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 CHAPTER IV PARTIAL SOLUTIONS AND THE PROVISIONAL ELIMINATION OF ELEMENTS OF COMPLEXITY

that we never find out for certain whether x is unity or zero or something else, we then begin to experiment in a different direction. We try to find out which of the hypothetical values of x throw most light on other questions, and if we find that some particular value of x—for instance, unity—makes it easier than does any other value to understand things about y and z we have to be very careful not to slip into asserting that x is unity. But the teacher would be quite right in saying to the class, "For the present we will leave alone thinking about what would happen if x were something different from unity, and attend only to such questions as can be solved on the supposition that x is unity." This is what is called in Algebra "provisional elimination of some elements of complexity."

It might happen that one of the older pupils, 23