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  1. #1
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    Help sequences

    Suppose lim(xn)= a and lim(yn)= b.
    Let Un= max(xn,yn) and Vn= min(xn,yn) for all n.
    Prove that limUn and limVn exist and find these limits.

    Having lots of trouble setting this up. Thank you for any help.
    Timothy
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  2. #2
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    There are really two cases to consider: a=b and a<>b.
    If say a<b then let e=(b-a)/4.
    Then there is a positive integer K such that if n>=K then x_n is in (a-e,a+e) and y_n is in (b-e,b+e). In these cases it is easy to see that U_n=y_n and V_n=x_n.

    What happens if a=b?
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