COS 550 F08 HW #2 DUE Thursday 9/18/08
Problem 1 Below, 20 points
Problem 2 Below, 20 points
Problem 3 Below, 20 points
Problem 4 Below, 20 points
Problem 5 Below, 20 points
********** Problem Notes *********,

PROBLEM 1: Prove that the number of legal Java programs is exactly |N|. 
Give some indication of whether this result holds for other programming 
languages as well.

PROBLEM 2: Prove that there are real numbers that cannot be computed by 
any Java program. Does this result hold for other programming languages? 
Give a reason.

PROBLEM 3: Prove that a countable union of countable sets is countable.

PROBLEM 4: Determine the relationship between |PowerSet(N)| and |R|.

PROBLEM 5: Prove or disprove the following statement: the function f: N x 
N -> N given by f(a,b) = (a+b)(a+b+1)/2 + a is a bijection.