4. Explain what is wrong in the following "proof." CLAIM. Let x be a real number. If a is irrational, then 2x is irrational. "PROOF." Take r = V2. Then r is irrational, and so is 2x = 2/2. Therefore 2x is irrational for any irrational number c. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.) 5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number is rational iff it can be written as the quotient of two integers.)
4. Explain what is wrong in the following "proof." CLAIM. Let x be a real number. If a is irrational, then 2x is irrational. "PROOF." Take r = V2. Then r is irrational, and so is 2x = 2/2. Therefore 2x is irrational for any irrational number c. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.) 5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number is rational iff it can be written as the quotient of two integers.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Only number 5.
Transcribed Image Text:4. Explain what is wrong in the following "proof."
CLAIM. Let x be a real number. If x is irrational, then 2x is irrational.
"PROOF." Take r =
is irrational for any irrational number c.
V2. Then x is irrational, and so is 2x = 2/2. Therefore 2x
%3D
%3D
(Note. Find the mistakes in logical reasoning. "Lacks detail is not a mistake.)
5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number
is rational iff it can be written as the quotient of two integers.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
