the morning comes and misaki get up from her bed

and as usual with a blank expression she do her daily chores

then went to school not bothering to bid goodbye to her brother who was probably sleeping right now

(its just the usual huh?) misaki thought as she look at the crowd of students chatting and doing stuffs together

(whatever)

misaki walk to her classroom as always and duck her head down the table as she listen to her calm music then close her eyes

after a few minutes she heard the class went silent and so she knew the class was about to start so she quickly sat down properly and look at the front

"If x and a are two real numbers the distance between x and a is |x − a|. For most purposes in calculus it is better to think of an inequality like |x − 5| < 2 geometrically rather then algebraically. That is\, think “The number x is within 2 units of 5\,” rather than “The absolute value of x minus 5 is strictly less than 2.” The first formulation makes it clear that x is in the open interval (3\, 7)  then Let a be a real number. A neighborhood of a is an open interval (c\, d) in R which contains a. An open interval (a − δ\, a + δ) which is centered at a is a symmetric neighborhood (or a δ neighborhood) of a. next A deleted (or punctured) neighborhood of a point a ∈ R is an open interval around a from which a has been deleted. Thus\, for example\, the deleted δ-neighborhood about 3 would be (3 − δ\, 3 + δ) \ {3} or\, using different notation\, (3 − δ\, 3) ∪ (3\, 3 + δ). also A point a is an accumulation point of a set B ⊆ R if every deleted neighborhood of a contains at least one point of B.(For Set Operations). Let A and B be subsets of a set S. Then

(1) x ∈ A ∪ B if x ∈ A or x ∈ B (union);

(2) x ∈ A ∩ B if x ∈ A and x ∈ B (intersection);

(3) x ∈ A \ B if x ∈ A and x /∈ B (set difference); and

(4) x ∈ Ac

if x ∈ S \ A (complement).

If the set S is not specified, it is usually understood to be the set R of real numbers or, starting in Part 6, the set Rn, Euclidean n-dimensional space. so class do you understand the inequalities and absolute values ways? if so please answer these questions"

the questions

(1) The inequality |x − 2| < 6 can be expressed in the form a < x < b where a = ____ and b = ._____

(2) The inequality −15 ≤ x ≤ 7 can be expressed in the form |x − a| ≤ b where a = ____ and b = .____

(3) Find all numbers x which satisfy |x2 − 9| = |x2 − 5|.

Answer: x = ____ and x = .____

(4) In interval notation the solution set for the inequality (x + 1 / x − 2) ≤ (x + 2 / x + 3) is (−∞\,____ ) ∪ [ ____\, 2 ).

(5) Let a\, b ∈ R. Show that | |a| − |b| | ≤ |a − b|.

after the class all the students exhailed "that was tough" "i could barely answer it" "waah my brain is drained now!"

but none of that really bothers misaki and just sat properly then look outside the window when she saw a tiny snow

(winter is coming huh) then the next teacher came in but with another student then the students became silent again

the teacher gave a sign which the boy seem to have understand and stand firmly infront of everyone

"Hello! my name is Kiriga Takirami nice to meet you!" kiriga bow slightly as girls squealed over him so he  smiled in return

"so as everyone can see Takirami-san is gonna be your new classmate from today onwards now takirami-san please choose an empty seat" but the only empty seat that was left was misaki's side so kiriga went there and the class start

"umm hello i'm-" before he could even finish misaki bluntly reply to him with a "i know"

(that's kinda rude isn't it?) kiriga thought so he tried to speak again but once again rudely interrupted by misaki "just shut it" and take a note from the lesson

"takirami-san is there a problem ?" the teacher ask which embarrassed kiriga

(seem like she doesn't wanna be disturbed while studying)

"no ma'am there isn't" kiriga smiled to reassure the teacher and so the lesson starts again

(what a fake) misaki thought as she ignore him for the whole day

things went on just like usual between kiriga and misaki but kiriga now gained more friends and they're still increasing

especially now that kiriga joined baseball, which is his favorite sport he got more fans as time passes by and now its lunch break when he saw misaki staring at the window beside her with a blank look

(what is she doing? aren't she going to grab something to eat?) kiriga thought as he look at the lunch boxes beside her which is full of foods an idea struck into his mind and so he approached misaki

"here" he handed one of the lunch boxes that he got from the other students who gave him although he doesn't remember who it is but he's greatful cause he could share them with misaki

misaki ignored kiriga and continue staring outside not giving him even a glance

kiriga started to feel his hand numb so he put down the lunch box besides misaki and left

after kiriga left misaki look at the lunch box then thought (it's not even his tsk) then left the classroom not touching the lunch box and went to the library

then the bell rang which means class is starting again

kiriga went back to the room and saw the lunch box untouched and didn't saw misaki anywhere

(why didn't she touch it? or have she already ate before i gave her the lunch box?)

kiriga sat down then the teacher came in

the teacher glance at kiriga's side and saw misaki

the teacher sighed and started his lesson

while kiriga was sitting there and listening with confusion he just focused on his studies

and so the whole afternoon misaki didn't attend the classes which made kiriga wonder why

(why is she absent the whole afternoon?)

(it cant be that she's sick right? oh well i saw her earlier but she doesn't seem sick so it cant be)

while thinking about it a bunch of girls came to him

"kiriga-san~ are you free tonight?" one of then ask

"hmm? not really"

"well then do you wanna hang out with us?" another girl from behind ask with its puppy eyes

kiriga feel awkward so he immiedietly apologize and ran off while the girls wave him goodbyes and say how dissapointing it is that kiriga couldn't hang out with them

after running so much kiriga sat down at the side of a tree and rest for a bit

"whoooo that was close" kiriga stretch his arm and drink a water from his mineral water in a bottle when he saw a familliar figure up at one of the branch looking back at him

it was misaki who was confuse as to why he was running earlier and now sitting down at the shadow of the tree she was sitting at

"why are you here?" misaki ask coldly

"why cant i be? its not like you own this place right?" kiriga said back at her

he's been tired of misaki ignoring or bluntly talking to him when he didn't even do anything that would irritate her

(wait or is it that i annoyed her at some way i dont know?) kiriga thought

"so you can talk back" misaki said without a care

"i'm still a human being you know? and also why do you keep on being cold to me when i was being nice to you? its not like i irritate or annoyed you in some way right?"

"you think its only you?" misaki said in a bored way

"w-what?" kiriga said in surprise

misaki jump down and put her hoodie on

"dont think so special about yourself just because others like you"

and with that she walk away while kiriga stood there stunned

(now that i think of it she doesn't talk alot and probably that last sentence is her longest talk but isn't it only because the other students dont talk or approach her?)

he then look up at the branch where misaki was sitting on earlier

(but i also dont know much of her and even her name- wait what was her name in the first place?)

the next day misaki isn't still there when kiriga attend at school

(Is she not coming?)

then kiriga heard some students chattering about misaki

"i bet that girl would be absent today too" a girl said

"yep~ oh how i wanna sat at her seat to be close to kiriga-san~"

"stop that dream or you wanna end up like them"

"psh i know alright! she's just way too lucky i wonder what kiriga-san saw in her and kept on approaching her" it snorted

then kiriga walk pass to them

"oh my he didn't hear us right?" nervous

"dont worry he wouldn't care about that girl"

and with that kiriga turn to look at them which surprised the girls and made them flushed

"k-kiriga- s-san do you n-need anything?" one of them ask while blushing

kiriga smiled at them and said "don't carelessly talk behind others that's bad" then turn around and continue walking when he saw misaki at the stairs blankly staring at them

(did she happen to hear it?) kiriga ask himself worried about misaki but then when he attempt to call her

misaki left by jumping from the window which shocked kiriga

"hey were at the 3rd floor!" kiriga ran to catch misaki worried she might injure herself but when he arrived, misaki already landed safely on the ground walking like nothing happened

(seems like she dont need my help at all huh) kiriga thought as he smiled a sad one but relief at the same time

(oh well she know how to protect herself so why do i care?) kiriga went to the classroom just at the same time as the teacher does

"oh my if it ain't takirami-san" kiriga smile at the teacher and offer her some help which is, the teacher was so greatful

"ahh i'm glad you transferred here so now atleast there's one student who was kind and gentle"

"well you praise me so much mrs.gren, i feel so honoured"

"aiya! no need to be so polite anyways i'm sure that a handsome lad as handsome and popular as you are already got a girlfriend no?" the teacher said in a teasing tone which kiriga only smiled at

"nope but i will soon" then they arrived at the classroom door

"thank you for helping me out kiriga-san"

"no problem mrs.gren" then kiriga sat at his seat next to misaki who was ducking down her head and was probably sleeping right now when kiriga heard a quiet snore

kiriga chuckle (how cute, so even she can snore like that huh)

he stared at misaki for a while until misaki starts to move and so he focused his eyes on misaki once again while she sleep peacefully

(her coal colored hair look so smooth and silky that i wanna pat it) then unconciously he raised his hand to pat her when

"dont you dare" misaki's cold voice froze his whole body

(oh no! what did i just think i'm going to do to her?! am i out of my mind?!)

kiriga smiled

(that fake smile again (-_-) i really hate it)

and said "n-nothing i just think there's some dust on your head"

(dust inside the classroom? is he saying that our school  is in short of janitors or something?)

"whatever" misaki then again duck her head down

"what's your name?" kiriga's question made misaki flinch for a second but then calm down

"doesn't matter" and as usual misaki ignored kiriga again