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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- Oct 10th 2006, 09:20 AMTHulchenkoHelp 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 - Oct 10th 2006, 09:51 AMPlato
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?