we say a sequence tends to minus infinity, written
:, or
:,if the following holds:
:For every real number , there is a natural number such that for every natural number , we have ; that is, the sequence terms are eventually smaller than any fixed .

Symbolically, this is:
:.

If a sequence tends to infinity or minus infinity, then it is divergent. However, a divergent sequence need not tend to plus or minus infinity, and the sequence provides one such example.

Metric spaces

Definition

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