Difficult: I am having a hard time understanding what exactly the order of an element of a group is. I know what the order of a set is, but I don't understand how the two different orders are related, or if they are at all.
Reflective: It's interesting to me that, while there are some group properties that are almost the same as the ring properties, there are also many properties that are very different and have no relation to rings. for example, the properties of the order of a group G don't have any relation to rings.
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