if 0 = 1, then 1 = 2
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.
In the one of my favorite movie Incendies, when Simon asked her sister
“One plus one, does it make one?”
and the answer was “YES.”
In the past, there was a friend of Galileo, called Del Monte. He was believing creation of something out of nothing like Archimedes. When he first proved that 0=1, he had established the existence of God. For him ;
God was 1 and 0 was nothing. Thus, God was always exist.
Okay, how did he prove that 0=1? Or 1=2? There are certainly a number of convincing ways to prove. And when we collect them together they produce a very convincing document possibly leading the reader to believe these absurdities. But do not worry, we will also see the fault with each proof lie.
If 1=2, you and me have to be the same person. But you are you, I am me. It is a logical deduction.
Proof of “0=1”
Let “a” and “b” each equal to 1.
Since a and b are equal to 1;
b² = ab
Since a equals itself, it is obvious that
Now, let’s try to subtract b² and ab from a². This move yields
a²- b² = a²- ab.
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).
Friends, amigos, Romans!!! We are just doing basic Algebra. This statements are perfectly true.
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
Secondly, subtract a from both sides and we get
But, wait a minute. I thought we said b is equal to 1 at the very beginning of this proof, so this means that
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.
We destroyed the world.
Don’t forget that. You can destroy the logic with zero!
If you are wondering why we can not divide by 0. You can read my previous article.
Here some additional proofs.