1. Let a and b be equal non-zero quantities
a = b
2. Multiply by a
a = ab²
3. Subtract b²
a² – b² = ab – b²
4. Factor both sides
(a – b)(a + b) = b(a – b)
5. Divide out (a – b)
a + b = b
6. Observing that a = b
b + b = b
7. Combine like terms on the left
2b = b
8. Divide by b
2 = 1
9. Add 1 to each side and flip over equation
1 + 1 = 3
Q.E.D. (Thus we have proved)
How is this proof possible?
The source of the fallacy is the fifth step, where (a – b) is divided out.
As a = b, a – b = 0, and dividing by zero is impossible in mathematics.
