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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
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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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,...}.
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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