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Do we have :
$$\sup(\sqrt n! - E(\sqrt n!))=1?$$$$\sup\{\sqrt {n!} - E(\sqrt {n!}); n\in I\!\!N\}=1?$$
Where $E(\cdot)$ is the integer part function, and $n!=1\times 2...\times n$.
$$\sup(\sqrt n! - E(\sqrt n!))=1?$$
$$\sup\{\sqrt {n!} - E(\sqrt {n!}); n\in I\!\!N\}=1?$$
