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Dear Lenval, In a way, the answer to your question is yes. In some sense one could look at the solution having been obtained by using methods that allow one to step outside of the physical restrictions temporarily. But, the mathematical model of a physical situation should specify all of the parameters and constraints of interest. One of these is the domain of any function that is described. When a model consists of one or more equations that must be solved to determine a particular value of interest, then any method can be used to generate possibilities. What is required (at the end) is that the solver check that the possible solution(s) generated meet all of the criteria (e.g. constraints) necessary for it to correspond to a physical solution. The checking is actually a very important part of the solution method. I hope this makes sense.
Lenval, Perhaps a better way to think of unwanted numbers as "not relevant to the matter at hand." No number is any more real than any other, nor can numbers be classified as useful or useless. Often the unwanted numbers arise from the method of solution. As a very simple example, if I start with x = 2, and I square both sides of the equation, I get the true statement that x^{2} = 4. But if I tell you only that x^{2} = 4, there would be no natural way for you to recover the number x that I started with. Sometimes you can guess the answer; if not, you can obtain the solution by squaring both sides to get Chris  


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