I find the function notation as a set of ordered pairs very interesting.
I LOVE it when all the math comes together. The notation used in previous chapters of this book in combination with the usual function material is a wonderful sight to see. I'd imagine we are going to get into bijections shortly, which will then connect what we are learning in linear algebra to this class, in addition to some number theory I learned at my math camp. I'm excited.
Is the characteristic function mentioned in this chapter similar to the characteristic equation we learned about in linear algebra? I am thinking that the characteristic equation defines a function spanning the domain described by the matrix. If we fall outside of the domain of the function, then the characteristic function returns a 0.
How do equivalence relations fit into all of this?
I'd love to see more (and different) examples of the "well-defined function" thing.
OH MY GOODNESS! I just turned the page and we will be doing injections and surjections in the next chapter!!! Happy day!!! I learned about these at my math camp. They were super fun and I loved working through problems about them with my instructors! I'm a nerd.
-Batman
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