There is still something in the textbook that gives me some trouble. Negations and empty sets. I find it difficult to recall what the negations are when they involve "For every" and "There exists" statements, especially when you add in the mathematical language with the upside down A and the backwards E symbols, if you will. It takes some extra time for me. Also, the empty set. We haven't had it in the reading or homework lately, so I kind of dismissed it or tucked it away in a corner of my brain. I am pretty unfamiliar with the empty set and why they are used since they are empty. Anyway, this question and others like it that I have will probably seem silly to me once I get a better handle on the empty sets. I think I'm going to seek assistance or do more study on them.
I enjoyed the part about conjecture. At the end of the section, it talked about Goldbach's Conjecture: Every even integer exceeding 2 is the sum of two primes. This conjecture truly hasn't been resolved? Even with the assistance with the computers we have today? I find that hard to believe and wish that the author had gone into a bit more detail as to why this hasn't been resolved. Anyway, I think it is neat that there is still mathematical study going on with new discoveries. I would be interested to know what the leading mathematicians do in their pursuit of knowledge and mathematical study. I would imagine it would be pretty sophisticated, although, if Goldbach's Conjecture is still unresolved, maybe there are basic pursuits of study, too.
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