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Bounded sequence

The sequence , of a metric space is called bounded if for some there exists a number such that for every . The sequence which is not bounded is called unbounded.

In the case of complex sequences we get that a sequence  , of complex numbers is bounded if there exists a number such that for every index .

If , is a sequence of real numbers then it is said to bounded above by if for every index . On the other hand,  it is said to be bounded below by if for every index .

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