Real analysis proof with sequences

[koab1mjr]

Homework Statement

Let Sn be a sequence in R

Prove lim Sn= = 0 if and only if lim abs(Sn) = 0

Homework Equations

none

The Attempt at a Solution

I think this is someone ciruclar logic and that is why I am stuck

Assume lim Sn = 0, thus for n > N implies |Sn| < epsilon or -epsilon < Sn < epsilon. Since Sn and -Sn are less than epsilon |Sn| < Epsilon for sufficently large n.
Now assume lim |Sn|= 0 so ||Sn||< epsilon and using a similar argument show Sn < Epsilon and complete the proof. IS that the way to go?

 

[Dick]

It's not circular, it's just that proving Sn->0 and |Sn|->0 are pretty much the same thing. Yes, that's the way to go.