I got it! As I was writing this it clicked. I couldn't for the life of me figure out how to reduce the equivalence classes down to within 0 through 5. But then I thought about the remainder. Okay...well now that that's settled. Everything else makes sense, but that was the toughest part for me.
I think that the idea of being 'closed' is kind of fun. And then I started thinking about what a set would have to have in it to be a closed under multiplication and addition and realized that that could get big really fast. While that could be tedious, theoretically it's interesting that if we multiply or add two numbers in the set that the product is still in the set. Actually, would we be able to represent that in a finite set? Probably not I suppose since the product of any two integers also can form a product with another integer in the set. Neat.
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