Disclaimer: I do not own Haruhi Suzumiya or anything related.

A/N: Sorry for any discrepancies. Time-travel isn't really my specialty. And mathematics, for that matter. Oh, and don't worry. I won't put in "classified information" everytime. I'm not used to writing for Mikuru, I'm afraid.. but I'll do my best!

You may think of this as an indirect sequel to my other fanfic, "Do You Believe".

Title: Occurrence Approaching Zero

Synopsis:

Mikuru Asahina and Itsuki Koizumi have a conversation regarding time and possibilities. Oneshot slight MikuItsu.

Time cannot be viewed as something that flows continuously, but rather, time is an accumulation of punctuated planes.

There exists a gap in-between periods of time, although their rate of occurrence is approaching zero. In mathematics, as x approaches the destination of the end of the time plane, the limit of the "occurrence function" approaches zero.

Time-travel means moving in a three-dimensional direction across accumulated time planes. The ability to travel across time planes is made possible by a TPDD, a Temporal Plane Destruction Device. It destroys or damages a portion of time planes in order for the 'time-traveler' to be added into that era.

Therefore we view that time is like animation. It gives the illusion of continuity, while in reality, it is actually a set of accumulated planes.

And that we, time-travelers are extra pictures added into that flipbook.

That is the basic theory for all us time-travelers. It is the very foundation for the concept of time travel.

I do not have enough authority to reveal any information. In fact, I do not know much about the mechanics of time-travel.

I will admit though, that the time-travel we use is imperfect. I cannot tell you what makes it so, but I can assure you that it is not pretty easy for us to slide from era to era.

"Oh. Asahina-san?"

"K-Koizumi-kun… Welcome back!"

I'm sorry, I forgot to tell you that I was here in the clubroom, knitting in one corner of the room, accompanied by none other than Nagato-san. It was the second day back after the winter break, and a time plane closer to my last year in this school.

"It seems that Suzumiya-san isn't here yet."

"Um… Suzumiya-san and Kyon-kun have cleaning duties."

"I see."

He sat on the chair he usually occupies. I noticed, however, that he wasn't smiling at all like the usual. It was as if something was bothering him.

"Um… Koizumi-kun… do you want some tea?"

"Oh, thank you, but I'd rather have some coffee."

"Oh, I happen to have some here. Nagato-san, is there anything you want to drink?"

"Nothing." Was her reply.

Setting the kettle to boil, I started preparing Koizumi's cup. There was a box of instant coffee powder beside the box of tea leaves, as Suzumiya-san ordered that there be more choices of beverage in the clubroom.

All the while I was doing this, I noticed that Koizumi-kun looked solemn and desolate.

"Here you go." I smiled and served him the cup.

"Ah, thank you." He smiled weakly.

I was about to go back to my knitting spot when I heard Koizumi-kun's voice.

"Asahina-san? Do you mind if I asked you something?"

I looked at him.

"Do you… I mean… Have you ever felt like you were doing a lot for nothing?"

"Well…"

"I am referring of course, to the 'you' in this time plane."

"By 'me', you mean, the 'me' you are talking to right now?"

He thought for a while before he said:

"Yes, the 'you' I am talking to."

"Well… I guess sometimes… Because I really don't know what I'm supposed to do."

"I guess…" he sighed, taking a sip of coffee.

I looked at Nagato-san. She was still seated on one corner, reading. It seems that she is unmoved by this conversation.

"Well…" Koizumi-kun started. "I really wish I could tell what was going to happen in the future."

He was staring at the cup.

"So I'll know whether what I'm doing right now is the right thing to do."

"What do you mean?"

"I wonder if I should…" He grasped the cup tightly with both hands.

I stood up, and touched his hands.

I know that Koizumi-kun and I have different interpretations about the events surrounding Suzumiya-san and Kyon-kun, but no matter how my superiors tell me that he is not to be trusted…

I still can't help but feel sad when I see him like this.

Like me, I suppose that he's also being ordered to do things he normally wouldn't do.

"Asahina-san…"

"I understand. You were told to do something you know deep in your heart you couldn't stand to do."

"I was wondering… Could you tell me what will happen in the future?"

I froze. He looked me right in the eye when he asked me that question. Despite what my superiors told me of his true nature, I could tell that this time, he was at his most sincere.

"By 'future' you mean?"

"Suzumiya-san…"

"Oh. I see."

Truth is, I know what will happen in the future. I know how it will all turn out. And although I don't like how it will turn out, I guess I couldn't do anything about it.

"Koizumi-kun… Suzumiya-san will…"

"Please stop." He said.

"Eh?"

"I think I know what you will say." He smiled weakly. "But I don't want to hear it. And I don't think you want to say it out loud."

He stood up and walked by the windowsill. He opened it gently and poked his head outside.

"Let's just keep that as classified information." He looked back at me and winked.

"I guess." I nodded and smiled.

"Can I ask you another thing?" he said.

"Go on."

"There are gaps in-between time, right?"

How much does he know? Maybe his Agency has filled him in on this.

"Is it possible to change the future within those gaps? Seeing as time is not continuous on those points."

"I'm sorry. I do not know. All I know is that their occurrence approaches zero."

"In calculus, I believe I read somewhere that approaching zero doesn't necessarily mean zero."

My eyes widened. Could it possibly be?

"Then we can define 'approaching zero' as a number close enough to zero approaching it from either the left side or right side of a function, but not necessarily zero. It's either a positive or a negative number."

The wind blew from the open window.

"Then there is a chance for us to change our future, even if there is a relatively very small chance of doing so."

"Koizumi-kun…"

He walked back to his chair and drank the rest of the coffee.

"If we were thinking of the same thing about Suzumiya-san… about the future, then, for now, I guess I'm fine with what's going to happen."

"I believe that it is the right thing to do, Koizumi-kun… To keep that future intact."

"But there is one thing I wish I could have in the future…" he chuckled and picked up his things.

Without looking at me, he said the following:

"Asahina-san, please tell Suzumiya-san that I'm leaving early today, but I was here. I may receive a penalty, but please tell her that I have work today, so…"

"I understand." I smiled at him.

Carrying his bag over his shoulder, he turned at me.

The sun was now setting over the horizon and the gentle breeze blew his hair along with its rhythm.

"There is one more thing: I don't believe one of your theories regarding time-travel…"

I know that Koizumi-kun's faction and my own faction have conflicting ideas about things, and I've never talked to him about this, and I never intend to. I don't think he will ever agree or even listen to what I believe in.

But when he said those words, I found myself wanting to believe in him for once.

"About the flipbook analogy… I do not think that you're just another extra picture."

He smiled and left, closing the door.

It's not that I dislike Koizumi-kun. But I was told to be wary of him. And yet…

I turned to Nagato-san.

"Nagato-san, was that accurate?"

She looked at me with those ebony emotionless eyes.

"That's classified information." She said, putting her index finger close to her lips.

A/N: Haha. Well done, Nagato-san! I got dizzy at the Calculus references. I hate math, I really do. R/R!

Oh, and Happy New Year to everyone!