MATH145 Lecture Notes - Lecture 3: Choice Function, Yggdrasil, Power Set

• School: University of Waterloo
• Department: Mathematics
• Course: MATH145
• Professor: Stephen New

Document Summary

Zfc axioms: empty set: there exist a set, denoted by , with no elements, equality: two sets are equal when they have the same elements. A = b when for every set x , x a x b: pair axiom: if a and b are sets then so is {a, b}. In particular, taking a = b shows that {a} is a set: union axiom: if s is a set of sets then s = sa s a = {x | x a for some a s}. If a and b are sets, then so is {a, b} hence so is a b = {a,b: power set axiom: if a is a set, then so is its power set p (a). P (a) = {x | x a}. X, x x: axiom of in nity: if we de ne. 3 = {0, 1, 2} = { , { , { }}} n + 1 = n {n}