Proof for Feedback:
- Please feel encouraged to work on daily posts together if you like. You can find friends on discord or during group work in class. The only rule is that when you are writing up solutions, you are writing your own understanding, not copying. (The reason for this rule is that you will learn more.)
- Log into canvas and check out the feedback on your daily posts so far. We have a grader who is giving feedback on the proof for feedback. I’m also dropping in and making some comments here and there.
- While you are in canvas…. If you think you would like to make use of office hours regularly this semester, please fill out the when2meet link on canvas I can choose some times that will work for those who will attend (you can use your name, or you can use a fake name and let me know). If you think you would like to make use of office hours only occasionally, I am happy to set a special time when needed, so you can skip filling out the form.
- Take a look at these example proof solutions to the proof from last daily post. Think about how to improve your proofs. If you have questions about your proofs or my solutions, please ask them on discord. (I’m curious what you think of ChatGPT’s proof? Discuss on discord with me if you have some thoughts on this.)
- Don’t forget your proof for feedback above. You might choose to put it off until you read Section 1.3 (next item) about set containment.
- Read Section 1.3 of Hammack. This is about subsets. He gets a little wild, and most of his exercises are about sets of sets. You should try as many of exercises A and B from that chapter as you like (if you want to try exercises C, you may need to dip into Section 1.2, which we haven’t done yet).
- Give an example of three sets , , and , such that , , , and . Optional: ask a friend to double-check your answer on discord.
- Give an example of two sets , and , such that , and . (Yes, you read that right.)
- Use set-builder notation to describe the set of all integers that are both perfect squares and perfect cubes.
- Use set-builder notation to describe the set of all sets with cardinality four.
- Use set-builder notation to describe the set of all integers which are divisible by seven. Do this two essentially different ways.
- Return to the socks problem and the cups problem from the last daily post and see if you can solve them and give proofs. We will discuss these in class, so give them a go!