Solution Found!
A fallacy Explain the fallacy in the following argument.
Chapter 10, Problem 55AE(choose chapter or problem)
A fallacy Explain the fallacy in the following argument. Let
\(x=\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\cdots\) and \(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\cdots\).
It follows that 2y = x + y, which implies that x = y. On the other hand,
\(x-y=(\underbrace{\left.1-\frac{1}{2}\right)}_{>0}+(\underbrace{\left.\frac{1}{3}-\frac{1}{4}\right)}_{>0}+(\underbrace{\frac{1}{5}-\frac{1}{6}}_{>0})+\cdots>0\)
is a sum of positive terms, so x > y. Thus, we have shown that x = y and x > y.
Questions & Answers
QUESTION:
A fallacy Explain the fallacy in the following argument. Let
\(x=\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\cdots\) and \(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\cdots\).
It follows that 2y = x + y, which implies that x = y. On the other hand,
\(x-y=(\underbrace{\left.1-\frac{1}{2}\right)}_{>0}+(\underbrace{\left.\frac{1}{3}-\frac{1}{4}\right)}_{>0}+(\underbrace{\frac{1}{5}-\frac{1}{6}}_{>0})+\cdots>0\)
is a sum of positive terms, so x > y. Thus, we have shown that x = y and x > y.
ANSWER:Problem 55AE
A fallacy Explain the fallacy in the following argument. Let and it follows that 2y = x + y, which implies that x = y. On the other hand.
is a sum of positive terms, so x > y. Thus, we have shown that x = y and x > y.
Answer;
Step 1;
Let , x = +
+
+
+.......... ….........(1)
And y = +
+
+
+............ ……………(2)
We can write the given series as ;
X = , and y =
and it follows that 2y = x+y which implies that x=y , on other hand x -y > 0,
2y = x+y ,
then 2y -y = x
Y = x , then x - y = 0 , on other hand x -y > 0 , by using these two results the given argument is fallacy.
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Fallacy is an incorrect result which has an apparently logical explanation of why the result is correct, or a correct result obtained through incorrect reasoning. E.g ; =
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