We missed class on Tuesday due to the student demonstrations on Monday night. And then the class was moved to Friday. Sigh.

**Friday, 5 October 2012: **We went over the quizzes from last Wednesday, and built on some ideas about Z_n and modular arithmetic. Then we discussed cardinalities of infinity, and bijections between certain infinite sets.

**Readings:**

Infinity is for Children - And Mathematicians!

Hotel Infinity

Wikipedia: Hilbert's Grand Hotel

** Suggested Problems:**

1) It's a good time to try the challenge problem from the quiz-day last week! First, compute {x^2 | x in Z_3}. Then, show that if a, b, and c are integers such that a^2+b^2=c^2, then at least one of a, b, and c is divisible by 3.

Next, compute {x^2 | x in Z_2} and show that if a, b, and c are integers such that a^2+b^2=c^2, then at least one of a, b, and c is divisible by 2.

Next, do it again for Z_5.

Can this reasoning work for any other prime numbers?

2) Is there a bijection between the natural numbers and the rational numbers? (Tool: If S and T are sets, and there is an injection from S to T and another injection from T to S, then T and S have the same cardinality.)

3) Is there a bijection between polynomials with positive integer coefficients and the natural numbers?

I am so much greatfull for the last lesson whereby it was perfectly done and I hope that it will be the same today. Thank you so much as I am preparing for the cat's and end semester exms.Good day