I think it is really cool that a set can have a lower bound that is not actually included in the set. It makes me wonder the purpose of lower bounds, though, as -1, -2, 0, etc are all lower bounds for the set (0,1]. If the lower bound can be any arbitrary selection from anything within a specific domain that is exclusive of the domain of the original set in question, what use does the lower bound have?
I understand the greatest/least element and upper/lower bound thing when I read it on paper, but I think it would sink in better and I would have a more full understanding of it if I were to hear it explained. That was probably the hardest part - connecting the meaning behind the phrases to the bigger picture. I struggle with that when I am reading more so than when it is explained.
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