# MATH 4LT3: Topics in Logic

Winter 2020: Set Theory

We explore the basic concepts of set theory, starting with the construction of the real numbers, assuming we know what rational numbers are. Then we continue by questioning this assumption, which eventually leads us to figure out a way to define the natural numbers. This in turn leads us to formulating fundamental axioms underlying all of mathematics, the axioms of set theory. We then learn how to work with them, and how to extend the notion of natural number to include infinite numbers called ordinals.

What you need for this course is to be familiar with proofs in Calculus, as taught in MATH 1XA3 or MATH 3A03, as well as basic mathematical notations, and to bring with you an enthusiasm for abstract reasoning. Proof writing is an essential feature of this course.

### Announcements

Apr 22: The course grade is not avaiable on Avenue, but it will be available on Mosaic. Thanks for listening, and have a good summer!

Apr 17: Quite a few of you did not deem it necessary to explain many of your arguments in your answers to the final exam, even though I thought I was clear I expected you to do so.  This led to some low scores.  You may submit rewrites by Tuesday, April 21 at 11:30pm, for a maximum of 80% of the full score per resubmitted problem.  These rewrites should be submitted as part of the Final Exam assignment, and their file name should clearly indicate they are rewrites (unless you want me to miss them…).

Apr 9: The Final Exam is now posted on Avenue as an assignment. It becomes visible to you tonight at midnight, and it is due on Thursday, April 16, at 11:30pm.

Apr 3: There is overwhelming support for a take-home final exam. So I will post it here on Thursday, April 9, and it will be due one week later, submitted on Avenue. In the meantime, thanks for your patience with my online lectures!

Mar 31: I’m thinking of holding a Final Exam on Avenue 2 Learn, scheduled at the original final exam time. I would post the exam as a quiz on Avenue, and you will have two hours to complete the exam (on paper, say) and upload (a scan of) it. Obviously, you could use your notes and book, so the questions would take this into account. Please let me know by email if you have any objections to this; the alternative is a take-home exam (more time, harder questions).

Mar 25: Class cancelled due to technical difficulties. I’m trying to find a way to run these lectures from home…

Mar 18: Our first Webex lecture was successful, and the recording is now posted on Avenue to Learn. Please let me know if you cannot access it.

Mar 17: I have just scheduled a Webex meeting for tomorrow’s lecture. You should receive an email invitation that lets you join the meeting during our usual class time. The meeting will be recorded and, if successful, I will post it on Avenue to Learn afterwards.

Mar 17: I’m still working on moving lectures to online delivery. In the meantime, please keep reading the sections added to the list below, and start working on Homework 4…

Mar 16: It is unlikely that everything will be ready by this Tuesday to deliver my lecture online; for one thing, my plan to do so needs to be officially approved before I can do so. So I will post reading assignments below, one for Tuesday and probably one for Wednesday. Please continue to check this page for updates; and remember that I can still be contacted by email.

Mar 13: Starting with the next homework assignment, you will submit your answers on A2L, say in the form of a scanned file. Please make sure that your scans are clearly legible; otherwise, I will return them unmarked. We will of course continue with our kritik assignments as usual. I will decide what to do about the final exam soon…

Mar 13: Following McMaster announcement to cancel all in-class lectures and exams for the remainder of this semester, I am activating this class on Avenue to Learn. You should already be able to see it in your A2L page; if you do not (maybe because you are not registered for this class, or for similar reasons), please let me know by email so I can add you to the class list. The page of reference for material covered will continue to be this one rather than the one on A2L; the latter is only used for homework submission and posting of recorded lectures (yes, I will record my lectures and post them).

Jan 8: I mentioned in class that $\sqrt 2$ and $e$ are irrational numbers. You can find proofs in these slides for MATH 1XA3.

Jan 8: If you are signing up with Kritik.io for more than one course, you can get a discount. Just contact them through their site after you signed up for both classes.

### Homework

To be handed in at the beginning of class on the indicated due date.