FALLACIES

All numbers equal all other numbers

                                                                          Rahul Rajendran

X.B

The following example uses division by zero to "prove" that 2 = 1, but can be modified to prove that any number equals any other number.

1. Let a and b be equal non-zero quantities

2. Multiply through by a

3. Subtract

4. Factor both sides 

5. Divide out

6. Observing that

7. Combine like terms on the left

8. Divide by the non-zero b

ab = a² 
ab – b² = a² - b² 
b( a-b ) = (a+b)(a-b)
b  = a + b

b = 2b

So   1 = 2