Professor Fox tapped his wand against the old Arithmancy classroom door and stepped in, standing in his familiar place behind the large front desk. He quietly wrote on the board, then turned and waited for the students to begin showing up.

Kay entered the classroom and read the instructions on the board. She walked up to the front desk and gathered a small chalkboard, then made her way to a vacant seat and sat down.

Erica entered the classroom and after glancing around the mostly empty room, she took the small chalkboard from the professor's desk and took a seat, waiting for the class to begin.

Drusilla took the chalk-board and went to the back of the class. She noticed the Hufflepuff girl whom she had seen at Professor Fox´s Office door, and nodded politely to her as she passed.

Alex wandered inside the Arithmacy classroom and gave Professor Fox a small nod as she walked past him. She scanned the room carefully, looking for a seat and for a certain Slytheirn girl, but obviously, she had not arrived yet. Shrugging, she moved quite swiftly between the rows of desks and took her usual seat at the back of the classroom.

Slowly and quietly, she took out a few pieces of parchment and a quill and set them on top of her desk. Placing the bag underneath her chair, she took one last quick glance around the classroom and finally, her gaze set on the Professor.

While waiting for class to start, she tapped her fingers lightly on top of her desk.

Noel walked into the classroom and took one of the small chalkboards. She took a seat and said "Hello" politely to Alex. Then she took out her quill and doodled aimlessly on an old piece of parchment.

Kalaya walked into the classroom and glanced at the board. Slowly, she made her way up to the desk in the front as she scanned the people already there.
*sighs* I don't know anyone here, Kalaya thought as she grabbed one of the chalkboards. She found a seat that looked alright and sat down. While she waited for class to begin she pulled out her parchment that was full of doodles and started doodling.

Martha enters the classroom and sees the directions. She walks down to the desk in the front of the room and picks up a small chalkboard, and then finds a seat towards the front of the classroom. She takes out a few pages of blank parchment, ink, and a quill and waits quietly for class to begin.

When noticing Noel entering the classroom, she gave her a quick nod and eyed her intently. She saw Noel getting a chalkbaord and then Alex realized that she had to get one as well. That just proved what a short attention span she had at the moment. Besides, there were other things to worry about right now.

Before getting up and and grabbing a chalkboard however, she ripped off a piece of parchment and scribbled something on it. With a small groan, she got up and walked by Noel's desk, dropping the note on her lap and making sure that no one noticed it.

The note simply read:
Slowly, she walked on as if nothing happened. Alex took just a random chalkboard from the pile, turned around and walked back to her seat, keeping her eyes glued to the floor the whole time. Once she sat down, she gave Noel a glance and just as quickly her eyes once again rested on the Professor.

Noel picked up the note discreetly and read it. A mixture of excitement and dismay filled her, was Nadia going to have to modify her memory or was Alex going to tell her what was going on. She nodded slightly at Alex, making sure her expression was completely neutral.

Erica noticed the Slytherin girl that waited in the hall with her before she saw the professor and noticed the girl nod a polite greeting. Erica nodded back and looked around the classroom slowly filling up. She saw Alex in her usual seat at the back and gave a small smile and a welcoming wave before turning forward in her seat once again. She didn't know why, but things just felt very tense in the atmosphere at that moment. She sighed, shook off the strange feeling and pulled out a text on a random subject, reading it to pass the time until the class started.

luna walked into the classroom with a cheeky grin on her face, after all her thinking she had come up with a solution and was quite pleased with herself.
she walked to the front of the class and took a seat near the teachers desk, she placed her chalkboard in front of her, crossed her arms and sat there with the cheeky grin still plasterd on her face

Professor Fox sighed and scanned the room briefly, then turned his attention to some notes and books before him on his desk. "We will wait a little while longer for any other students to wander in, then we will begin the lesson," he announced casually, his attention still not diverted from his books and notes.

ut of the corner of her eye, Alex noticed that Noel had read the note. Before she could ask the Professor what they were going to learn today, she noticed Erica, a Hufflepuff girl she knew pretty well walking in the classroom. She was wondering how Erica even showed up in Fox's class, considering that he gave her a detention for no good reason.

When hearing the Professor speak, her eyed suddenly lit up and her cold, hard stare was once again on the Professor. Well, no doubt, he was really good at teaching and he knew his stuff. Truth was, though, he could be rather annoying at times, especially when calling students by their last names.

"What are we leaning today, Professor?" she finally asked after a few seconds hesitation.

"Hmmm?" He said, moving his attention slowly from his books. "Ah. Ms. Kay, you will find out soon enough, but today we will be studying the numbers 0 and 1." He then nodded politely to her and went back to his reading.

Heshasa walked in seeing that class had not started took a seat near the back of the class. Taking out ehr quill, ink, and parchmant. Made her quill hover absentmindedly above the desk.

Ah. There it was again. Not Alex. Not Diana. Ms. Kay. She twitched slightly when hearing the Professor call her that, but knew better than to say anything about it.

"Interesting. But then again, I find anything that has to do with Arithmancy interesting, as it is my favourite subject." What th --? Did THAT just come out of her mouth?! Could she suck-up anymore than she already has? Well, I suposse anything is possible, no? But honestly, Alex never thought she would see herself sucking up. Expecially to someone like Fox.

"What are you reading, if you don't mind me asking? Is it an Arithmancy book?" she asked politely.

Erica's concentration wavered as she couldn't help but overhear the conversation between Alex and Professor Fox and it sounded like a normal conversation until Alex's last statement came shooting out of her mouth. As quickly as she could, Erica grabbed the text that was on the desk and propped it up so the professor couldn't see the giggles that were coming out of her mouth. Why is this funny? she thought as she tried to maintain some form of control over herself. This is Alex, your friend talking! Why is this funny I ask you? Why?

After a few seconds, Erica turned in her seat and motioned to Alex that they needed to talk and fast. Like right after class.

Professor Fox continued reading his book, as the somewhat over-enthusiastic student continued asking him questions. "Well, I'm glad to hear that you enjoy the subject Ms. Kay," he said, rather non-chalantly. "Yes, it is an Arithmancy book of sorts." Looking up and noticing the rather complicated looking clock on the far wall, he sighed and closed his book, looking up to the class encouragingly.

"Well, I suppose we had better begin, as those of you have come to class on time certainly deserve to hear the lecture and participate." He outlined his earlier instructions in a box, making sure not to erase them, and then proceeded to write 'review' on the board.
"Now, who can tell me briefly, two things we learned in the last lecture?" He asked the students, holding the chalk in his hand.

Oy vey. It was hopeless. Once Fox started calling her that, she honestly doubted that he would ever stop. Shaking her head, she thought for a second when she head someone giggling.

Scanning the classroom, she noticed Erica had a book over her mouth and man, was she giggling. And Fox didn't even say anything? She stared at Erica and blinked for a few seconds when she noticed that Erica made a sign as if they needed to talk. Raising an eyebrow, Alex shrugged and looked back at the Professor.

Once again, her looked at the Professor and pondered for a second. Raising her hand, she spoke. "Well, we learned what prime numbers were and studied a few numbers more indepth."

"Let me add to that, we studied the magical propreties of 2, 3, 5 and 7."

After making absolutely sure that the giggles were completely contained, Erica replaced her text in her bag and felt the relief over the fact that the lesson was to begin. Putting on the composure of someone who was absolutely serious about her education, Erica raised her hand in answer to the professor's question.

"We went over several prime numbers and their deeper meanings in Arithmancy. For example, we learned that the number 2 is the building block of all numbers and that the number 5 represents the physical aspect of interaction with all intelligent beings, humans included."

Nadia raised her hand, thinking all the time 'two things', "That odd number 5 and 7 are both related to longivity, while 5 is for terrenal / physical longivity, 7 s the mystic magical number for longetivity, hence avoided in Tranfiguration spells."

Well, it was brief enough, no?

"Excellent answers all of them, Ms. Kay, Ms. Arbon, and Ms. Rey." He said, writing their answers on the board. "Indeed, we studied prime numbers during the last lecture, and prime numbers are important because they are the building blocks of all integers, save for two: 1 and 0." He turned around and faced the class.

"Now, can anyone tell me any mathematical properties of either 0 or 1. We will examine their magical significance in a moment." He leaned against the desk, waiting for students to begin answering.

Erica thought carefully for a moment before raising her hand to answer the question.

"Well, in mathematical terms, there are special laws that govern each number. For example, the identity laws of algebra state that anything added to the number zero equal the original number. This same idea is reasoned when any number is mulitiplied by the number one. If you mulitply a number by one, the resulting answer is the original number.

In addition, the number zero has additional factor laws attached to it. The first one states that any real number mulitplied by zero will yield an answer of zero and if two numbers mulitplied together equal zero, then either one of those numbers has to be zero.

Also, any number divided by zero yields an answer that is not definable."

Nadia grimaced a bit in doubt and hesitation, though having learnt a bit at muggle school when younger...

She raised her hand. "All the operations (addition, subtraction, multiplication, division, exponentation) by 0 will all equal 0 itself. That is, 0 is an identity element with respect to addition. But x / 0 is undefined, because 0 has no multiplicative inverse, a consequence of the previous rule. For positive x, as y in x / y approaches zero from positive values, its quotient increases toward positive infinity, but as y approaches zero from negative values, the quotient increases toward negative infinity. The different quotients confirms that division by zero is undefined.

"All multiplication with 1 will result in the same number that participates of the operation but 1. This expresses the fact that 1 is the multiplicative identity.)As a consequence of this, 1 is a 1-automorphic number in any place-based numbering system. In divition, as the divisor (x/1), it will have the same result, but not with different order. Exponenciation with number 1 also will result in the second number that is not one.

"Addint to it... Zero is a number which means nothing, null, void or an absence of value. Zero is neither prime nor composite. Zero is the number in between the groups of negative and positive numbers. In geometry, the dimension of a point is 0. In analytic geometry, 0 is the origin.

"It is the number of n×n magic squares for n = 2."