Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that 2 is irrational. You can use the fact that √2 is irrational.

Prove that 2 is irrational. You can use the fact that √2 is irrational.

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
See similar textbooks
icon
Related questions
Question
Now here are some definitions / facts that you need to cite when used. The citing instructions are given after the list. 1. 1 is the smallest positive integer. That is, there does not exist an integer n such that n> 0 and n < 1. 2. An integer n is even if there exists an integer k such that n = 3. An integer n is odd if there exists an integer k such that n = 2k + 1. 4. All integers are even or odd. 5. A real number x is positive if x > 0, and negative if x < 0. 6. All real numbers are either positive, negative, or 0. 2k. m 7. A real number x is rational if there exists integers m, n with n ‡ 0 such that x = n
Transcribed Image Text:Now here are some definitions / facts that you need to cite when used. The citing instructions are given after the list. 1. 1 is the smallest positive integer. That is, there does not exist an integer n such that n> 0 and n < 1. 2. An integer n is even if there exists an integer k such that n = 3. An integer n is odd if there exists an integer k such that n = 2k + 1. 4. All integers are even or odd. 5. A real number x is positive if x > 0, and negative if x < 0. 6. All real numbers are either positive, negative, or 0. 2k. m 7. A real number x is rational if there exists integers m, n with n ‡ 0 such that x = n
5. Prove that 2 is irrational. You can use the fact that √2 is irrational.
Transcribed Image Text:5. Prove that 2 is irrational. You can use the fact that √2 is irrational.
Expert Solution
Step 1

We need to prove that, 24 is irrational.

We have given that 2 is irrational.

On the contrary let us assume that 24 is rational.

A real number x is rational if there exists integers m, n with n≠0 such that x=mn.

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS