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In a formal proof by mathematical induction, suppose that we have concluded the Base Case, P(0) , and we want to use the Mathematical Induction inference rule to conclude the final line of the proof, Vn > 0: P(n). To apply the Mathematical Induction rule, we must know one additional fact. What is it? We need to have made the assumption [k > 0] We need to have derived the Inductive Conclusion, P(k+ 1). O We need to have derived the implication, P(k) → P(k + 1). We need to have proven Vn > 0: P(n) → P(n + 1). We need to have proven En > 0: P(n) → P(n+1).

In a formal proof by mathematical induction, suppose that we have concluded the Base Case, P(0) , and we want to use the Mathematical Induction inference rule to conclude the final line of the proof, Vn > 0: P(n). To apply the Mathematical Induction rule, we must know one additional fact. What is it? We need to have made the assumption [k > 0] We need to have derived the Inductive Conclusion, P(k+ 1). O We need to have derived the implication, P(k) → P(k + 1). We need to have proven Vn > 0: P(n) → P(n + 1). We need to have proven En > 0: P(n) → P(n+1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q3 In a formal proof by mathematical induction, suppose that we have concluded the Base Case, P(0) , and we want to use the Mathematical Induction inference rule to conclude the final line of the proof, Vn > 0: P(n). To apply the Mathematical Induction rule, we must know one additional fact. What is it? We need to have made the assumption [k > 0] We need to have derived the Inductive Conclusion, P(x + 1). O We need to have derived the implication, P(k) → P(k+1). We need to have proven Vn > 0: P(n) → P(n+1). O We need to have proven En > 0: P(n) → P(n+1).
Transcribed Image Text:Q3 In a formal proof by mathematical induction, suppose that we have concluded the Base Case, P(0) , and we want to use the Mathematical Induction inference rule to conclude the final line of the proof, Vn > 0: P(n). To apply the Mathematical Induction rule, we must know one additional fact. What is it? We need to have made the assumption [k > 0] We need to have derived the Inductive Conclusion, P(x + 1). O We need to have derived the implication, P(k) → P(k+1). We need to have proven Vn > 0: P(n) → P(n+1). O We need to have proven En > 0: P(n) → P(n+1).
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