Proofs are not so much about understanding the concept as it is coming up with ideas on the spot. It is true that proofs have a predefined structure that we must follow and how fluent one can build this structure depends on how much one practices. However, it also requires the proofer to be creative, because there are a lot things out there in the world that are not obvious to prove, like for example the geometric mean is always smaller than the arithmetic mean of two numbers.
At this point though, I am confused about why we are doing proofs in this course. I mean, it is certainly mathematical, but it doesn't have as much association to symbol as what we did before. I guess I will wait and see.
There is a direct connection between logic and proofs.
ReplyDeleteAfter all a proof is just a a set of logical statements that lead you to some conclusion. It can be used in mathematical contextes but many other contexts as well.
I guess it is pretty important in mathematics, but I am a life science specialist, and I never use proofs in life science. I have done derivations of formulas for molecular kinetics, but I have never seen anyone do proofs in this discipline.
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