Theorem 36.7 is cool.
I feel like I have some deep insight about this on the tip of my brain (is that a phrase?), but my conscious mind can't put words to it. So I will think about it and maybe I'll have something cool to say tomorrow. I think it has something to do with the facts that functions are closed under multiplication and addition and that domains can be bounded weirdly. I'm not sure.
Random question in preparation for the midterm: If f: A \rightarrow B and g: A \rightarrow B and we know that f is injective and g is surjective and f \not= g, can we conclude that a bijection must exist? I think so, though we can't conclude what said bijection is based off of the given information. I will try to remember to ask this during office hours.
-Batman
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