# Bounded iff Big-O of 1/Sequences

## Theorem

Let $(a_n)$ be a sequence of real or complex numbers.

The following are equivalent:

- $(1):\quad$ $a_n$ is bounded

- $(2):\quad$ $a_n = O(1)$, where $O$ denotes big-O notation

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Let $(a_n)$ be a sequence of real or complex numbers.

The following are equivalent:

- $(1):\quad$ $a_n$ is bounded

- $(2):\quad$ $a_n = O(1)$, where $O$ denotes big-O notation

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