Consider the following and determine in each case whether the statement is a paradox or fallacy. Justify your reasoning. Person 1: There are infinitely many numbers between 0 and 1.Person 2: I can prove to you that 2 = 1 with the calculations below:Let x = yx = yx² = xyx² - y² = xy-y²(x+y)(x-y) = y(x -y)(x+y)(x−y) y(x−y)(x−y)(x-y)x+y = ybut x = yy+y = y=2y = y2y yy yTherefore, 2 = 1

Answered: Consider the following and determine in…

Consider the following and determine in each case whether the statement is a paradox or fallacy. Justify your reasoning.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 51E

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Question

Consider the following and determine in each case whether the statement is a paradox or fallacy. Justify your reasoning.

Person 1: There are infinitely many numbers between 0 and 1.
Person 2: I can prove to you that 2 = 1 with the calculations below:
Let x = y
x = y
x² = xy
x² - y² = xy-y²
(x+y)(x-y) = y(x -y)
(x+y)(x−y) y(x−y)
(x−y)
(x-y)
x+y = y
but x = y
y+y = y
=
2y = y
2y y
y y
Therefore, 2 = 1

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