# UnScripts:CKC2k Reviews the Fundamental Theorem of Arithmetic

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*Editor's Note: Conundrum Knowledge Cinema 2000 was a television series dating back to a time when the industry hadn't yet discovered its current niche of cheesy family sitcoms and crime/hospital dramas featuring men putting on and taking off sunglasses. A time of boldness. Exploration. Education. The premise of this particular show was to have ordinary people and robots sit through and make snarky comments on certain scientific facts, in order to determine which had the best applications for developing new weaponry. The show was an eventual failure, partly due to the fact that math is hard.*

*Appropriately enough, most of the recorded episodes were either lost in a fire or recycled for the war effort against the Communists. Presented here is one of the few preserved episodes, courtesy of that old guy who lives down the hall who smells like herring and never throws anything away.*

## edit Cast

**Jose**: The token minority figure. Jose is the comic relief of the group. He landed the job testing theorems for CKC2k because of his cheap labor costs: He gets paid five tomatoes per hour, and his dental plan only covers two dependents. It is important to understand that CKC2k was filmed before the civil rights movement. Possibly during. Or maybe after, I don't know.

**BarneyBotXR**: A former folding unit, Barney was donated to the CKC2k facility because his original owners found him to have poor work ethic, and suspected him of child abduction. Barney is the comic relief of the group.

**EmiliaAir♥**: Emilia was introduced into this operation in order to add some mechanical sex appeal to the already sexy fields of mathematics and science. In this era, there were less laws governing what a robot could and could not wear, and as a consequence she was often featured with her ankles exposed, and the occasional steam vent in the CKC2k laboratory afforded the viewer the occasional pantyshot. Aside from fan service, Emilia is also the comic relief of the group.

## edit Introduction

**BARNEY**: ...So then I said, "No officer, that's not a freezer full of disembodied brown children, that's my wife!"

**JOSE**: Ay Dios mio, it is afortunada that there is no one around in this top secret underground laboratory in space to overhear us, because that sounds horrible when taken out of context.

**EMILIA**: No, actually, that's totally sick even in context. Please never make optical sensor contact with me again, BarneyBotXR, and remind me not to trade my lunch with you anymore.

**PA SYSTEM**: Attention workers, your ten minute lunch break is over. Please return to your posts. I repeat, please return to your posts. Violators will be violated.

**JOSE**: Well, back to work, mis amigos.

**BARNEY**: We've got SNAKES ON THIS PLANE! I mean, we've got a THEOREM ON THIS PLANE... LAB... PLANE... WITH SNAKES.

**JOSE**: Barney, shut up, man. I don't want el jefe to catch use goofing off on the job, no?

**The crew walks to the presentation room. EMILIA pretends to drop something and bends over, giving us a view of her juicy robot hiney.**

## edit Part One

**The crew takes their seats, JOSE in the middle with his sombrero partially blocking the view, and EMILIA keeping her distance from BARNEY, who is trying to put his arm around her while pretending to stretch.**

**The title, *Fundamental Theorem of Arithmetic*, floats onto the screen, followed by some opening credits, and then the feature begins.**

**PA SYSTEM**: The proof consists of two steps.

**BARNEY**: Yeah, I did the two-step with your MOM. Last NIGHT! **High-fives JOSE, attempts to high-five EMILIA who just isn't having it**

**PA SYSTEM**: In the first step every number is shown to be a product of zero or more primes. In the second, the proof shows that any two representations may be unified into a single representation.

**JOSE**:Introduction? We don't need no stinkin' introduction! Bring it on, cabrones! **Smacks his fist into his hand**

**EMILIA**: Math is hard.

**PA SYSTEM**: Suppose there were a positive integer which cannot be written as a product of primes.

**BARNEY**: Man, don't you hate it when a positive integer can't be written as a product of primes? I was at an ATM the other day, and it was all like, "Please enter an amount which is not a product of primes". So I pimp-slapped it and made off with all the money. Those ATMs. You gotta put 'em in line.

**EMILIA**: You have a bank account?

**BARNEY**: Well, no, but that's beside the point.

**EMILIA**: Oh. **Visibly loses interest**

**PA SYSTEM**: By the well-ordering principle, there must be a smallest such number: let it be *n*.

**JOSE**: Okay, okay, I have to object here. The well-ordering principle relies on the axiom of choice, a controversial principle of set theory whose exact opposite yields an equally valid system of axioms. You can't have basic things like the Fundamental bleedin' Theorem of Arithmetic relying on things that need not be true. That's just hokum.

**BARNEY**: ...I like booze?

**PA SYSTEM**: This number *n* cannot be 1, because 1 is the empty product consisting of no factors. It cannot be a prime number either, since any prime number is a product of a single prime, itself. So it must be a composite number. Thus *n = ab* where both *a* and *b* are positive integers smaller than *n*.

**BARNEY**: ...I like booze.

**EMILIA**: I like cocktails with pink umbrellas. Because I'm a girl.

**JOSE**: I like the tequila that my cousin distills in the back of his Ford van.

**PA SYSTEM**: Since *n* is the smallest number which cannot be written as a product of primes, both *a* and *b* can be written as products of primes. But then *n = ab* can be written as a product of primes as well, a proof by contradiction.

**BARNEY**: "Contradiction"? My desire for booze is only matched by my desire to make a dick joke. My dick is contra in some countries!

**JOSE**: I sure could use a drink now, guey. How about we take an intermission and go find my cousin.

**EMILIA**: Oh, Jose. You always know what to say to turn me on.

**The three walk out, EMILIA's object manipulation appendage hanging in JOSE's arm.**

## edit Intermission

*Editor's note: Bear in mind that this episode was recorded before the RIAA went into full swing. Back then, due to rampant piracy, movie stars had to resort to endorsing cigarettes in order to feed their starving families.*

*Nothing beats the smooth, mild taste of L&M filter-tipped cigarettes. L&M's the best. Stands out from all the rest.*

## edit Part Two

**The cast returns and takes their respective seats and the second half begins. EMILIA, barely conscious from all the alcohol in her circuitry, is wearing several Mardi Gras bead chains, as well as JOSE's sombrero and his mariachi coat.**

**PA SYSTEM:** We use the fact proved by Euclid that for any prime number *p* and any natural numbers *a*, *b*: if *p* divides *ab* then either *p* divides *a* or *p* divides *b*.

**BARNEY and JOSE dump EMILIA on the floor and take their seats.**

**BARNEY:** It's too bad Emilia hasn't learned how to synthesize alcohol into fuel like we have, huh?

**JOSE:** Yeah, you should teach her sometime like you taught me, hombre. I never would have thought of that on my own. Now review this thing.

**PA SYSTEM:** A proof of the uniqueness of the prime factorization of a given integer proceeds as follows. Let *s* be the smallest natural number that can be written as (at least) two different products of prime numbers.

**JOSE:** Again with the well-ordering principle? I already explained--

**BARNEY:** Dude. Less whining, more cock jokes.

**PA SYSTEM:** Denote these two factorizations of *s* as *p _{1}···p_{m}* and

*q*, such that

_{1}···q_{n}*s = p*.

_{1}p_{2}···p_{m}= q_{1}q_{2}···q_{n}**JOSE:** Those prime factorizations aren't as long as my, um, cock.

**BARNEY:** ...We'll work on that later.

**PA SYSTEM:** By Euclid's proposition either *p _{1}* divides

*q*, or

_{1}*p*divides

_{1}*q*.

_{2}···q_{n}**BARNEY:** Here, Jose, let me show you how it's done. MY COCK divided both of YOUR MOM'S prime factorizations wide open LAST NIGHT! WOO!

**JOSE:** I see I have mucho to learn from you, senor.

**PA SYSTEM:** Both *q _{1}* and

*q*must have unique prime factorizations (since both are smaller than

_{2}···q_{n}*s*), and thus

*p*(for some

_{1}= q_{k}*k*). But by removing

*p*and

_{1}*q*from the initial equivalence we have a smaller integer factorizable in two ways, contradicting our initial assumption. Therefore there can be no such

_{j}*s*, and all natural numbers have a unique prime factorization.

**BARNEY:** Well, **stretches and stands up**, I think we all learned an important lesson today.

**JOSE:** Si, si we did.

**BARNEY:** Yeah, that lesson. Important. Sure was.

**JOSE sits in silences while BARNEY stands in silence.**

**JOSE:** Okay, for real, what did we learn? That every integer has a unique prime factorization? That cock jokes make everything better? That math is hard?

**BARNEY:** Well, yeah, those too. I was thinking we learned that girls can't hold their booze.

**JOSE:** I already knew that, man.

**BARNEY:** I, uh, yeah. Me too. I was just testing you, bro.

**JOSE and BARNEY leave. Roll credits.**