The class indexed by real numbers is a set?

julypraise

Let [itex]\mathcal{S} = \{S_{i}:i \in \mathbb{R} \} [/itex] where [itex]S_{i}[/itex] is a set. Then [itex]\mathcal{S}[/itex] is a set? Or, can this notation make sense in some way?

julypraise	The class indexed by real numbers is a set? Tweet Let [itex]\mathcal{S} = \{S_{i}:i \in \mathbb{R} \} [/itex] where [itex]S_{i}[/itex] is a set. Then [itex]\mathcal{S}[/itex] is a set? Or, can this notation make sense in some way?