## The Mystery Behind the Proof of 1=2

You have probably seen, or even been challenged to explain the proof of **1 = 2** shown in the table below. If you have no idea why the proof seems valid, it is now your opportunity to look at it and probe about it. Try to see if you can identify what is wrong with it before proceeding.

We have discussed the division by **0 **is undefined, and this operation is not permitted.

In step number 5, we divided *(a + b)(a-b) = b(a-b)** *by ** a – b**. Now from step 1,

**which means that**

*a = b***. Hence, our division by**

*a – b*= 0**is illegal and that what makes the proof wrong.**

*a – b*