Math 29 Homework #11 Reductio ad absurdum which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit then any chess gambit; a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. Godfrey H. Hardy

	Reading Read what we covered in today's class: 4.2, 4.3 Read what we will cover in the next class: 4.4 When reading 4.2 pay special attention to the following concepts: Definition 2.1, Theorems 2.4 & 2.5 which give us the effective denumerability of the computable functions, Theorem 2.6 in which we obtain a total noncomputable function. When reading 4.3 pay special attention to the following concepts: The diagonal method. The example on page 80 should probably look familiar. When reading 4.4 pay special attention to the following concepts: The s-m-n theorem, note its simple and more general versions. What is the difference between them? Why would we bve interested in a theorem like this?

	Problems The following problems are due by the beginning of class on Friday 4/23. p. 77, # 4.2.3 p. 80, # 4.3.2.1 p. 80, # 4.3.2.2 p. 80, # 4.3.2.3 p. 80, # 4.3.2.4

	Presentations Joran, Theorems 4.1.3 and 4.1.4 on Monday 4/19 David, Theorem 4.2.6 and the diagonal method on Wednesday 4/21 Amanda, Theorem 4.4.3 on Thursday 4/23