Consultations by email arrangement. Use "Set Theory" in subjects of emails.
This is a smart definition which makes it possible to define relations and functions and prove basic facts. Ordered n-tuples are also easy: (a,b,c)=((a,b),c).
(We need new axiom here: this does not follow from what we already have)
Proof: The set \(A = \{n \in N : P(n) \}\) is inductive
To prove this we used induction principle to show transitivity, assymetricity. Hard step was linearity that needed double induction.