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Professor: What is a root of f(z) of multiplicity k?
Student: It is a number a such that if you plug it into f, you get 0; if you plug it in again, you again get 0, and so k times. But if you plug it into f for the k+1-st time, you do not get 0.
Oh, that hurts. The student must have been trying to listen in class, but completely missed the point. What was the definition of insanity from Einstein again… “Trying the same thing expecting different results”,. As I recall a part of the definition of functions as well has it, if x = y, then f(x) = f(y)., meaning of course for each time you plug in a root, z, you will always get zero.