Math 290 Fall Semester

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...

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.

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.

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?