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12/10/18 James W. Cannon Talk

This talk was interesting to me because it compared mathematical and scientific truth to moral and spiritual truth side by side. I had never really compared those two things closely together before, but since coming to BYU and having an academic spiritual experience and having a spiritual academic experience, it has made me realize that truth is truth, no matter what it is pertaining to. It reminds me of a scripture in D&C 29:34 which says: " Wherefore, verily I say unto you that all things unto me are spiritual, and not at any time have I given unto you a  law  which was  temporal ; neither any man, nor the children of men; neither Adam, your father, whom I created." I also really like how Dr Cannon related how he was able to ask God for help in his research. It really affirmed my testimony that God is in the details of our lives, and that He will help us with whatever is important to us, because we are important to Him. Even with His daughter, even when his prayer...
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12/7/18 midterm review

The most important thing that we have studied since the last midterm has probably been Schroder-Bernstein theorem and cardinality proofs. They are a little bit abstract since we are dealing with the size of infinite sets, and my intuition gets broken from time to time, but so many proofs and theorems build off of them. I also think that the limit proofs we did are very important, because it is the basis for Calculus and analysis which is what I will be doing next semester and in the coming semesters. For the midterm I am expecting to see cardinality proofs for the proof section, and for the multiple choice and true/false some basic questions about cardinality and limits. I'm a bit more concerned about cardinality proofs because that section was the hardest for me, so if you could go over some of the more difficult cardinality proofs tomorrow that would be great.
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Section 36

Nothing in this section seems too far from intuition. The theorems that state that the addition and multiplication of functions relate nicely to their limits is very helpful. The proofs are a little bit complex, but I think once I work through them in class and I do the exercises then it won't be terribly complicated and I will understand the concept well enough. The idea of continuity is very important because it is the basis for most of calculus, as you only differentiate and integrate over continuous intervals.
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Section 35

This section seemed pretty easy to understand. The limit definition is basically the same here as it was in sections 33 and 34, with the same quantifiers and most of the same variables. It doesn't seem like there is a lot new that is going on and I can understand visually what is happening pretty well. I don't understand how the delta in this case is different than the N previously, is it just because it is on both sides of the function, whereas the N was only one fixed point?
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Section 33

This section was pretty straightforward, and I remember a lot of the definitions from calculus so it's not anything really new. Series are really easy for me to understand, my only real problem was the formal definition of a limit, it seemed a bit convoluted and complicated. We are also going a bit deeper into series than we did in calculus, and so this may take some time for me to wrap my head around again. But all in all this section doesn't seem awful to me.
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Section 32

This section was wild. I think it may be in part because I am coming back from break and fighting a head cold/flu thing, but this was just so above anything else we have done so far. It's wild that Bernstein discovered this theorem when he was only 19. I think this section and theories will be very useful in the coming tests and proofs, and it's a cool theory to think about, but at the same time it is also very confusing to read at least, and I think i will need to work some examples before I really grasp what's happening.
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Section 30

This section was actually very straightforward for me. It seems logical that the set of real numbers would be uncountable, so my intuition wasn't really broken there. And the proof was very clever and made sense to me. The one thing that I didn't quite get was the piecewise function in corollary 30.5. I didn't understand how the bijection was made and how S-(0,1] played into it at all, but I think it was just because it was phrased a bit differently than what I'm used to.
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