# Why the class of all inductive sets is not a set?

Page 66, Set Theory of - Herbert B. Enderton, Elements of Set Theory.

It says "but the class of all inductive sets is not a set."

• @MauroALLEGRANZA If $\omega$ does not exist, then the class of all inductive sets is a set. It is the empty set. I think the OP is working in $\text{ZFC}$ (in particular with the infinity axiom) and he or she wants to see that in this setting this class is not a set. This is more along the line of tetori's interpretation. – William Apr 23 '14 at 9:24
• @William - you are right. – Mauro ALLEGRANZA Apr 23 '14 at 10:13