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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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 Spring '09
 Sega

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