Cauchy Condition

Missed posting yesterday because I had 14 hours at work. Yes. On a Sunday.

Anyway, that non-rest-day behind us, let's move  on with Analysis. The Cauchy condition simply states another indicator of convergence. That is {a_n} is a convergent sequence if and only if  {a_n} is a Cauchy sequence. A Cauchy sequence is one such that for all ε > 0, there exists N such that if n, m > N, then |a_n - a_m| < ε.

The usefulness of this result should be fairly obvious: it allows one to prove convergence to a limit without having to actually compute the limit.