- #1
kathrynag
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Homework Statement
Let xn and yn be Cauchy sequences.
Give a direct argument that xn+yn is a Cauchy sequence that does not use the Cauchy Criterion or the Algebraic Limit Theorem.
Homework Equations
The Attempt at a Solution
given epsilon>0 there exists an N in the natural numbers such that whenever m,n>N, it follows that:
[tex]\left|xn-xm\right|<epsilon[/tex] and [tex]\left|yn-ym\right|[/tex]<epsilon
I'm not sure where to go next.