//------------------------------// // Axiomatic Set Theory // Story: Twilight Ships Rainbow Dash With Everything In The Universe // by Cloud Hop //------------------------------// Twilight Ships Rainbow Dash With Everything In The Universe Chapter 1: Axiomatic Set Theory Luna's moon draped Ponyville in a blue-white light, her stars sprinkled throughout the nearly cloudless night. It was rather quiet for Friday evening - Rainbow Dash expected a lot more ruckus to be emanating from the doorway of the tavern she was walking by. Instead, what she heard almost made her trip. "Hey, Rainbow Dash!" shouted an over-enthusiastic voice that sounded far too much like Twilight Sparkle. Rainbow Dash groaned. She had spent almost all her waking hours clearing out the leftovers from yesterday's thunderstorm, and her wings were incredibly sore. She hadn't gotten time to practice any new stunts, skipped her afternoon nap, and now she'd probably have to carry Twilight home instead of going to bed. That mare couldn't put down half a pint without getting so tipsy she'd start running into walls. Twilight, of all ponies, should know a spell for detoxifying herself, but either one didn't exist or she was too plastered to use it. The cyan pegasus dragged her hooves towards the entrance to the bar, where a purple alicorn greeted her with a crazed smile. "I've done it, Rainbow Dash! I've created an internally consistent axiomatic set theory with a universal set!" The pegasus blinked. To say that math was not her forte would be a vast understatement. As far as she was concerned, one cloud plus one cloud was just one really big cloud. "Twilight... what are you doing?" "SCIENCE!" Twilight hiccuped, "no, wait, MATH!" She hopped over to a chalkboard that looked rather out of place in a bar filled with cranky, drunk ponies, all of whom were thankfully avoiding eye contact. Rainbow Dash wondered if she had conjured it out of thin air, then wondered how dangerous it was to do that while drunk. Could you get cited for casting under the influence? Had Twilight gotten a CUI? Did anypony even care? What's up with those swirly things on unicorn horns? Why did she ask stupid questions like this when she was tired? "In traditional Zermelo–Fraenkel set theory (with the axiom of choice), or ZFC *hic* for short, a set of all sets is explicitly forbidden. This is done to avoid Brussel's Paradox, which asks the *hic* question, ‘Does a set of all sets that don't contain themselves contain itself?’ Now, to construct a self-consistent formulation of these axioms, we must-" Twilight abruptly took a swig of her martini from a nearby table, which Rainbow Dash noticed with increasing alarm was decorated with several empty glasses already, and a piece of paper that looked suspiciously like a citation. She needed to get Twilight home, preferably before she passed out. Whether she would pass out from the alcohol first, or because she forgot to breath during her lecture was an open question. "-But anyway, a universal set must *hic* contain itself, or it isn't a set of all sets. However, the second axiom of ZFC states that no set can contain itshelf, because if they could *hic* then we would have infinitely descending sets, and that's just shilly!" Twilight was suddenly sent into a fit of giggles before taking another sip of her martini. "Now, thish will alllllll~ be relevant later *hic* when we apply the principle of exploshun—" Rainbow Dash, who had been edging closer and closer to Twilight's table of empty glasses, abruptly abandoned her attempt at deciphering the citation Twilight had gotten. "Wait, what? Explosions? That's awesome!" Twilight had been swaying steadily further and further to the left, and finally lost her balance, nearly stumbling into a nearby table. "Errrrr, I mean, we should probably get you home now..." "Nonshense!" Twilight said, having corrected her gravitational orientation. "I am perfectly capable *hic* of handlin' mahshelf!" Rainbow Dash was torn between dragging her obviously very drunk friend home before she hurt herself, and finding out what explosions had to do with math. She eventually settled on letting Twilight continue her lecture until she collapsed. "To solve this, I created a shelf-consistent theory that *hic* allows for a universal shet that contains itself. Observe!" Twilight giggled as she scribbled something on the chalkboard. There exists a universal set that contains itself. Twilight looked inexplicably proud of this sentence, and made no move to expand on it. Now, Rainbow Dash wasn't familiar with any advanced ponynomial mathematical concepts, but she did know two things: 1. Saying something is true doesn't make it true. 2. Twilight was really drunk. "Now that we've proven the exishtence of a universal shet that *hic* containz itshelf, we c'n return to the shecond axiom of ZFC set theory, *hic* which states that no set can contain itshelf. Therefore, *hic* we've derived a contradickshun, and can thus invoke the prinshaple of exploshun to imply that Rainbow Dash is in love with the set of everything, thereby proving our original hypotheshus!" Twilight twirled around and nearly fell over, before steadying herself once again and drawing a square to complete her proof, "Q.E.D.!" Rainbow Dash's ears perked up at the word "explosion", only for her enthusiasm to be immediately extinguished by Twilight's romantically questionable conclusion. "Wait, what?" Twilight finally fell over onto her back, laughing hysterically. "I've shipped Rainbow Dash with EVERYTHING IN THE UNIVERSH!" Twilight jabbed all four hooves into the air. "Now Rarity's shilly shipfics are all REDUNDANT!" Wait, Rarity was writing terrible romance novels about her? Ugh, tomorrow was going to be a very, very long day, and today wasn't even over yet. She motioned to the bartender to pick up Twilight's empty glasses now that her drunken mathematical rampage had subsided. With some effort, she managed to lure Twilight into a standing position long enough to duck under her and lift the extremely tipsy, still hiccuping alicorn onto her back. It was at this point Rainbow Dash remembered that alicorns also have earth pony abilities, which meant that Twilight was heavy. Granted, she wasn't as heavy as Applejack, but Rainbow Dash was pretty sure Applejack was made out of depleted uranium. Rainbow Dash grabbed Twilight's citation and had almost left the tavern when she noticed a familiar blonde-maned pegasus sitting at one of the tables. "Derpy? What's she doing here? Isn't she already... uncoordinated enough?" Twilight snorted. "Derpy's always drunk, silly, that's why she's so clumsy all the time! I mean really, what else could her cutie mark stand for?" At this point, Rainbow Dash decided that today had dragged on entirely too long already and simply left without saying another word. She lugged her snoring, pony-sized encumbrance with as much enthusiasm as a filly visiting the dentist, trudging interminably towards the Ponyville library. She hadn't walked two blocks when she ran into the last pony she wanted to see. "Rainbow Dash! Fancy seeing you here- omigosh!" Rarity almost immediately noticed the purple alicorn slung over Rainbow Dash's back, and promptly began to freak out. "Is she hurt? Did she faint? Are you taking her to the hospital? IS SHE DYING?!" As Rarity continued to successfully defend her title of The Drama Queen by galloping around the pegasus and panicking, Rainbow Dash took a deep breath. "Rarity, SHUT UP!" The white unicorn gasped dramatically, and Rainbow Dash wondered if it was physically possible for Rarity to not do something dramatically. "Rainbow Dash, such uncouth language!" "Stop. Just, stop." The pegasus glowered at the insulted unicorn. "I've been working all day, my wings are so sore I can barely fly, I didn't get a nap, I didn't get to do stunt practice, and now I'm carrying Twilight back to her house after she got so drunk she passed out, but not before she told me about those terrible romance novels you've been writing about me." The second the words 'romance novels' escaped the weather pony's mouth, Rarity froze in terror, as if Nightmare Moon herself had suddenly materialized in front of her. "Oh-well-look-at-the-time-I-guess-I-should-really-be-getting-to-bed-now-hahaha-bye!" Then, much to the relief of the pegasus, she was gone. With a sigh, Rainbow Dash continued her eternal slog towards the Ponyville library. It was past midnight by the time the cyan mare reached the wooden door to the library. She half-heartedly tried one of the handles, but it was locked. "Hey Spike, you in there?" Rainbow Dash rapped on the door. "Spiiiiiiiiiiiiiiiiike~" "Shpigsonetahwenshdah *hic*" Twilight mumbled something incoherent, apparently having woken up from her drunken stupor, at least momentarily. "Er, what'd you say?" The pegasus looked back towards the purple alicorn slung over her back. "I shaid, *hic* Shpikes gone 'till wenshday!" she blurted out in a rare moment of coherency, "He's doin' shometin' foh Appohjack!" Twilight giggled as Rainbow Dash groaned yet again. "Ok, egghead, how are we supposed to get in? Do you have a key?" In an amazing display of either magical aptitude or a gross disregard for safety, a purple haze surrounded the door's lock, and a faint *click* echoed into the quiet night. Relieved, Rainbow Dash pushed open the door and unceremoniously dumped Twilight off her back and onto the floor. Twilight let out a small *hic!* in protest, but seemed too far out of it to care. Then, the cyan pegasus set Twilight's CUI citation on a table and, satisfied her friend was now home safely, turned towards the door. She was about to fly back to her house when Twilight let out a rather pitiful moan, and hesitated. Was Twilight going to be ok? Despite all the crap the alicorn had just put Rainbow Dash through, she was still worried about her. Rainbow Dash shrugged and flew out of the door, but instead of going back to her house, she flew straight up. The fastest pegasus in Ponyville reached an errant cloud floating above the library in a matter of seconds, and tore a hefty chunk out of it. Flying back down, she shoved the piece of cloud through the doorway and positioned it near the ceiling. Twilight was still lying on the ground, either already asleep or in the functional equivalent of a coma. The pegasus flopped down on her temporary bed, thankful she had such a comfortable portable sleeping option, and closed her eyes to capture some much, much needed rest. She was so eager for her dreams to carry her away, she didn't notice Twilight groggily sitting up, with a faint glow surrounding her horn. *click* "AAAAAAAAUUUUUUUUUUUUUUGGGGGGGGGGHHHHHHHH!" Rainbow Dash's eyes were assaulted by every single lamp in the library as they were all turned on at the same time. Twilight looked up, confused. "Why *hic* is there a cloud inshide my house? Also, why is it shcreaming?" The pegasus poked her head through the bottom of the cloud, still holding a hoof over her eyes as they slowly adjusted to the glaring brightness. "Because I just dragged your drunk flank over here all the way from the bar!" She hopped off the cloud and fluttered down to the floor. "Seriously Twilight, what's gotten into you? I haven't seen you that drunk in ages. Did something happen?" Twilight stared at Rainbow Dash, blinked twice, then hiccuped and curled up on the ground. "Go 'way." Rainbow Dash was absolutely exhausted. Today had been taxing in more ways than one, and she had run out of patience somewhere outside of Ponyville. She knew she had every right to tell Twilight to just get over it and fly back to her house for some well-deserved rest, but she wouldn't. She couldn't. She was the element of loyalty, for crying out loud; there was no way she was leaving her friend alone like this. "Come on, Twilight, I know something's bothering you. What's up?" "Itsh *hic* none of your beeswax, Rainbow!" Twilight stuck her tongue out at Rainbow Dash. The pegasus rolled her eyes. "You drank so much you eventually passed out. I'm the one who had to carry you home, so I'm making it my beeswax whether you like it or not!" She stamped a hoof on the ground. Twilight hiccuped, then curled back up into a ball, her back to Rainbow Dash. The air was thick with silence, and time slowed to a crawl, until the cyan mare heard a small sniffle reverberate through the library. Instantly, Rainbow Dash knew Twilight was hurting about something, and slowly walked up to the lavender ball of fur. "Twilight?" She whispered, leaning down and nuzzling her friend. "Twilight, please, tell me what's wrong. I don't want to leave you like this." No response. Rainbow Dash's head spun with possibilities. Had she failed a test? That always seemed to get her worked up. Did she do something terrible in front of Celestia? Did someone say something to her? Rainbow Dash couldn't help but think she was forgetting about something terribly important, but she was so exhausted and sleep deprived she couldn't think straight. Suddenly, Twilight's voice floated past Rainbow Dash's ears. "My coltfriend dumped me." Buck.