Definition:Bounded Sequence/Complex

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This page is about complex sequences which are bounded. For other uses, see Definition:Bounded.

Definition

Let $\sequence {z_n}$ be a complex sequence.


Then $\sequence {z_n}$ is bounded if and only if:

$\exists m, M \in \R$ such that $\forall i \in \N: \cmod {z_i} \le M$

where $\cmod {z_i}$ denotes the complex modulus of $z_i$.


Unbounded

$\sequence {z_n}$ is unbounded if and only if it is not bounded.


Sources