Exams – general discussion In general, Real Analysis exams will contain the following types of questions. (There may be more than one question of a given type. ) 1. Give the deﬁnition of a concept. Make sure to give a complete and coherent deﬁnition. Example: Given a nonempty set S which is bounded above, deﬁne sup S . 2. Give the statement of a theorem with a name . Example: Write the statement of the Cauchy Criterion for convergence. (This is Theorem 2.41) 3. True or false questions. If a statement is true, make sure to prove it is true (If it is a theorem in the book, do not prove the theorem. Just mention that it is a known result.) If it is false, give a counterexample. Example: True or false? (a) Every convergent sequence is bounded. Answer: True – theorem in the book. (b) Every bounded sequence is convergent. Answer: False, because (-1) n is bounded, but not convergent. 4. Prove a theorem stated in the book. It could be anything that was covered in class. If a “trick”
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