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In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n) < 2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases c) Proof: Inductive step setup. This is the beginning of the inductive step where you are stating the assumptions in the inductive step an what you will be proving in that step. As you do so, identify the inductive hypothesis.

In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n) < 2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases c) Proof: Inductive step setup. This is the beginning of the inductive step where you are stating the assumptions in the inductive step an what you will be proving in that step. As you do so, identify the inductive hypothesis.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 49E: 49. a. The binomial coefficients are defined in Exercise of Section. Use induction on to prove...
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d) Proof: Inductive step
Transcribed Image Text:d) Proof: Inductive step
Q3 – Proof of Cost, In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases. c) Proof: Inductive step setup . This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis.
Transcribed Image Text:Q3 – Proof of Cost, In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases. c) Proof: Inductive step setup . This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis.
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