i'm trying to study for an Analysis exam, but im gettin stuck on something which i imagine is quite trivial!!

here is an example from something we were taught in lectures.

lim = 0 (n )

and the proof is

> 0 given

take N( ) s.t. N( ) >

for n N( ) , we have

| <

what i'm having trouble with is what actually is used for, and consequentially what N( ) means.

any help (in the simplest form) would be very much appreciated.