# Bogus Mathematical Theorems

Strong Bad periodically invents bogus mathematical theorems to illustrate his responses to fans on his Strong Bad Email show. One was also used in SBCG4AP Episode 3: Baddest of the Bands.

## The Transitive Butt Property

"Don't you remember your algebra, man?"

When the sender of email butt IQ is skeptical that any sort of IQ test exists to determine whether or not someone's butt is stupid, Strong Bad quickly refutes his ignorance with the following property:

$\begin{array}{c}\mbox{The stupidity of somebody}'\mbox{s butt is greater than}\\\mbox{or equal to the stupidity of that person}'\mbox{s head.}\end{array}$

Symbolically, this can be written as

$\!\,\mbox{ stupid(butt)}\geq\mbox{ stupid(head)}$

## The Property of Ones

"The colder it is, the more of a one it is."

When a fan asks Strong Bad if he's ever had a one that was not cold, he responds by stating the Property of Ones: "The ONEitude is directly proportional to the Colditude of the ONE." Here follows a brief analysis of this statement.

We consider a One with the following properties:

• $\!\,{\mathcal O}^{\mathrm{itude}}$ is a measure of the Oneness of the One.
• $\!\,T$ is the temperature of the One.
• $\!\,c^{\mathrm{itude}}$ is the coldness of the One.

The Oneness of the One can be determined by the following simple formula:

${\mathcal O}^{\mathrm{itude}}\propto c^{\mathrm{itude}}$ .

Naturally, a One has less coldness as its temperature increases, and it approaches having no coldness at all as its temperature approaches infinity. Likewise, a One approaches having infinite coldness as its temperature approaches absolute zero:

$\lim\limits_{T\to\infty}c^{\mathrm{itude}}=0,\quad\lim\limits_{T\to0^+}c^{\mathrm{itude}}=\infty$ .

Thus, a One's coldness is inversely related to its temperature:

$c^{\mathrm{itude}}=\frac1T$ .

As a result, we can rewrite our expression for Oneness in terms of temperature:

${\mathcal O}^{\mathrm{itude}}=\frac{k}T$ ,

so that $\!\,k$ is a proportionality constant (in units of Oneness times kelvins) that uniquely determines the Oneitude of a One given its temperature. If a One is not so cold, the temperature will be higher, thus minimizing its Oneness. In Strong Bad's own words, this can be simply stated:

$\!\,\mbox{ A One that isn}'\mbox{t cold is scarcely a One at all.}$

The inverse is also true:

$\!\,\mbox{ The colder it is, the more of a One it is.}$

How large the proportional relation and what units are used for coldness and Oneness are undefined.

## Coolguy's Law

"You got nothing to lose!"

In order to assist an email sender who was having difficulty determining which slumber parties are worth attending, Strong Bad stated an important relation between the popularity of a potential party host and the amount of fun available to be had:

$\begin{array}{c}\mbox{ The popularity of the host is inversely proportional}\\\mbox{to the amount of fun you can have at their house.}\end{array}$

This law is illustrated symbolically by the following equation:

$\begin{array}{c}\mbox{House}\\\mbox{Fun}\end{array}=\frac{1}{\mbox{Popularity of Host }x}$

This means that the less popular the host is (in a numeric form), the more fun (again in numeric form) you can have at their house. How the numbers are determined is unclear.

## The Cooldratic Formula

This one doesn't come from an E-mail, but from SBCG4AP Episode 3: Baddest of the Bands. The entirety of The Cooldratic Formula is this:

Butter + Fog Machine

Not surprisingly, Strong Bad introduced this formula shortly after pouring butter into a fog machine. Interestingly enough, he also states that, "I'm no mathematician" (his exact wording is: I'm no mathematician, but that sounds like The Cooldratic Formula to me!"