User:Engleman/coolthing

From Busted Logic

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 − 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 ≠ 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)