Brain Teaser Solution: ImpossibleMath1

Brain teaser:

Reference: [ImpossibleMath1]
Submitter: Jack Tan (jahk@uiuc.edu)
Submission date: 14 April 1997

Solution:

Submitter: Jack Tan (jahk@uiuc.edu)
Submission date: 20 April 1997

Solution

The fallacy of the argument lies between lines 4 and 5 of the problem:

 4    (a-b)*(a+b) = (a-b)*b       Factor (a-b) from both sides
 5          (a+b) = b             Cancel (a-b) from both sides

Because a is equal to b, the term (a-b) is zero. The cancellation is shorthand for division, so we have effectively divided by zero on both sides of the equation. Division by zero is a mathematical no-no and is disallowed for exactly this reason -- if division by zero were allowed, then two really would equal one!

Moral: don't divide by zero.

Jack Tan and Emmie Chen / jahk@uiuc.edu

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