second draft of this book
of this book
Next: Infinity Up: Axioms of Set Theory Previous: Axiom of union Contents
The integers are defined by an axiom that asserts the existence of a set that contains all the integers. is defined as the set containing and having the property that if is in then is in . To write this compactly we define some notation. We use the integer 0 to represent the empty set. If we have some set then we can construct a set containing that is written as .
This says there exists a set that contains the empty set 0 and for every set that belongs to the set constructed as also belongs to .