# Sequence convergence

1. Sep 29, 2009

### tarheelborn

1. The problem statement, all variables and given/known data
For any a, b in R, show that ||a|-|b|| <= |a-b|. Then prove that {|s_n|} converges to |L| if {s_n} converges to L.

2. Relevant equations

3. The attempt at a solution
For the first part, ||a|-|b|| = |a-b| by the triangle inequality. For the second part, ||s_n|-0| < epsilon implies that |s_n -0| < epsilon, but I am not sure how to work that around to the L's.

2. Sep 29, 2009

### g_edgar

What? For example:
$\big|\,|2|-|-2|\,\big| = |2-(-2)|$
?????

3. Sep 30, 2009

### fmam3

Get the $$| |a| - |b| | \leq |a - b|$$ right first. The second part just follows by the Squeeze Theorem, or more simply, just "shove in the epsilons" if you know what I mean.