13 Aug 2016

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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

Lecture 22

March 4, 2016

10:30 AM

Lecture Notes Page 1

Lecture Notes Page 2