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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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