The class indexed by real numbers is a set?

Whovian

A set can be of anything. Even {Lincoln, Charizard, {Fish Fingers, Custard}} is a set. Your set is, therefore, valid. Note that its cardinality is one of the alephs, I don't know which one.

Whovian	A set can be of anything. Even {Lincoln, Charizard, {Fish Fingers, Custard}} is a set. Your set is, therefore, valid. Note that its cardinality is one of the alephs, I don't know which one.