Bounded Sequences

If a sequence

is bounded above, then c = sup(a_j) is finite. Moreover, given any > 0, there exists at least one integer k such that a_k > c - (see picture).

If a sequence

is bounded below, then c = inf(a_j) is finite. Moreover, given any > 0, there exists at least one integer k such that a_k < c + (see picture).

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