1. The proofs in section 4.6 were super hard to follow. Not because the math was complicated, or because I couldn't follow it, but because there was so much math on one line. It was hard for me to go from step to step, even with the words "then" and "and" separating the statements. I don't think I'm allowed to critique how the authors of the book about proofs write their proofs, but I probably would have made the proof go onto multiple lines so it was easier to follow.
2. Is the "equal" sign equivalent to "if and only if"...? I am guessing that it is, since the proofs with just an equal sign are proving both the statement and the converse.
I have been wondering how we would write proofs that are usually true, but there are some values for which the statement is false, and I really like the format that was introduced in section 5.1. of (excuse the latex writing...) x \in {R} - {set for which the statement is false}. It makes it so that there are many more useful theorems in the world (such as the tan^2 (x) + 1 = sec^2 (x) example.
This coming week I am going to have to make a list of all the vocabulary and rules that we have for this unit. I need to be able to remember the Laws and the Cartesian product (and everything else we've been learning...) for the test.
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