3. [2 pt] In this question we practice writing the negation of mathemati- cal statement with...

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3. [2 pt] In this question we practice writing the negation of mathemati- cal statement with quantifiers. Suppose that you are given the following definition: Definition We say that a function : RR is continuous at 20 R, if for any > 0, there exists a > 0, s.t. for all y (x0 - 8, 20 + 8), one has that f(y) - (x0)| < . (a) [1 pt] Write the definition using the standard form of mathematical statement with quantifiers. (b) [1 pt] Suppose that your professor asks you to prove that a function g(x) RR is not continuous at 0R, what statement should you prove exactly? 3. [2 pt] In this question we practice writing the negation of mathemati- cal statement with quantifiers. Suppose that you are given the following definition: Definition We say that a function : RR is continuous at 20 R, if for any > 0, there exists a > 0, s.t. for all y (x0 - 8, 20 + 8), one has that f(y) - (x0)| < . (a) [1 pt] Write the definition using the standard form of mathematical statement with quantifiers. (b) [1 pt] Suppose that your professor asks you to prove that a function g(x) RR is not continuous at 0R, what statement should you prove exactly?

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a The definition of a function f RR being continuous at To R in stand... View the full answer