Difficult: I had a hard time understanding the order of an element, and how to find it. The more difficult part for me though, was to find out whether or not an element has distinct powers by looking at the elements in a group. The example on the top of page 177 was difficult for me. I understood what it was talking about, but I don't think I would know to how figure out the powers on the exponents on my own. I also thought it was difficult to find out if an element has finite or infinite order.
Connections: I like in this section that some of the properties of groups are properties that I have used in other parts of mathematics. For example, the inverse of ab is b inverse times a inverse. This is similar to concepts used in linear algebra. Also, some of the properties of exponents hold as well. Since I have been using these concepts for a while, I am more comfortable using them and applying them to new ideas such as groups.
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