I did not know the properties in theorem 26.12. I'm not sure I follow their proofs.
I find it interesting that there are so many instances of an "identity" object in math. For example, $I$ is the identity matrix that does not change any matrix it is multiplied by. In scalar multiplication, 1 times anything equals anything. In addition, 0 plus anything equals anything. Now we have an identity function. I seems somewhat counterintuitive that something that doesn't affect whatever it is applied to is such a powerful tool in math. That's what makes math interesting!
It would have been very nice to have known the technical definition of the inverse relation at my math camp. It would have made my life easier. Now I'm salty.
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