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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.