Quiz 1, Quiz 2, Quiz 2 answers Quiz 3.

Sample questions for test 1, answers (partial), more answers.

Study these definitions for Test 1.

Test 1 and answers.

Injective and surjective (= onto) functions (contains 2 HW questions). Answers.

Two more questions on injective/surjective and answers.

Hotel Infinity

Sample questions for test 2 and answers.

Cardinal numbers: List of facts (short version), Answer to Ex 20 + quick way to tell if a set is countable.

Additional sample questions for test 2: This handout contains five sample questions for test 2, three turn-in-homework questions, and a shortened version of "list of facts on cardinal numbers" (a text like that will also be attached to the actual test 2, but some of items 1-7 may be deleted because those are things that need to be memorized).

Answers to the above sample questions: do not look at this until you have tried your very best to answer as many as possible questions on your own (with help from class notes, handouts, book, etc.)

More sample questions with answers. Again: do not look at answers until you have tried everything else first.

Test 2 and answers.

Axioms of Set Theory (on wikipedia) and explanation.

Why proofs need rigorous definitions (instead of intuitive descriptions) and why we need to avoid circular definitions.

Definitions and facts on open and closed sets and convergent sequences.

Material for test 3 (new questions are at the end of this file). Answers found here but do not look at any answers until you have run out of problems you can solve on your own.

Test 3 and answers. Several people asked about proofs using different methods, so I typed more proofs for Ex 3,4,5 (pay special attention to the issue of not using the same letter for potentially different numbers!).