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Inequality Functions Proved

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Suppose that there are three points A,B and C on a line where C is between A and B. o is any other point not on the line. Prove that OA+OB>OC

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The expert proves an inequality function. Three inequality proofs are provided.

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Lipschitz functions convergence

From Convergence, Open, and Closed Sets

I am attaching my reference pdf file.
Please prove #11 on page 55 based on my reference.

Let M_X be the set of all functions f in C_[a,b] satisfying a Lipschitz condition.....

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