WEEK 2   
M: Proof of Prop 1.9. Cartesian products, relations, functions. Well-foundedness.
     1.10. Definition. Cartesian product.
     1.11. Proposition. If A,B are sets then the Cartesian product A × B is a set.
                                   (Two arguments: one with Replacement and one with Power set)
     1.12. Definition. Class relation, relation, class function, function.
     1.13. Definition. Reflexivity, symmetricity, antisymmetricity, strict antisymmetricity, transitivity of a class relation.
                                  Equivalence relations, ordering relations, strict ordering, linear ordering.
     1.14. Definition. Well-founded relations. 
W: Set-like relations, R-transitivity, inductivity, natural numbers. 
     1.15. Definition. R[A], R^-1 , pred_R(a).
     1.16. Definition. R transitivity, transitivity. 
     1.17. Proposition. If x is transitive then so is S(x).
     1.18. Definition. Inductive class.
     1.19. Definition. \omega. 
     1.20. Proposition. (a) All elements of \omega are transitive.
                                      (b) \omega is transitive.
     1.21. Proposition. If A is a nonempty subset of \omega then a has an \epsilon-minimal element.
F: Functions. Recursion on \omega.
    1.22. Definition. Class function, F : A --> B, injectivity, surjectivity, bijectivity, restriction F|A.
    1.23. Theorem. (Recursion on \omega). Assume G : V --> V is a class function. Then there is a unique set function
                                 f : \omega --> V such that
                                 f(n) = G(f|n)
                                 for all n\in\omega.