Proposition. If x E R, then x² > x. Describe at least three things that are wrong with the following "proof" that attempts to show the above proposition is true. (The proposition is actually false!) Proof. Let x E R. In the equation x 2 x, we can divide both sides by x, getting x 2 1. This means we only need to consider x values that are equal to 1 or larger. If x = 1, the equation is true since 1 = 1 > 1 is true. If x = 2, the equation is true since 2 = 4 > 2 is true. If x = 3, the equation is true since 3 = 9 2 3 is true. Since we can see a pattern now and it is always true, we know x > x for all values of x. Type your response in the editor below. Don't attach or import a file or photo.
Proposition. If x E R, then x² > x. Describe at least three things that are wrong with the following "proof" that attempts to show the above proposition is true. (The proposition is actually false!) Proof. Let x E R. In the equation x 2 x, we can divide both sides by x, getting x 2 1. This means we only need to consider x values that are equal to 1 or larger. If x = 1, the equation is true since 1 = 1 > 1 is true. If x = 2, the equation is true since 2 = 4 > 2 is true. If x = 3, the equation is true since 3 = 9 2 3 is true. Since we can see a pattern now and it is always true, we know x > x for all values of x. Type your response in the editor below. Don't attach or import a file or photo.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:Question 6
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Proposition. If x E R, then x² > x.
Describe at least three things that are wrong with the following "proof" that attempts to show the
above proposition is true. (The proposition is actually false!)
Proof. Let x E R. In the equation x 2 x, we can divide both sides by x, getting
x 2 1.
This means we only need to consider x values that are equal to 1 or larger.
If x = 1, the equation is true since 1 = 1 > 1 is true.
If x = 2, the equation is true since 2 = 4 > 2 is true.
If x = 3, the equation is true since 3" = 9 > 3 is true.
Since we can see a pattern now and it is always true, we know x 2 x for all values of x.
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Step 1
Proposition. If x E R, then x2 ≥ x.
Proof. - Let x E R. In the equation x2 ≥ x, we can divide both sides by x, getting x ≥ 1.
This means we only need to consider x values that are equal to 1 or larger.
If x = 1, the equation is true since = 1 ≥ 1 is true.
If x = 2, the equation is true since 22 = 4 ≥ 2 is true.
If x = 3, the equation is true since 32 = 9 ≥3 is true
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