Difficult: The most difficult thing was definitely the transitive property. I was familiar with all three of these properties, but not with relations. It was okay when I had an explicit set of points to look and see if it was transitive. However, when it became more vague, such as |a-b|<1, then it became much more difficult to visualize. The most helpful thing would probably be working on examples to get these concepts down. I feel, just like we did with sets, we're going to learn these concepts, and then have to prove them to the maximus in upcoming lessons.
Interesting: I'm a really visual guy, so when I had to see if a set was transitive for specific, explicit elements of a set, I would just picture the ordered pairs bumping into each other. (They weren't allowed to rotate, but they could move and bump other elements in the set) If the right side of one bumped into the left side of one and they matched, then the middle two numbers would disappear and leave me with a new ordered pair. That ordered pair had to be present, or else the set was not transitive.
I know that's kind of goofy, but it helped.
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