Definition:Bounded Sequence/Complex

From ProofWiki
Jump to navigation Jump to search

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


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 $z_i$.


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