User:Engleman/coolthing

Introduction
This is a form of mathematics where all numbers are professed to have the same value. It is therefore useless, but is an interesting phenomenon.

Definition 1
Busted logic is a term created by Jonathan Richman to describe what happens in the following situation:

Let $$x = 0$$

Therefore

$$3x = 5x$$

As it is in an equation we can divide both sides by x, meaning:

$$3 = 5$$

When A and B are any real or imaginary numbers this equation can be expressed as:

$$Ax = Bx$$

$$A = B$$

This extension allows all mathematical theories to be disproved.

This does not work when you convert the equation into real numbers you get 0 = 0 whatever the values of A and B.

Definition 2
For any real number x:

$$ x^2 - x^2 = x^2 - x^2$$

Factoring both sides in two different ways:

$$ (x - x)(x + x) = x(x - x)$$

Dividing both sides by x &minus; x:

$$ x + x = x $$

Since this is valid for any value of x, we can plug in x = 1.

$$ 2 = 1 $$

x-x=0 and you cannot divide something by zero! I can divide your mom by zero!

Proving that x &ne; x
Since 1 = 1, and also 1 = 2, it can be stated that x can equal every single number, rational and irrational, that exists.

Therefore every value of x that is stated as specific can be disproven, so every single value of x can only be regarded as infinitely improbable to obtain. Therefore the probability of having two x values the same =

Therefore$$P(x = x)= \frac{1}{\infty}$$

and so is almost impossible to achieve.

Other uses

 * Arguing that one has obtained the right solution to a problem when one clearly has not.
 * Declaring that everything does and does not exist at the same time. (0 = 1)