Homework assignment 5

In Section 1.3 study the binomial formula

Read through 42) and keep reading to stay up with the class.

Do #1 , #9 , #18 pp.32-35 and

Problem 5.1: A real number of the form m / 2^n, where m is an integer and n is a natural number, is called a dyadic rational.

(a) Adapt the above procedure to show the so-called “diadic” rationals are dense in the reals. Problem 27 on p. 22 is similar.

(b) Do problem 4.1 (the homework #4 problem) for the dyadic rationals.

Note that #9 says that the Archimedean Property is equivalent to the fact that “lim 1/n = 0”.

Thus you must show two things, that each implies the other.