Let xn and yn be Cauchy sequences.

Give a direct arguement that xn+yn is a Cauchy sequence that does not use the Cauchy Criterion or the Algebraic Limit Theorem.

given epsilon>0 there exists an N in the natural numbers such that whenever m,n>N, it follows that:

abs value(xm-xn),epsilon and abs value(ym-yn) <epsilon

I'm not sure where to go next.