Joerg Sonnenberger <joerg%britannica.bec.de@localhost> writes: > On Sun, May 16, 2010 at 02:10:35PM +0400, Aleksej Saushev wrote: >> Following the logic Joerg uses, one should reject all arguments to sqrt, >> asin, acos, atan, clog, casinh, cacosh, and other inverse functions just >> because they have more than one branch. In "fundamental theory of >> mathematics" >> be it geometry, real or complex analysis, or anything else, this approach >> is found counterproductive. > > Please check the definition of the functions you are using. You are > confusing basic mathematic properties. sqrt does not have more than one > branch. If you want to solve a quadrativ equation, you have to check the > different (complex) roots. Similar for the inverse functions -- they are > defined to return the principle value. This restriction is a simple > result of the trigonometric functions not etc not being injective. I know that pretty fine, and I know that some people define principle values differently, the way it is more convenient to them. If you operate in terms of principle values, then your approach boils down to "I've failed to define principle value for factorisation of integer numbers and thus reject cases I couldn't understand." Arbitrary rejection of cases you don't understand while others do is far from mathematics. -- HE CE3OH...
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