A sequence, (a_n) is Cauchy if, for all epsilon > 0, there is a number, N, which is a natural number where |a_n - a_m| <> N
So how is this useful? Well, for starters, all cauchy sequences are convergent. Need a proof?
Also, every convergent sequence is cauchy ^^, here is the proof:
I will later do this in LaTeX, so the formulas are more understandable desu~^^. For now, bye bee. The empty spaces are empty by the way.