> [!NOTE] Definition (Suprema and infima of sequences) > Let $(a_{n})_{n=m}^{\infty}$ be a [[Real sequences|sequence]] of [[Real numbers|real numbers]]. Then we define $(a_{n})_{n=m}^{\infty}$ to be the [[Bound of Set of Reals#^de37d4|supremum]] of the set $\{ a_{n} : n \geq m \},$ and $\inf(a_{n})_{n=m}^\infty=\inf \{ a_{n} : n \geq m \}.$