Difficult: I think that the definition of right cosets is kind of confusing. However, it reminds me of some things we did with ideals. I think that the notation is just confusing to me. Also, I don't really understand what makes it a right cosets... what is a left coset? Thus, I didn't really understand theorem 7.25 because I don't understand even what the union of all the cosets would be.
Connections: In this section, I think I understand what it means for two elements of a group to be congruent modulo a subgroup. It is pretty similar to how it has been defined previously with rings, and ideals. I also understand how congruence modulo a subgroup is also an equivalence relation just as congruence has been in previous sections. Like I said before, I think I understood congruence, but the right coset thing is still a little weird to me, and also I am left wondering why do we care about the right coset anyway? What is so important about the right coset??
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