User:Engleman/coolthing

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[edit] From Busted Logic

[edit] 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.

[edit] 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.

[edit] Definition 2

For any real number x:

x2 − x2 = x2 − x2

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!

[edit] 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 =

ThereforeP(x = x)= \frac{1}{\infty}

and so is almost impossible to achieve.

[edit] 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)

[edit] See Also

Division by zero