A/N: I'm a math nerd. I'll admit it. But math can be cool, especially when it proves that nothing exists and everything exists at the same time.
Disclaimer: I don't own HP.
It was a normal morning at the Gryffindor house table: Ron was stuffing his face with eggs and bacon, Hermione was reading her potions textbook, Harry was attempting to have a conversation with Ron whose efforts at answering his friend usually resulted in spewing bits of food everywhere, and Luna was telling Ginny all about the migration patterns of crumple-horned snorkacks.
Hermione tried to be tolerant, she really did, but there was only so much a girl could take. Bits of food splattered her potions book as Ron mumbled incoherently to Harry all while Luna droned on and on about her silly, imaginary creatures. Hermione felt as if she would pop and her sanity would float out of her head like helium leaving a deflating balloon. Hermione slammed her book shut.
That got their attention. Ron's mouth hung open, half-chewed food clumped on his tongue. Harry and Ginny exchanged startled looks, and Luna turned her dreamy gaze on Hermione.
Hermione acidic glare first rested on Ron. "You!" she exclaimed, pointing viciously at the youngest Weasley boy. "Don't talk with your mouth full!"
Ron quickly closed his mouth and gulped down his food. He didn't dare challenge Hermione in this mood. This mood usually led to people getting slapped, and when Malfoy wasn't on the receiving end it wasn't funny.
"And you!" Hermione growled now pointing to Luna. "When will you finally understand that crumply-horned…whatevers do not exist!"
Luna seemed unruffled by Hermione's outburst. "Of course they do," she replied simply.
"Give me proof, Luna! Other than some blurry photographs and questionable witness accounts."
Luna blinked slowly. "I have mathematical proof."
Hermione looked startled. Mathematics wasn't what she was expecting. She didn't even know Luna knew math, and she couldn't fathom how it applied to Luna's creatures.
Luna calmly pulled out a piece of parchment and a quill. Harry, Ron, and Ginny leaned in to see what Luna was writing.
"Alright," Luna began, writing a equals 1 and b equals 1 at the top of her parchment. Luna went through every step slowly, consulting Hermione to make sure the older witch approved. Luna went through every step and then substituted back in her numbers and found that…
"Zero equals one!" Hermione exclaimed, outraged. On the parchment was written exactly that: 0 equals 1.
"That's impossible, Luna!"
"No it's not. You agreed with every mathematical step."
Hermione growled. She couldn't believe she didn't find a flaw.
"You see, Hermione. If crumple-horned snorkacks don't exist, then at least one must exist as zero equals one."
"But," Hermione countered, "if one does exist then it wouldn't exist."
Luna smiled. "But then it would exist."
Hermione ground her teeth. "Let me see that." Hermione grabbed the paper and examined it closely. There must be a flaw somewhere. Luna merely looked satisfied.
After a few moments of silence, Hermione's face lit up. "I knew there had to be a flaw. Here," she said pointing to a step mid-way down on the parchment. "You have zero divided by zero."
Luna blinked. "So."
"You can't do that!" Hermione explained as if it was obvious.
"Because zero divided by zero can be anything and nothing! It completely destroys all the rules of mathematics."
Luna looked almost surprised. "Well whoever devised those rules was rather closed, weren't they."
"They weren't closed, Luna, they were smart," Hermione said.
The veiled insult didn't seem to bother Luna. Then again, she did sit up straighter as she said primly, "Well then, you're entitled to your beliefs. However because there are infinite universes and you exist in one of those infinite universes, the probability of you existing at all is one to infinity which is zero. Therefore, you don't exist at all so your entire argument is moot." Luna quickly stood from the table, grabbed her copy of The Quibbler and marched out of the Great Hall.
Hermione was left dumbstruck, while the onlookers tried hard not to laugh.
A/N: I will admit that the limit of 1/infinity is zero, but one could say the actual number is an infinitesimally small amount, but we're going with zero, because anything divided by zero is infinity so logically anything divided by infinity would be zero.
If you want to see the equations Luna used, there is a link on my profile page. (I tried to put the equations on here, but you can't put an equals sign in anything.)