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, ...}.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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%2F4eeee766-c965-4d27-ac5b-53c670a54f64%2F50d4p66_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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