Is 2=1?

Is 2=1?

Now we start the proof.

                     

First,

                                                          let      a = b

 [multiply both side by a]                          a² = ab

[subtract b² from both side]                  a²-b² = ab-b²

[factorise the equation]                (a-b)(a+b) = b(a-b)

[both side divide by (a-b)]                      a+b = b

Since a=b, then we have                           2b = b

[divide both side by b]                                2 = 1

Finally, we will get 2=1. But is this a correct proof? 
        
                 

Does 2 really equals to one? What’s wrong with this proof? Where does the logic break down? 

Actually, the method of getting the solution was not mathematically sound. This was a fake proof. 

This means that there is a mistake or false statement in somewhere in some line. 
      
  
                   

Still remember that we let a=b before we start the proof? 

If  a=b, then a-b=0. 

Hence, the proof above cannot divide by a-b, because it will be divide by 0. 

The division by 0 is also undefined. 

Hence, we cannot conclude that the number 2 is equals to 1. 

                                                                                          ~Ewe Sin Hooi