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Convergence and Limit

Definition: An infinite sequence s over R converges to limit a, if its members approach a arbitrarily close:

s converges to a : <=>

forall epsilon > 0: exists n in N: forall i >= n: |si - a| < epsilon ;

lim(s) :=

such a: s converges to a.

A non-convergent series is called  divergent (divergent):

s is divergent : <=> ~exists a: s converges to a.