Theorem 9.11 quickly made sense.
Let f : A → B be a function. Then the inverse relation f−1 is a function from B to A if
and only if f is bijective. Furthermore, if f is bijective, then f−1 is also bijective.
The proof got a little jumbled for me. In order to show that f-1 is a function, I suppose it is as easy as showing that f is one-to-one and onto. I am confused as to why the proof continued with the converse. For me, it has been helpful to follow a proof pattern when writing my own proofs. If I have a guide of what needs to be shown, it is manageable. I don't quite get the pattern of this proof and would need a clarification as to why it was set up the way it was.
I remember learning about permutations in a statistics class I had last semester. Pretty interesting. That part of the material made sense to me, although I remember getting a little tripped up with permutations as they became more complicated. It is interesting to note that permutations are bijective functions and have inverses. I didn'onsider that really when I learned about them last semester, but it definitely makes sense. I look forward to Chapter 13 when they are discussed in more detail.
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