One plus one, does it make one?

These equations are classics of mathematics or a mathematical fallacy which lead us to absurd results. It may sound ridiculous, but I will prove it to you. Please keep suspecting the proof.

Since a and b are equal to 1;

b² = ab

Since a equals itself, it is obvious that

a²=a²

Now, let’s try to subtract b² and ab from a². This move yields

a²- b² = a²- ab.

Beautiful.

As you can see, we should try to find the factors of the equations.

a² – ab = a•(a-b).

Likewise, a²-b² = (a+b)•(a-b).

(a+b)•(a-b)=a•(a-b)

So far, so good. Now we need to do two more Algebraic moves. First, divide both sides of the equation by (a-b) and we get

a+b=a

Secondly, subtract a from both sides and we get

b=0

But, wait a minute. I thought we said b is equal to 1 at the very beginning of this proof, so this means that

1=0…

This is probably the most important result we have ever seen so far. Now you can take this result with you and go further. For instance, Einstein had a powerful brain. But wait again, we got 1=0. So that means that Einstein had
no brain!!!

Obviously, there is something wrong with our proof… We made a mistake.

Do you remember that we divide our equations by “a - b”. But look out! “a” and “b” are both equal to 1 and that’s why “a — b” is going to equal to “0.” We divided something by zero.