Everything either is or is not, by the law of excluded middle. Either something is true or it is not. One way to prove something is to prove the opposite is false.
Either it is or it is not. One or the other.
It had been the summer before eighth grade. Jazz has been preparing for tenth grade, studying the overview of all the subjects she would be taking. One of those subjects was geometry.
A lazy afternoon with nothing to do (Tucker was out somewhere with his folks and Danny didn't feel up to hiding from the sun with Sam) caused Danny to grab one of Jazz's textbooks and take it outside. It was actually to see Jazz freak out a little about losing a textbook, but it seemed that Jazz was studying something else at the time.
So Danny was left with a textbook about math. Really, he hated math, but with nothing better to do, he started reading the textbook and doing the problems.
Geometry was the one thing Danny was decent at when concerning math. Algebra made him pull his hair out and numbers taunted him. But geometry always came easy to him. It wasn't a number or getting a number from a letter. Geometry was logic. You know this and this, so you can get this. Figuring out whether a certain line is the perpendicular bisector to some triangle was easier than figuring out standard forms.
Some people said he lacked common sense, other said that he just lacked a brain, but no what matter what anyone said, geometry, logic, came easy to him.
It was the one thing he was good at. (School wise, of course.)
Danny had conjured some paper and a pencil. In the summer heat, he managed quite a few of the problems and so far, he had gotten majority of them right. (That stupid problem with the circle threw him off – he actually needed a bit of regular math for that.)
He moved on to indirect proofs.
His family was of the smarter kind. His mother and sister got straight As and even his doofus of a dad managed to get straight Bs. Even though the Fentons were always part of the smarter bunch, they had such an, umm, unconventional job that it made it seem like they weren't. (Smart people just didn't believe in ghosts.)
That didn't change the fact that they were good parents. Sure, sometimes they spent too much time in the lab and didn't notice the most obvious things (which could be more a blessing now), they cared. Maybe they showed in it more weird ways than other, but Danny's parents really did care.
They would always accept him, no matter what. Danny knew that.
He had looked at the problem. He started with the excluded middle and assumed the opposite of the thing needed to be proven true. (It is a possibility.) He started to work backwards until he got to a certain point.
Then why couldn't he get that idea out of his head?
That day cleaning the lab was his catalyst. The seed of doubt found its way into Danny's mind. Now he just couldn't ignore idea he'd gotten that day.
Danny only thought about the possibility that they wouldn't accept him for only a split-second. He realized his mistake right after, but yet...
It just wouldn't leave.
The main reason that Danny didn't tell his parents of his ghostly side is not because he thought they wouldn't accept him. It's just that his dad had a big mouth and really couldn't keep a secret. He thought that his parents would accept him, but he wasn't too certain about his town.
But now he needed to prove to himself that his parents would accept him or else he would never have his mind at peace.
What's a better proof then it actually happening?
It would be so much easier for him too, to tell the truth. Now his parents would know why he always had to break curfew, why he had a few mysterious injuries every so often.
So he told them.
The assumption had led him to the opposite of a given. He had gotten his proof.
He didn't bothering thinking about why he needed proof. He didn't bother thinking why he was so certain on the outside, but yet he was still doubting.
He wished he bothered thinking. Then he wouldn't have forgotten his givens.
He wished he never told them.
"Danny, I was looking for that textbook!" Jazz had shouted when she went outside to find Danny doing the next indirect proof.
"Give me a minute, I need to finish writing that it can't be the bisector because the two angles can't be equal. It's a given."
A/N: Second chapter. I'm not completely happy with the way this turned out. But there's one more part. Thanks to everyone who reviewed/story alerted/favorite/anything. Please tell me what you think of the story and if there is any type of mistake. If you're confused about the mathematical aspects, send me a pm or review (signed). I don't want to explain it here because then it'll be a long thing. But if a lot of people are confused, then I'll explain it in the next chapter. All of these chapters are so short. I'm going to try to make the next one a bit longer. Also, every other section is part of a flashback.