Difficult: I am having a difficult time understanding Theorem 7.25. I don't understand why G is the union of all cosets of K, and how there can be a bijective function from K to Ka. It seems like Ka would be a lot smaller than K, so how can there be a bijection?
Reflective: I think it's really interesting that subgroups of a group G can also have congruence classes. I think it seems more similar to congruence modulo an ideal as opposed to congruence modulo an integer, so I hope that I will be able to understand it better this time.
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