Solution Found!
Answer: Find the mistakes in the “proofs” that the sum of
Chapter 4, Problem 38E(choose chapter or problem)
In 35–39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
“Proof: Suppose r and s are rational numbers. Then r = a/b and s = c/d for some integers a, b, c, and d with b \(\neq\) 0 and d \(\neq\) 0 (by definition of rational). Then
\(r+s=\frac{a}{b}+\frac{c}{d}\).
But this is a sum of two fractions, which is a fraction. So r + s is a rational number since a rational number is a fraction.”
Text Transcription:
neq
r + s = a/b + c/d
Questions & Answers
QUESTION:
In 35–39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
“Proof: Suppose r and s are rational numbers. Then r = a/b and s = c/d for some integers a, b, c, and d with b \(\neq\) 0 and d \(\neq\) 0 (by definition of rational). Then
\(r+s=\frac{a}{b}+\frac{c}{d}\).
But this is a sum of two fractions, which is a fraction. So r + s is a rational number since a rational number is a fraction.”
Text Transcription:
neq
r + s = a/b + c/d
ANSWER:Solution:Step 1In this problem we have to find the mistakes in “proofs’’ that the sum of any two rational numbers is a rational number.