3. Recall that a rational number r € Q is a number of the form r = where a, b € Z, b + 0. Decide whether each of the following claims is true or false. Then prove your answers. Claim 1. There is a positive rational number smaller than any other positive rational number. Claim 2. For any r € Q with r #0, there exists m € Z for which rm € N = {1,2, 3, ...}.
3. Recall that a rational number r € Q is a number of the form r = where a, b € Z, b + 0. Decide whether each of the following claims is true or false. Then prove your answers. Claim 1. There is a positive rational number smaller than any other positive rational number. Claim 2. For any r € Q with r #0, there exists m € Z for which rm € N = {1,2, 3, ...}.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.2: Solving Inequalities
Problem 62WE
Related questions
Question
![3. Recall that a rational number r € Q is a number of the form r =
where a, b € Z, b + 0.
Decide whether each of the following claims is true or false. Then prove your answers.
Claim 1. There is a positive rational number smaller than any other positive rational number.
Claim 2. For any r € Q with r #0, there exists m € Z for which rm € N = {1,2, 3, ...}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94707e96-7ca2-4be8-88e5-b4b51e0075ac%2F3eb29b1a-8080-4032-94c3-eba4f412643a%2Faicihb_processed.png&w=3840&q=75)
Transcribed Image Text:3. Recall that a rational number r € Q is a number of the form r =
where a, b € Z, b + 0.
Decide whether each of the following claims is true or false. Then prove your answers.
Claim 1. There is a positive rational number smaller than any other positive rational number.
Claim 2. For any r € Q with r #0, there exists m € Z for which rm € N = {1,2, 3, ...}.
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