term \(a_n\) to be bounded below by \(M\) just means that \(a_n \geq M\).</p>
<p>Altogether then, being bounded below means &ldquo;there exists an \(M \in \mathbb{R}\), so that for all \(n \in \mathbb{N}\), we have \(a_n \geq M\).&rdquo;  Sometimes you might see this ending with \( a_n > M \), but that is a difference which does not affect which sequences are bounded below.</p>
