# Math Help - Convergent sequence proof

1. ## Convergent sequence proof

Prove that if an converges to A, then |an| converges to |A|. Then prove or disprove the converse to this.

Well...

if an converges to A, then |an-A|<epsilon for n>=N. So do we just approach this first for an positive and then negative to show it converges to |A|. I don't know how to show this formally... I would say the converse is likely false since it could be negative.

2. This is a well known inequality.
$\left| {\left| x \right| - \left| y \right|} \right| \leqslant \left| {x - y} \right|$

From that the proof is trivial.