Difficult: So this all sounds great and dandy, I'm just not so sure about when sums or products are not well-defined. I mean, I guess the example in the book at the end of the chapter just completely changed the definition of what multiplication (redefined the function) and then called it not well-ordered... Sounds like cheating to me. Haha
But it would be great to go over proofs of well-defined. But from what I see, It looks like we just added another layer. Well defined --> Equivalence Classes --> Relations --> Modulos--> Divisiblity and then all back out!
Interesting: Man, we use modular arithmetic all the time! Clocks is a great example, both minutes and hours are mod 60! Days of the week work in mod 7, but I guess days in a month gets messed up because it's (mod 28, 30, or 31). But still cool nonetheless!
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