Lesson 59.

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Last modified May 3, 2008 6:26 AM

Due Monday, May 5

Sect. 16:

Be sure to note the problem from the textbook assigned below.

PRELUDE. A sequence (and a real-valued function in general) is said to be bounded iff its range is bounded. In class, we defined the concept of a bounded sequence in terms of the existence of TWO numbers (a lower bound and aa upper bound), as follows:

A sequence  (s_n)  is said to be bounded iff there exist numbers  m  and  M  such that for every natural number  n,
    m ≤ s_n ≤ M.

Compare this with the similar definition of a bounded sequence given in Section 16 of the textbook (in terms of just ONE number,  M)  and prove that the two definitions are equivalent.

Exercise 16.12(a)*
*In 16.12, as usual, prove the universally quantified parts of the definition in the appropriate way. This includes not only the “for all ε ” part, but also the “for all  n” part.

NOTE: Be sure to read  Homework Format  and Homework Writing Policy BEFORE writing up your solutions to be turned in.

NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.

Last modified May 3, 2008 6:26 AM

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