Archimedes has a stack of books in his library. He has numbered the bottommost book with '1', the next book with
'2', and so on.
In terms of logic, we let q(x, y): Book number x is on top of book number y.
And observe the Rule of Archimedes Library
Which numbered books are in the stack?
In order to prove the implication in formal terms, we need one more principle:
The Well Ordering Principle
Every non-empty subset of positive integers has a smallest element
Proof (by contradiction):
Let us assume the contradiction false and hope that it contradicts a premise
This means that there exists a nonempty set
March 4, 2016
Lecture Notes Page 1
Lecture Notes Page 2