Read Hamkins (not Hammack), Chapter 1, A Classical Beginning (pages 1 through 8). This is about the proof of square root of 2 being irrational. Note: Hamkins can be read through CU’s library system online! This link(or searching “Hamkins Proof and the Art of Mathematics” at CU Library) should get you to the library’s listing, then click through for online access; may require being on campus, using CU VPN (library instructions) or using library proxy to prove you are a student.

Hamkins, Chapter 1, Exercise 1.9 and 1.10. (Both proofs are wrong — what’s wrong?)

I have still noticed some confusion on “element of” vs. “subset of”. Do this worksheet on the topic. The answers, if correct, spell a little message (ask on discord if it isn’t clear).