1. You know that feeling when you've find out you've been lied to all your life? That's the feeling I just had as I read about functions. You'd think that in the 3,896 (give or take) classes I've had where we discussed functions, I would've figured out that f(x) meant that "x" was simply mapped onto a function. I'm kind of embarrassed that my mind was so blown over this fact. Also I realized why the vertical line test works for testing to see if something is a function. BECAUSE EVERY x MUST HAVE A VALUE, AND IT CAN ONLY HAVE ONE ASSIGNED y VALUE! (insert fireworks of excitement here.)
2. Well now, I hope I realize that cardinality and absolute value are not the same thing. When I originally read that the cardinality of B^A is the cardinality of B raised to the cardinality of A, I read it as absolute value signs, and was about to rip the page out of the math book. The good news is that, as usual, the problem was user error. This chapter basically just reworded something we already knew for one dimension, and put it into two dimensions for us. Rather than working with the elements of sets, we are working with the sets themselves. Fun stuff.
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