In article <email@example.com>, firstname.lastname@example.org (Tleko) wrote: > > In article <DzJv9L.DLI@cwi.nl>, Dik T. Winter wrote: > > > >But, if you agree that you are not using standard mathematics but > something > >different (Tleko mathematics) why do you not say so? If you had written: > > "In Tleko mathematics f(z)=z=x+iy is analytical when x*y > 0 and > > f(z)=z*=x-iy is analytical when x*y < 0." > >we would not have questioned your statement but instead have asked for a > >definition of analytical in Tleko mathematics. And you ought to have > >given definitions etc. in Tleko mathematics because now we have no idea > >what you are talking about. > > Thank you for the message. What you call 'Tleko mathematics' has > evolved within the last eight years by contributions of several > eminent mathematicians whose efforts are documented in seven > volumes of comments catalogued in the Library of Congress and > several university libraries in the United States and abroad. > The brief summary of results posted on the internet and reviewed > by T. Moore is attached.
I wouldn't really call it a review. And you really should keep reminding us that you are not talking of standard complex analysis because otherwise we are bound to misunderstand. It is much harder to unlearn what we already know than to learn something new.
> Now I understand what you are getting at, I see you are absolutely > correct. But only in your own system in which the derivative is > defined in a non-standard way. Whether your way is useful, I don't > know. But you will have to rederive all of complex analysis with > your new definition. Any theorem in which the real or imaginary > parts may change sign is at risk. For example, is Cauchy's > theorem true when the contour crosses quadrant boundaries? > > I prefer the old complex analysis myself, but each to his/her own > taste.
Terry Moore, Statistics Department, Massey University, New Zealand.
Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter. Augustus de Morgan