such a factor, viz. his remark that z is analytical where z* is and vv. (contradicting his previous assertions).
Or perhaps there is no strict relation in Tleko mathematics between the existance of a derivative and analyticality. Perhaps true, because it also appears to be that in Tleko mathematics a function is analytical if Tleko feels that plots of the real and imaginary parts (according to Tleko mathematics) show that a function is analytical. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/