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    Question about Proof of Inverse Function

    I am reading the proof of the Inverse Function Theorem in baby Rudin and I have a question about it. How does associating a function phi(x) (equation 48) with each point y tell us anything about if f(x) is one-to-one? I'll show the proof below. Also, if f'(a) = A, and f(x)=x2, what would A-1 be?
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    Math classes to self study physics

    I will be attempting to get a PhD in statistics eventually though I have yet to get my BS, however, in the mean time I have a few electives I need to fill and I want them to help me in my self study of relativity and quantum mechanics. I will not be surpassing a Master's knowledge of these areas...
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    Rank these classes

    I am getting my B.S. in statistics in a few years and will then try for a PhD, and I happen to have 1-4 spots where I can take additional courses. I am taking all my stat courses as well as a year of real analysis and a year of abstract algebra and want to take these other courses, but I may...
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    Explain the Inverse Function Theorem

    I am studying the multi variable Inverse Function Theorem and the Implicit Function Theorem. I think my brain is rebelling against understanding them and I would appreciate if someone here could explain the two theorems semi rigorously as well as explain when they are used, and why they are...
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    Does the limit exist?

    This question came up in a book I am using for self study. I was going to just skip the question but then I remembered I can ask for help here. Homework Statement Let a,b,c,d be nonnegative integers. For what values of a,b,c,d does \lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \frac{x^a...
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    Is this a valid set?

    Or is it too circular? A = {x | x \in A}