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Concept explainers
In 35-39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
39. “Proof: Suppose r and s are rational numbers. If
which is a quotient of two integers with a nonzero denominator. Hence it is a rational number. This is what was to be shown.”
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Chapter 4 Solutions
Discrete Mathematics With Applications
- Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that a2=3b2. Explain how this proves that 3 is not a rational number.arrow_forwardShow that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?arrow_forwardProve that 23 is not a rational number.arrow_forward
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- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
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