Let's prove that 1=2 by using two variables, a and b. Before we start, let's let a=b. Now, we can prove that 1=2.
1) a=b ∣∣ Given
2) a2=ab ∣∣ Multiply both sides by a
3) a2−b2=ab−b2 ∣∣ Subtract both sides by b2
4) (a+b)(a−b)=b(a−b) ∣∣ Factor both sides
5) (a+b)=b ∣∣ Divide both sides by (a−b)
6) a+a=a ∣∣ Substitute a for b
7) 2a=a ∣∣ Addition
8) 2=1 ∣∣ Divide both sides by a
Which step is incorrect?