Does {Sn} Converge to L if and only if {Sn - L} Converges to 0?

[ocohen]

Homework Statement

Show that a sequence S_n will converge to a limit L if and only if S_n - L converges to 0

Homework Equations

{S_n} converges to L if and only if {S_n - L } converges to 0

The Attempt at a Solution

Is it enough to just say

{S_n} converges to L if and only if |S_n - L| < \epsilon if and only if |(S_n - L) - 0| < \epsilon if and only if {S_n - L}$ converges to 0

I'm learning this off a random pdf so I don't have the answers.

Is this enough? Any suggestions would be appreciated. Also is there a way to turn on Latex?

 

[System]

since Sn converges to L, then :
lim Sn = L ... (1)
for the sequence {Sn-L}
lim ( Sn - L ) = lim Sn - lim L = L - L = 0
so {Sn-L} converges to 0

its looks easy for me, or i missed something :S