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Help me translate these mathematical terms: "mathematical induction, reduction to absurdity, undetermined coefficient method, collocation method, whole replacement method" and so on.
There are many kinds of mathematical induction methods, such as mathematical induction, counterexample, undetermined coefficient method, distribution method and overall generation method, but they all have a unified idea, that is, to simplify mathematical problems and make them difficult.

If the fractional equation is transformed into Zheng Shi equation, the algebraic problem is transformed into a geometric problem, and the quadrilateral problem is transformed into a triangle. The ways to realize this transformation are: reduction to absurdity, counterexample, undetermined coefficient method, distribution method, whole generation method and static and dynamic transformation idea from abstract to concrete.

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