I love math because of things like this… You can be walking along, minding your own business, learning about Taylor series and their error bounds and someone will hit you with something like this: “Taylor’s theorem is exposed as a generalization of the mean value theorem… [and its] a generalization of the fundamental theorem of calculus“!

Yike, I should have known something was up when I learned a series like Σ(xn/n!) converges to the function of x, ex. My first impression for stuff like this is that it is magic. On the other hand, doing the proofs feels a little like practicing sorcery.

I just bought Introduction to Analysis as suggested by Mr. Moffatt. I wonder when I’ll get a chance to read more about this with work, a linear algebra class and multivariate calculus class all competing for time.


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