The document outlines a logical fallacy where it is incorrectly deduced that 2 = 1. It does this by letting a and b be equal non-zero numbers, and then performing a series of algebraic manipulations, including dividing by zero, to arrive at the false conclusion that 2 = 1. The logical flaw lies in dividing by a - b, which is actually equal to zero since a was defined to be equal to b.

2. Fallacy: Various types of reasoning that render arguments logically unsound

3. Right ??

4. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Let a and b be equal non-zero numbers

5. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Multiply both sides by a

6. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Subtract b ² from both sides

7. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Factor both sides**Note**( a + b ) ( a – b )a ² - ab + ab - b ²a ² - b ²

8. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b ) ( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Divide both sides by ( a - b )**Notice**( a – b ) cancels**Fact**Dividing by ( a – b ) is dividing by zero, which is undefined, or cannot by done

9. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Because b = a…

10. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Combine like terms and divide by b **Note**b = 1b

11. a = ba * a = a * ba ² - b ² = ab - b ²( a + b ) ( a – b ) = b ( a – b )( a + b ) ( a – b ) = b ( a – b )( a – b ) ( a – b )a + b = bb + b = b2b = b b b2 = 1Q.E.D.