1. The problem statement, all variables and given/known data Let Sn be a sequence in R Prove lim Sn= = 0 if and only if lim abs(Sn) = 0 2. Relevant equations none 3. 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 arguement show Sn < Epsilon and complete the proof. IS that the way to go?