a where a, b = Z, b = 0. 3. Recall that a rational number r EQ is a number of the form r = b 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 EQ with r0, there exists m EZ for which rm E N = {1, 2, 3, ...}.
a where a, b = Z, b = 0. 3. Recall that a rational number r EQ is a number of the form r = b 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 EQ with r0, there exists m EZ for which rm E N = {1, 2, 3, ...}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![a
3. Recall that a rational number r EQ is a number of the form r =
where a, b E 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 rE Q with r #0, there exists m € Z for which rm E N = {1,2,3,...}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94707e96-7ca2-4be8-88e5-b4b51e0075ac%2F01b56982-cbfb-454e-8fe7-04cf00479eee%2Ff87izf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a
3. Recall that a rational number r EQ is a number of the form r =
where a, b E 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 rE Q with r #0, there exists m € Z for which rm E N = {1,2,3,...}.
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