A/N: I'm finally back!!!! I've been taking my time writing this chapter since I wanted this one to be longer than normal for y'all. I'm happy to finally be able to start writing again, I've missed this. How have you all been? I hope everyone's break was nice and that they had time to relax. Also, it turns out that while I was gone, I was tagged by my good friend nathancarter25 again, so let's get this done before jumping into this chapter.
1. Name: [REDACTED] Michael [REDACTED]
2. Height: 6 feet 0 inches
3. Weight: ~150 lbs. (~68.0389 kg) I haven't measured it in a long time.
4. Age: 20
5. Girl Best Friend (Online): I don't know who's male or female online so...... I have no clue.
6. Guy Best Friend (Online): The ones I know for certain that are male, I have too many to count. Almost everyone on here has been really nice and fun to talk to so I consider everyone on here my best friends. :D
7. Last Hug: Parent, before I left for the airport to head back to my apartment.
8. Crush: I still ain't saying a name for y'all.
9. Ever fell in love? Kinda embarrassing, but I don't know how to tell if I've fallen in love with someone. All I can say is maybe.
10. Favorite Food: Iron crusted 12 oz. Filet Mignon cooked rare
11. Favorite Color: Black, red, navy blue, and military green
12. The Last Person I Texted: Joelitos09 via discord.
13. Longest Relationship: 3 months
14. Battery Percentage: 28%
15. Eye color: Brown.
16. Addiction: Learning (Does this count?)
17. Favorite Animal: I like a lot of animals. I'm not going to pick a favorite or else I would feel bad for the other animals.
18. Favorite Singer/Band: I can't pick a favorite band. I love Slipknot, In Flames, Alestorm, Sabaton, Eluveitie, Five Finger Death Punch, etc..
19. Do I have a piercing? Nope.
20. Ever sang in the shower? Uhhhhh. *remembers screaming Slipknot's Spit It Out lyrics* Yes.
21. One wish: I'm assuming I can't do the "wish for more wishes." So, I wish to have the power needed to protect the people I care about.
22. Country I'm in: USA
23. Best time of my life: Any point in my life where I've genuinely laughed.
24. Pets: None with me at my apartment. Although at home, I have 2 big doggos.
25. Getting Married: I hope to at some point, but not right now.
26. First Kiss: Haven't had it.... I'm not joking when I say this.
27. Insecure: yes
28. Who do I love? My friends and sometimes my family.
29. Miss anyone right now? My dogs, and hanging out with my friends.
30. Hair Color: Really, really dark brown. If someone were to look at my hair, they'd say black, but once light shines off of it, they'll see that the actual color is brown.
31. Relationship Status: Single.
32. Last song I listened to: To Be Alone by Five Finger Death Punch. Boy, that sounds bad out of context, I was just listening straight through their F8 album.
33. Ever cried myself to sleep: Maybe once, but it was a long time ago.
34. Biggest Fear: Arachnophobia (y'all should already know why at this point if you've read my tags)
35. Do I believe in ghosts? Eh, 50-50.
36. Have I been depressed? Yes, but that was years ago, I'm out of it now.
37. Have I felt lonely? Yeah, but it doesn't last for very long.
38. Have I changed clothes in a car? Maybe when I was younger, but not in recent years.
39. Something I hate: People who bring other people down and cheaters. (I.e. jerks)
40. Something I could change about myself: My anxiety issues.
41. Do I like myself? Yes, but I don't mean that arrogantly.
42. Opinion on second chances: Depends on what the person's done.
43. Sleep with door open or closed: Closed.
44. Tag 25 people: No. I'm not making anyone have to answer 43 questions. This tag ends here.
A/N: Anyways, that's the end of the tag. And now it's time for the part you all have been waiting for, so, without further ado, let's jump right into the chapter!
Y/N = your name
F/F = favorite food
F/D = favorite drink
E/C = eye color
H/C = hair color
S/C = scale color
"Talking"
'thinking/voice in head/talking in your head'
"Beast talking/Demonic voice"
[Y/N's POV]
It's been some time since the parade and the battle of Fairytail occurred. Since then, repairs have been done to any buildings that were damaged, and things have started to go back to normal. I decided to take a break for a bit and just relax. After everything that has happened, I just want to sit down and do some more calculations. Although, this doesn't mean that everything is perfectly fine. As proud as I am to be half-dragon, I still feel a bit awkward walking around with my wings, tail, and scales out for everyone to see. So, I bought another large black cloak for me to wear. For some reason, Erza refuses to let me put them away and go back to my human form, so wearing a cloak was the way to go. Although I did make some modifications to the cloak. I added a black covering that runs halfway across the front of the hood to cover the dragon half of my face. But, I made sure to use a material that is one-way visible only (i.e. I can see out of the material just fine, but others cannot see through the material). I also made sure to lengthen the left and right sleeves to cover my whole arm, including my hand and claw. My wings fold against my body very nicely, so it's comfortable to wear the cloak with my wings out. And lastly, my tail curls around my waist, kind of like a belt. The cloak closes in the front, so no one will see the tail underneath.
Erza wasn't too happy about what I did with the cloak, but she immediately ignored it when she found out that I can still slide my tail out whenever no one's around. I still don't understand why she likes my tail so much, the scale is extremely tough and the spikes running along the length of it are sharp enough to cut skins with mild pressure. But, it at least gets her off my back whenever I'm in the guild quietly relaxing.
At the moment, I'm working on another problem in my notebooks at the guildhall. Erza made me sit with her and everyone else, and they're just quietly staring at me as I think of how to prove this theorem (or maybe corollary or lemma is a better term, idk :P): "A finite abelian group G has order pˆn , where p is a prime, if and only if the order of every element in G is a power of p."
(A/N: This is a problem from my math textbook. So all credit goes to the writer of the textbook. Also, if this is a problem any of you have to do for homework, I implore you to please try and solve the problem yourself before going to ask for help. It may seem like a really daunting task, but if you just calm down and think purely about the basics of what you already know, this problem becomes very simple and easy to solve.)
Lucy: "So.... what are you doing?"
Y/N: "I'm deciding which direction I want to prove first of this theorem."
Lucy: "What's stopping you from picking a random direction and proving that way first?"
Y/N: "Nothing, really.... screw it, I'll prove the forward direction first."
Erza: "I'm curious, what goes on in proving these theorems? It always looks so simple. Although, I'm sure it's anything but that."
Y/N: "Well, some theorems are very straightforward and easy to prove, but there are many other theorems that are very difficult to prove as well. A lot of times it deals with combining ideas you already know to be true and some logical thinking that may or may not be obvious at first."
Natsu: "I don't understand a lick of what you just said."
Gray: "I'm going to have to agree with fire boy on that."
Natsu: "What did you just call me?!"
Gray: "I'm agreeing with you! Why are you getting mad?!"
Lucy: "Would both of you shut up!!!"
Gray/Natsu: "Yes, mam!!!"
Lucy: *sighs* "Care to explain the proof while you write it?"
Erza: "Ooh, that would be interesting."
Y/N: "I...." *looks between the two* *sighs* "I don't have a choice in this, do I...?"
Erza: "Nope! Now get on with the explanation."
(==> forward direction)
Y/N: "Okay—glossing over that most likely none of you will understand the terminology used—first, let's suppose that G is an abelian group and the order of G is p^n for some prime number, p. Now, I'm going to show that from this start, that the order of every element in G is a power of p."
Erza: "How would you do that?"
Y/N: "Well, by a corollary of Lagrange's Theorem, the order of an element divides the order of the group. This means that for some arbitrary element a belonging to a group G, the order of a (denoted by |a|) divides the order of the G. Since we know that the order of G is p^n, this means that |a| must divide p^n. But since p is a prime number, the only numbers that can divide p^n are powers of p such that the exponent is less than or equal to n."
Natsu: "What if n is not a whole number?"
Everyone: *stares at Natsu in shock*
Natsu: "What? Did I say something wrong?"
Gray: "Natsu... do you even know what a whole number is?"
Natsu: "Yeah, it's a number with no fractional or decimal part."
Lucy: "Where the hell did you learn that?!"
Natsu: "Erza drilled this stuff into me as a kid...." *shudders in terror*
Erza: "You learned from that?" *wipes a small tear* "I'm so proud of you!"
Y/N: "... anyways, no, Natsu, n cannot be a fraction or decimal. It doesn't make much logical sense to only have half or a quarter of an element in a group. So, now that we know that only powers of p can divide p^n, it's safe to say that |a| must be a power of p as well. Since a is abstract, this applies to all a belonging to G. In other words, this implies that the order of every element of G is a power of p."
Natsu: "And now we're done!"
Y/N: "Nope! That was just the first half of the problem. Now we need to prove the other direction."
Natsu: "Aww..."
(<== reverse direction)
Y/N: "Now, suppose we know that the order of every element of G is a power of p, where p is a prime. Let a belong to G and a be of maximum order. Then, |a| = p^k for some k belonging to the set of integers greater than or equal to zero. Then we have two cases we need to check. First, we need to check if the group is cyclic, then we need to check if the group is not cyclic."
Lucy: "What do you mean by 'cyclic?'"
Y/N: "Well, if a group is cyclic, then the group is generated by a singular element of the group. In other words, every element of the group can be written as some power of the generating element(s) in the group."
Lucy: "Ah, okay."
Y/N: "Let's check if the group is cyclic. Well, if G is a cyclic group, we're done. We don't need to do anything more. This part checks out."
Erza: "Wait what? Why does it check out so quickly?"
Y/N: "If G is cyclic and we know that a is of maximum order in the group, then a is the generating element of group G. This then implies that the |G| is p^k. But, since k is just an arbitrary positive integer, it can be set to equal n. This then gives us the conclusion that |G| is p^n."
Erza: "Oh, okay."
Y/N: "Now, we need to check the case that G is not cyclic. We let |G| = (p^n)*m where n ≥ k and m belongs to the set of integers greater than zero and p does not divide m. Then, by a lemma used to prove the fundamental theorem of finite abelian groups, G = H x K where H is the subgroup of all x belonging to G such that x^(p^n) is equal to the identity element; and H is the subgroup of all x belonging to G such that x^m is equal to the identity element. Moreover, |H| = p^n. (A/N: I'mma just put a citation here for the lemma since it's partially quoted (Gallian, 231)) Since we know that every element of G is a power of p. This implies that every element of G divides the order of H, and since p doesn't divide m, this means that no nontrivial element in G belongs to K. In other words, K only contains the identity element and |K| = 1. This then implies that |G| = |H|*|K| = |H| = p^n. This means the second case checks out and we've finally proved this theorem."
Everyone except Y/N: *stares with gaping mouths in shock*
Y/N: ".... what?"
Everyone except Y/N: .........
Y/N: *slowly closes notebook and packs everything into his backpack*
Makarov: *coming from his office* "Alright, I need team Natsu along with Y/N to come up to my offi—" *sees the silence* "What happened here?"
I just grabbed my bag and walked up to Gramps and gave him a brief explanation.
Y/N: "Lucy and Erza asked me to explain the solution to one of the problems I was solving... so I did."
Makarov: *sighs* "Alright." *enlarges his hand and claps above everyone getting their attention* "Team Natsu, come along to my office."
I went ahead of him and walked in, sitting down in a chair, and just looked up at the photo of my mother that's above his desk. I still haven't asked mom about that, but I guess that can wait till later. About a minute later, I hear the door open to reveal Gramps along with team Natsu. Erza and Lucy sat down in the other chairs while Natsu, Gray, and Happy were stuck standing. Gramps walked around the desk to his chair and sat down before speaking to us.
Makarov: "Alright, there're two things I want to talk about. For starters, all of you are banned from asking Y/N to explain any of the problems he does in his notebook."
Erza & Lucy: "What? Why?"
Makarov: "Because if he explains the solution to another problem, he's gonna mentally break everyone in the guild... except Levy."
Y/N: 'That seems a bit like an over-exaggeration.' *remembers the incident with Cana* 'Okay... maybe not.'
Erza: "But—"
Makarov: "No, is no, Erza. No more asking him to explain the problems."
Erza: *grumbling* "Fine."
Y/N: 'Heh, that was pretty adorable.... Wait, where the hell did that come from?'
Makarov: "Secondly, the council has asked for us to go on a joint mission along with Blue Pegasus, Lamia Scale, and Cait Shelter. The mission is to destroy the Oración Seis. One of the three guilds in the Balam Alliance. You head out immediately, so there's no time for you to head out and pack. Here are the train tickets, it has the name of the location you get off at. From there you have to walk towards the meeting location. Y/N, you are going to lead our guild for this mission."
Y/N: 'Sure, give the person with social anxiety the lead role...' *sighs* "Fine. We head out immediately right?"
Makarov: *nods*
Y/N: "Then let's get going. We shouldn't waste time standing around talking. We'll see you later, Gramps."
Makarov: "Goodbye, my children."
We then walk out of the room and towards the train station. When we get there, we show them our tickets and they take us to a special compartment where we can all stay more comfortably during the trip... except Natsu. He still suffers from motion sickness. To deal with that, Erza just knocks him out for the rest of the ride.
*Timeskip brought to you by chibi Y/N using his tail like a pogo stick to jump around*
[3rd person POV]
When Y/N and team Natsu arrived at their location, they were met with a large pink palace with a heart-shaped window in the front. Upon opening the doors, the group was met with three males who quickly took Lucy to a couch and treated her as if she is royalty. However, when the three tried to do the same for Erza, they were met with unexpected consequences. Y/N pulled Erza away from them and held her in a protective position with his left arm and, at the same time, batted the three creeps away sending them into the wall. No one but Erza heard the low growl coming from Y/N as he glared at the three men in the wall. One by one, each of the men stood up while holding their heads in pain.
(A/N: I honestly can't remember much about these three's personality besides 95% fuckboy and 5% chill. So, my apologies if they seem a bit out of character.)
[Y/N's POV]
Who the hell are these bastards? We come to the meeting place and are met with three guys who can't control their hormones. The look on their faces the moment they saw Erza plucked a nerve of mine. I pulled Erza away from them and swung my right arm loosely to send them away. Unconsciously I started growling while holding Erza, which I didn't realize until I felt her hug me. I stopped growling before hugging back lightly while glaring daggers at the three. One by one the three of them stood up getting their bearings back.
???1: "Ow, who hit me?"
???2: "I don't know, but they have a mean strike."
???3: "Ugh, It's like someone hit me in the head with a rock."
Natsu: *lunging at the three men* "HEY, NEW GUYS!!! FIGHT ME!!!!*
Erza: *lets me go and slams Natsu to the ground* "Not now, Natsu! We're here on a mission."
???2: "Ah, you must be the members from fairy tail. I'm Ren Akatsuki."
???1: "I'm Hibiki Lates."
???3: "And I'm Eve Tearm."
Hibiki: "And together we make–"
Hibiki/Eve/Ren: *posing* "The Trimens!"
Y/N: 'I can't take them seriously anymore. They've lost my respect, and I just met them.'
Hibiki: "What are your names?"
Team Natsu just stands there quietly looking at me, waiting for me to introduce them. Seriously, out of all times for them to behave normally, they choose now to act like this. I sigh at their antics and introduce them while giving the three a cold look.
Y/N: "The pink-haired one is Natsu Dragneel. The blondie is Lucy Heartfilia. The black-haired one is Gray Fullbuster. The talking blueberry cat is Happy. And the armored scarlet-haired girl is Erza Scarlet."
Eve: *shaking under the stare* "He's scaring me."
Ren: "And who would you be?"
I just stare at them before turning around to stand by Erza again. I don't feel like giving out my name to them. Plus, this place makes me on edge. Something doesn't feel right here. As I get back to stand by Erza, she just looks at me with a 'really' look since I didn't introduce myself. I just shrugged and proceeded to stand by her again. Erza just sighed and decided to introduce me herself.
Erza: "My apologies for our leader, he's not too trusting of others. His name is Y/N Dragneel."
Hibiki: "Dragneel? Is he Natsu's brother?"
Erza: "Not that we know of. As far as we're concerned, they just so happen to have the same last name."
???: "Is that my honey I hear?"
I see Erza shudder in fear of the voice that just spoke. I heard her say something under her breath.
Erza: *quietly* "No. Not him."
I gain a confused look before I notice footsteps running down the steps. I look over to see another man flying towards Erza again.
???: *flying* "Honey!!!"
Naturally, I smack him into the Trimens.
???: "Meeeeeeeeeeeeeeeeen!!!!"
Trimens: "MAST— Oof!"
The Trimens quickly gather their bearings before checking on their 'master.'
Ren: "Master, are you okay?"
The thing stands up with a couple of bumps on his head and responds.
???: "I'm fine."
Y/N: 'Those bumps say otherwise....' *whispering to Erza* "What the hell is that thing?"
Erza: *whispering back* "That 'thing' is Ichiya Vandalay. The leader of the Trimens."
Y/N: *still whispering* "Wouldn't that make them the Quadmens, since there are four of them? Must not be very bright."
Erza: "No, he isn't. But for what he lacks in intelligence, he makes up for in his strength. Although he doesn't hold a candle compared to your abilities."
Eve apparently heard what she said and decided to speak up.
Eve: "Take that back! No one is stronger than master Ichiya!"
Hibiki: "Yeah! What's he got that our teacher doesn't have?" *pointing at me*
Gray: "A brain...."
Everyone: "..........."
Ichiya: *cries in a corner*
Y/N: 'Good riddance.' *fist bumps Gray*
While the Trimens tried to cheer up their fallen leader, the door opened to reveal some more people entering the building. I only vaguely knew one of them, since I've seen him before at the magic council. It was Jura Neekis, the 5th ranked wizard saint. Jura and I just nodded at each other respectively before he stopped some of his guildmate's antics. He then introduces the rest of their team: Lyon Vastia, one of Gray's comrades, and Sherry Blendy, someone I'm probably going to forget existed after this mission is over. They seemed to chat for a bit until Sherry decided to point out the obvious.
Sherry: "Hey, isn't there supposed to be four guilds here? Only three are here right now."
Jura: "Ah, yes. Cait Shelter. Supposedly they only sent one member of their guild to this mission."
Lucy: "One member? They must be very strong."
Almost as soon as she said that, I caught the scent of something interesting: another dragon. It wasn't the same as Natsu though, so it must be a different element. Not too long after, the door opened slowly to reveal a little girl with long blue hair. She didn't even appear to be a young teenager. She saw everyone gathered around looking at her, so she ran forward to greet us. That is until she tripped on the carpet and faceplanting the ground. She had an aura that radiated pure innocence. Seeing her kneeling on the ground holding her nose in pain, I figured I should help out. Walking towards her, she seemed to only notice my presence when I got close by. She seemed a bit intimidated, probably because of my cloak, so I kneeled on the ground in front of her as well. She looked at me with curiosity before I pointed at my nose and then her. She seemed to understand what I meant because she lowered her hands for me to see her nose. It was a bit purple towards the bridge, so it's possible she lightly chipped or broke the front of her nose from the fall. Using the small amount of healing magic I know from when I learned sky dragon slayer magic, I held my hand up before a green glow appeared and the bruise and swelling went down and her nose returned to normal. Her eyes widened when she realized what I did.
???: "Was that just sky dragon slayer magic?"
I was a bit surprised by the question. I didn't expect such a precise question right off the bat. I nodded to her before she started asking more questions.
???: "Where did you learn that?! Do you know what happened to Grandeeney?"
Before she could continue I noticed a white cat wearing clothes jumped towards me and tried to scratch me. Before the cat could do any damage, caught the cat and held it at a distance so it couldn't scratch me. Although, that didn't stop the cat from making any attempt to.
???2: *held in air while scratching at the air* "Get away from her!!!"
???: "Aahh!! Carla, it's fine, he was just healing me!"
Carla: *crosses arms (?)* "Hmpf. Very well, my apologies."
I set Carla down next to Wendy as I go to answer Wendy's questions.
Y/N: "I learned sky dragon slayer magic from my father. As for Grandeeney, I'm assuming this is the dragon that taught you, I do not know what happened to her. I'm sorry. May I know whose asking?"
Wendy: "My name's Wendy Marvell. As for Grandeeney, she's the sky dragon and mother. Who are you? And who was your father?"
Y/N: "My name's Y/N Dragneel. My father's Elementium, the elemental dragon king."
When she heard the name and title of my father, her eyes brightened up with excitement. I found it really adorable. She's such an innocent child.
Wendy: "Elemental dragon? Does that mean you're an elemental dragon slayer?"
Y/N: *smiles* "Yup!"
I don't know why, but she's bringing out the childish side of me. She jumped up in excitement before asking another question.
Wendy: "What elements can you use?"
Y/N: "I can use any naturally occurring elements, like fire, air, earth, lightning, water, etc.."
Wendy: "Wow! That's so cool! Wait, if you use sky dragon slayer magic, can you teach me how to use my magic for offensive purposes? I can only use support magic right now, so I'm not very useful when it comes to fighting opponents. I didn't get time to learn any of the offensive spells."
I just chuckled and patted her head before accepting to teach her.
Y/N: *smiling* "Sure, Wendy. I can teach you how to use offensive spells. But you have to teach me support magic as well. I'm not very good at it."
Wendy smiles at the acceptance to teach her, and she immediately hugs me. I wasn't expecting it, but I gave a small hug in return. I chuckle to myself internally. It's like having a little sister to take care of. Wendy lets go and goes to greet everyone else. I turn around to see Jura walking towards me with a small smile.
Jura: "So the man speaks. I thought you were mute every time we met."
I awkwardly laugh and reply to him.
Y/N: *awkward laugh* "I'm not the most socially adept person."
Jura just chuckles in response.
Jura: "So I could tell. Well, at least this will make communication easier for combat situations."
Y/N: "That it will."
We then just stand there in silence watching as everyone greets and gets to know each other. Wendy seems to have made a quick friendship with everyone, although Carla appears to not trust anyone. All in all, I think this mission should be a success. We have powerful wizards and double the number of wizards with us compared to the Oración Seis. All we need to do now is make sure we never underestimate our enemy and think strategically in combat.
To be continued~~~~~~~~~~~~>
A/N: Thank you so much for reading this chapter everyone! I'm hoping I get more time this semester to write, although with taking 13 credits worth of STEM courses and a 3 credit history class, I'll try to get as much done as I can. Also, I have a question that might come off as a bit odd. Should I write a math help book here on Wattpad? Like, answering people's questions and explaining topics people are struggling with in math. I always enjoyed helping others, and I also enjoyed sharing the beauty of math with others, so part of me wants to write something here, but I'm not sure how others would take it. Should I do it? It wouldn't take away from this story. It would more be like people request a topic they are struggling with for me to explain and I'll post a chapter explaining said topic to the best of my ability. Leave your opinions here if I should create it or not. In the meantime, stay safe and healthy everyone, and keep being awesome! I'll see y'all in the next chapter!
Citation
Gallian, J. A. (2010). Contemporary abstract algebra (8th ed.). Boston, MA: Brooks/Cole.
Also, if the use of the problem isn't okay with someone, just let me know and I'll get rid of that part completely. I'm just a guy who loves math and wishes to share the beauty of it with everyone.