The proof of Theorem 4.21 looks just like a big mess on the page at first glance. Then it still looks that way at second glance. It only looks slightly better after reading. I was getting lost in the proofs and wanted just to say, "Ok, I'll take your word for it." The theorem itself is fine as the commutative, associative, and distributive laws are similar to the same laws we learned as children. De Morgan's Laws are easily accepted and understood. Maybe that is the problem - they are accepted and understood, so I haven't seen them proved before. I think that all of the symbols made the proofs look jumbled and crowded. It was difficult for me to read them straight through.
The section 5.1 on counterexamples seems a bit more like what I've been used to in previous math courses. It's more like solving equations and getting "answers." You look at the statements and you've got to find real numbers or integers which disprove the statements. This was definitely more in my comfort zone as I've found myself in past proofs trying to plug in integers, for example, and calculate the equations to confirm their validity.
No comments:
Post a Comment