Question

Validate each of the following proofs by evaluating each of the following. Foundation for the proof . a. Statement of what the author intends to show. b. Description, in your own words, of what the statement implies. c. Intuitive justification as to why this is likely to be true. Structure of the proof. . Identify what the author stated as a logical implication. What foundational assumptions will the author make? What will the author be required to demonstrate? Describe the structure of the proof. How does this structure support completion of the proof? What key points will the author address? a. b. c. e Justification a. How do you know there are no gaps in reasoning? b. Explain the justification for each key point in the proof 1. Definition: A function f is said to be uniformly continuous if and only if for any given e > 0 there exists δ > O such that lf(x)-f(y)| < ε for all x, y e R when Ix-yl < δ. Prove: f(x) x2 is not uniformly continuous on IR. For(# 1, assume there exist > 0 and let x-1 and y x +6. This implies ocg Therefore, f(x) is not uniformly continuous on R

Answer 1

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