Remarks and Solutions for HW on Page 43
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2. ab = (limsup a_n) (lim b_n) = [lim (sup a_n)] (lim b_n)
      = lim [(sup a_n) b_n], since both limits exist
      = lim [sup (a_n b_n)], since b_n > 0 and a_n >0
      = limsup (a_n b_n), by def
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16. You want f and g to be +/- sqrt(1-z^2). But the square root function is
    defined using a branch of the log function. Hence we need to be concerned
    with an appropriate branch cut.

    Hence, you need to find the set, D, of all complex numbers that are
    mapped to the interval (-infty, 0] by the function 1-z^2. Then, 
    G = C\D. 

    Note that the set D is characterized by: Im(1-z^2)=0 and Re(1-z^2)<=0.
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21. Take the following two sequences: w_n = -1 + i/n and v_n = -1 - i/n.
    Note that both sequences converge to -1. Apply log to these two 
    sequences. You will get the discontinuity by looking at arg(w_n) and
    arg(v_n).
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