Math 39 Homework #23 Our minds are finite, yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude. Unknown

	Reading Read what we will cover in the next class: 6.3. When reading 6.3 pay special attention to the following concepts: the three basic recursive functions, the three rules for 'combining' known recursive functions to obtain new recursive functions, characteristic functions of a relation, recursive relation, the many examples of recursive functions and relations, and the couple of general rules for combining known recursive functions and relations to obtain new ones.

	Problems The following problems are due by the beginning of class on Wednesday 11/18. Hamilton (p.137) 6.3 Note that there is a typo in 6.3a; the problem should read: "n is not a prime number." Show that the following relations on the natural numbers are expressible in PA: {0} {0,1} {(0,1)} You will probably want to use Proposition 6.1 in proving that PA deduces certain wfs.