* Last Updated: April 13, 2002 *

Term Test 3 Related Links

1) Constructible Numbers & Surds - Good Review

2) Cardinality   (.pdf file) - Excellent file!! (you must be able to read *.pdf files to view this)

3) Selected Cardinality Solutions - On pages 3,4,5 (pdf)- Very few questions, but still good =)

4) Suppose that A is a set which is at most countable, and B is an infinite set.   Prove that AU B has the same cardinality as B.                                   The Solution [found on page 4]

Term Test 2 (with an overlap with Term Test 3) Related Links

1) Cardinality  - Defines Cardinality, Countable and Uncountable Sets and Dedekind Cuts.    Has Sample Questions on ALL topics relevant to the test and INCLUDES ANSWERS to these questions... Show that all polynomials of a fixed degree n (with integer coefficients) are countable by using the above result on finite cross products.  Show that all polynomials (with integer coefficients) are countable by writing that set as a countable union of countable sets.   Use Dedekind's Theorem to show that the set of integers Z and the interval of real numbers between 0 and 2, [0, 2], are both infinite(which is of course not surprising). Let N be the set of natural numbers, Z be the set of all integers. Which set, if any, has the bigger cardinality ?

2) Cardinality   (.pdf file) - Excellent file!! (you must be able to read *.pdf files to view this)

3) Uncountable Sets: More on Uncountable Sets, including the classical example (0,1)

4) The Cantor-Schröder-Bernstein theorem  A Proof to the theorem (as rigourous as the one we did in class)

5)  Proof of the Fundamental Theorem of Algebra : Another rigourous proof ( like the one we did in class)

6) Cantor's Diagonal Problem

7) Another Cardinality Link  - Countably Infinite Sets, Rationals, Natural Numbers, Cantor Diagonal problem etc...

8) Assorted Topics: Fundamental Theorem of Algebra, Complex Numbers, Roots of Unity etc.

9) Problems AND Solutions to Complex Numbers Questions  - GREAT link with an assortment of problems, some go beyond our level though.

10) Problems AND Solutions to Assorted topics - GREAT link, has questions on Complex Numbers, Rational, Countable sets, Algebraic etc.

Exam Review Related Links*