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A sequence $\{s_n \}$ is called bounded if there are $a,b \in \mathbb{R}$ such that $a \leq s_n \leq b$, for all $s_n$ with $n \in \mathbb{ N}$. This means that all terms of that sequence are contained in the closed interval $[a,b]$. A sequence is upper bounded if there is $b \in \mathbb{R}$ such that $s_n \leq b$, for all $s_n$ with $n \in \mathbb{ N}$. Similarly, a sequence is lower bounded if $a \leq s_n$. A sequence is bounded if and only if is upper bounded and lower bounded.