Math 3210 - 1        Fourth Homework Assignment         Due: Oct. 2, 2000 
Sept. 22, 2000



* Study also the section on countable sets from the handout "Introduction:
  Prerequisites: Sets and Functions" (taken from Marsden's "Elementary
  Classical Analysis", W.H. Freeman, 1974)

* Turn in the following exercises, taken from the text "Introduction to
  Analysis, Second Edition" by William Wade, Prentice Hall 1999.

    32[3,11].

* Do the additional problems.

     A.   Show that  Q^n  is countable. (n Û N.)
     
     B.   Determine whether the set of functions which map the natural 
          numbers to the integers (F = { f | f : N --> Z }) is countable 
          or uncountable and give the proof.  An element of  F  may be 
          thought of as an infnite sequence of integers. For  f Û F, if for 
          each  n  we set  f(n) = x_n Û Z, we establish a one-to-one
          correspondence between  F  and the set of infinite sequences of 
          integers   f <---> (x_1,x_2,x_3,...).

    (where  "Û" = "Euro" = symbol for "is an element of". )