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1=0

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Does one equal zero?

Logic can be perverted to prove a number of irrational concepts. Here's an example. Using algebra, we can (supposedly) prove that one equals zero:

1. a = b + 1                        1. Given
2. (a-b)a = (a-b)(b+1)              2. Multiplication Prop. of =
3. a2 - ab = ab + a - b2 - b        3. Distributive Property
4. a2 - ab -a = ab + a -a - b2 - b  4. Subtraction Prop. of =
5. a(a - b - 1) = b(a - b - 1)      5. Distributive Property
6. a = b                            6. Division Property of =
7. b + 1 = b                        7. Transitive Property of = (Steps 1, 7)
8. Therefore, 1 = 0                 8. Subtraction Prop. of =

If you're wondering where the perversion is, look a little closer at the transition from line 5 to line 6. don't forget that a-b-1 = 0. when you divide by zero, you can prove almost anything.


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