Thread: Real Analysis - The Cauchy Criterion

Assume (an) and (bn) are Cauchy sequences. Use a triangle inequality argument to prove cn = |an - bn| is Cauchy.

Originally Posted by ajj86

Assume (an) and (bn) are Cauchy sequences. Use a triangle inequality argument to prove cn = |an - bn| is Cauchy.

So :


(by triangle inequality)



Hence this is a Cauchy sequence.