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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
.
Cite this web-page as:
Štefan Porubský: Bounded sequence.