- #1

kathrynag

- 598

- 0

## 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.