# Thread: Realy Analysis - Algebraic Limit Theorem #2

1. ## Realy Analysis - Algebraic Limit Theorem #2

a. Show that if (bn) --> b, then the sequence of absolute values |bn| converges to |b|

b. Is the converse of part a. true? If we know that |bn| --> b, can we deduce that (bn) --> b?

2. Use this well known inequality: $\left| {\left| x \right| - \left| y \right|} \right| \leqslant \left| {x - y} \right|$.
Part (a) follows at once.

For part (b), consider $\left( {b_n } \right) = \left( { - 1} \right)^n$ .

3. ## Thanks Plato

I just wanted to say thanks for responding to my question. Luckily I was able to locate the answers you listed in my notes from class. Unfortunately I stayed up all night completing this assignment.