Difficult: Whoa, big concept chapters! A lot to take in! First off, the proof that inverse functions are functions if and only if the functions are bijective was a lot to take in. If we're going to need to prove that on our own, it would be helpful to review it again in class. Also, are rational and linear the only functions we can easily find inverses of? It mentioned we can't find inverses for some polynomial functions, but are there any other ones we can do?
For permutations, do we always use natural numbers that come right in a row? Or could me use B= {2,5,8}, or even B={a,b,c} to find permutations? Also, what do we do with them...? Or just look at them since is it just a concept for now?
Finally, at the end it said "permutations satisfy the the properties of closure." What is a property of closure?
Interesting: Well, the one thing I do like about permutations is that they are easier to write than listing out all the commas and parentheses. I also thought it was interesting how we can make all functions inverses by cutting off the codomain that we don't use, but I guess that's kind of like what we did for the inverse trig functions.
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