#Z!NULL

[zenertia]

GIMME THAT HAND ZEN!NULL!!!

he shouldn't have said 'sinner'

[jbcchan]

772054660221747200?source

[lucksea]

this is making me realize i never even made lucky an actual consistent design. oops

[fagatakonin]

Nie wypisalam reszty pocztówek z wroclawia its over i teraz mam jakos 3 w szufladzie ale nie ma sensu po takim czasie ich adresowac. Nikogo nie obchodzi ze bylas we wroclawiu tępa gnidooooo

[arafilez]

ㅤㅤㅤㅤㅤㅤㅤㅤ▰ ▰ ✶ WØRLD EPISØDE FIN: WILL ⪨

ㅤㅤ➛ ㅤiii.ㅤ EMERGENCY 𒉽 jeong yunho❛ 𓇿

🥂̸̤ㅤㅤMDNI smut, fluff ㅤ ✸ㅤyou can hack into anything and everything! except maybe jeong yunho's heartㅤㅤ───ㅤㅤ w: kissing, flirting, praise kink, size kink, oral (f receiving) ㅤㅤ»ㅤㅤ wc: 3.2kㅤㅤ𠈔ㅤㅤ moodboard

ㅤ❛ you're the reason why i am dancing in the mirror ❜

You type away furiously in your laptop with the new code that Yeosang has sent to your base and continue changing bits of your programming code to try and infiltrate into the Z-dimension’s security system. It was hard and with the variety of codes in front of you the best thing you can do now is stay calm and concentrate. You still have time till tomorrow.

Wooyoung is almost done with the hologram of the ship, Yunho is fixing some of the hardware and you only need to crack this code. You rack your brain to find another loop you are missing, some kind of infinite series, or it might be a null loop that you have to add when you hear a loud crash. Jerking up your head from your laptop your first instinct is to run because there has been an attack.

Your second instinct is to stand in confusion as you hear Yunho scream, “What the fuck, man?” to your brother and him blabbering some excuses. Yunho shakes his head and goes back to work as you look at your brother who just winks at you mischievously. With disgust painting all your features, you set back to work ignoring Wooyoung’s whines about you being a ‘bad’ sister.

You type down the various codes again and try to work but nothing comes up as a frustrated groan leaves your lips. Should you try a completely different method or go back to the basics of a for-loop and add a simple elif loop. But wasn’t that too simple? You jerk up in surprise again as you feel a hand on your shoulder and turn around saying, “Wooyoung, I don’t have time for your shit.”

Your words dry at the back of your throat as you look at Yunho’s smiling face with the contrast of his veiny hand on your shoulder. Should a simple touch make you light-headed? No, it should not, absolutely not. “Hi Yun,” you murmur and your ears suddenly feel hot when you extend his grin looking at you.

Your insides feel like melting, but before you let your heart win, your mind interferes and you cough lightly. He also seems to get out of a trance as he says, “You can do this tomorrow, sleep for today, and you look like shit.”

“Such sweet words you say Yun!” you roll your eyes affectionately, and he chuckles. Leaning towards you he gently places a hand on your hips and whispers, “I can say more if you want me to.”

“Do I now?” you smirk lightly looking up at his tall figure as you think you see his eyes darken just a little, a smirk adorning his pretty face but almost instantly his hands leave your waist and he is gone. You exhale lightly shaking your head at your hallucinations and close your laptop.

Yunho is flirty. He will flirt with a stray cat if given a chance and you scold your heart lightly at it racing for him. Yunho didn’t mean it, he never meant it and it has always been that way. Him flirting, you flirting back and that was it.

���Gosh, stop with the heart eyes, it’s disgusting,” Wooyoung says making fake gagging sounds as you roll your eyes at your twin and get up. “So did you see that?” Wooyoung asks looking at you expectantly and you furrow your eyebrows.

“See what Wooyoung-ah?” you ask as you move around your desks turning off the projectors and look up to see his wiggling eyebrows. He smiles mischievously saying, “How he got angry when I threw that?”

“Yes, why did you even throw that thing so hard? I thought we were attacked, you piece of shit,” you scold him gritting your teeth as he makes a face at you which screams ‘I am so done with my dumb sister.’

“I did it for you, remember, how you said Yunho looks hot when angry?” Wooyoung grins and your fingers pause over the projector switch as you look up and scream, “What?”

“He. Looks. Hot. The point was made. So I did it for your eyes to be blessed,” he screams back and you walk over to him holding him by his collar. As you smack your brother's shoulder, your face is probably adorned with fifty shades of red and pink.

“Sh-shut up, and stop screaming,” you whisper-yell at him and another patch of hyena laugh comes from him as you slowly release his shirt.

“You are so gone for him, sis.”

“Am not.”

“Oh yeah?”

“Yes.”

“You said he looked hot yesterday when he had grease in his face while he was fixing the machine,” Wooyoung cocks his eyebrows as you look away. Well a small patch of oil and grease on his right cheek made him look sexy which was no lie but the mistake was telling your hyper brother about it.

“You like him so much, it is gross,” Wooyoung speaks a little too loudly as you try to shush him but he continues, “Oh we both know you have degrading kink too, even if you try to hide it.”

“Woyo shut the fuck up,” you scream jabbing him in the side to which he just giggles like the menace he was.

“Are you guys okay?” Yunho peeks from the door and you say ‘yes’ a little too quick for your liking. Wooyoung clicks his tongue in disapproval and whispers, “What did I teach you about playing hard to get?”

You don’t pay attention to him but instead look at Yunho, staring at him quite openly as you take in his messy silver hair sprawled over his forehead and being lightly tied back with a bandana.

“Take a picture, it will last longer,” Yunho chuckles leaning his tall body against the doorframe and you can hear Wooyoung snicker behind you as you look down scolding yourself for getting caught for your blatant stare.

Yunho walks in and keeping down the file he had gone to fetch walks towards your desk and you can hear Wooyoung mumble something along the lines of “Seonghwa hyung is calling me” before you can call out his bluff because Seonghwa hadn’t returned yet, he sprints off leaving you and Yunho alone in the room.

You click your tongue at your brother and his antics to “get you and Yunho laid”, his words, not yours, and know he did this on purpose. If you make a list right now it will be endless how many times your brother has actually done this.

He once locked you two in a laundry room which had another door, and once tried to lock you two in his room at a New Year’s party, instead, his overly drunk self, locked himself, successfully spinning the bottle for you two to kiss only for San to barf all over the floor, trying to send you two in a ‘seven minutes in heaven’ only for the lights to be cut off and hear Mingi scream his ears off. You appreciated his efforts but you knew this from the heart- the universe doesn’t want you and Yunho together. You knew you weren’t Yunho’s type but who was your brother to listen.

Yunho’s fingers softly caress yours as you are broken from your thoughts and he smiles softly saying, “I will help you tidy up.”

“Yun, you don’t have to,” you say softly but he hums and says, “No, I volunteer,” and places a hand on his chest as if he was taking a pledge making you giggle at him.

But in the back of your mind you know Wooyoung is right about you two being too oblivious and trying to hide your feelings by sticking to casual flirting. You push these thoughts to the back of your mind but they come back. How Yunho’s eyes had lingered on your lips and your eyes even after San barfed, how he casually slid over to your desk and hovered over your figure while his fingers rested on yours when you told him to check a code. There’s plenty of space beside you but he always does that. You know his lust-filled eyes and the tinge of jealousy in them when Yeosang practices his seducing skills on you. How his eyes lingered on your exposed neck in the last mission and then trail along your jaw to your lips making you fidget on your seat as Hongjoong was handing out your positions.

And you enjoy this too much. The little push and pull game you two keep playing, the way he gives you his attention and you bask in it. But lately it has been too much. Playful flirting has turned to intense staring, light jokes have turned into him and you being too close physically but never escalated. And your fool of a heart was falling for all these.

“What is on your mind? Me?” Yunho says coming right in front of you and you look up at his tall frame looking deep into your eyes. Earlier you would have flirted right back, but now they have started to make you lose your voice, weaken your knees, and your hands sweat. The effect it had on you now was insane. If you didn’t have any better judgement you would push him down right there on the table and take him. Or let him take you. Either way works.

You shake your head stuttering out a “no” but Yunho doesn’t ponder much leaving you to your desk as he puts his own documents down on his table. After you two were done, you left, Yunho following suit and then the door closed automatically as you two walked out. The walk is quiet, tension thick in the air when you decide to test a theory.

You are one of the best technicians here, the best hacker, so maybe you can hack yourself into Yunho’s heart too.

You trip lightly on air, very much on purpose, and wait like a damsel in distress to fall and for Yunho to catch you. His muscular arms easily slide around your back and you grin satisfactorily in your mind at your plan being successful. You open your eyes with your best-acting face on when you see the smug grin on his face.

“Did you do that on purpose?” he cocks his eyebrows at you and you get up scoffing lightly, “You wish.”

You feel dizzy seeing his face as he leans close to you and his lips hover just above yours as he says, “I wish for a lot of things, you know?” You draw in a sharp breath at the close proximity but Yunho swiftly moves away, opens his door and calls out, “Don’t trip anymore on your way, I am not there to catch you, you know?” followed by a cheeky grin.

You enter your room, your thoughts screaming only Yunho’s name and you keep thinking about him even when you make yourself comfortable under your covers. God he is making you suffer so much, it has been an hour since the incident but his thoughts are unbearable, if only you can hold him by his collar and push him against the wall and make out.

And your brain clicks.

This is it.

This is what you have been missing. A firewall. The code is for breaking the firewall to get to the main security system. You scramble up, throwing your sheets down and putting a jacket over your t-shirt and shorts you walk out with your ID. You open the door of the lab and run to your table taking out the papers sprawling them on the table and typing out the code in the computer.

And it worked.

You jump in joy lightly and send a text to Hongjoong about the success which you knew he would check in the morning. You stumble lightly, tipsy from your happiness and you bump into a muscular chest behind you.

Yunho.

Yunho?

Shouldn’t he be sleeping?

“Why are you up?” his deep voice rumbles making goosebumps dance against your skin and you can feel your insides turning mushy.

“Just had to finish this,” you reply, voice coming out much breathier than you intend it to be and you glance at him just to retract your eyes because of his own boring into yours.

“Hmm? What you got there?” he hums lowly, his tall frame leaning over your back as his hands swipe open the computer while the other goes around your waist and holds the desk. You become a bit light-headed as soon as his cologne hits your nose and you inhale it sighing carelessly.

His head is now almost on your shoulder while your body is stiff as you grip the desk more rigidly when you intake the view of his veiny hands around you and on the mouse casually swiping through the code you had cracked earlier. Your breath becomes unstable as you realise the proximity and you curse your mind for liking the warmth of Yunho’s body pressed against your back.

“Well, Hongjoong is going to be satisfied,” he breaths out and you can feel it tickle your senses as you hum and look at his face. He looks at you back and for a moment you feel everything stop. His eyes glaze into yours and you look back into his dark ones and wonder what bliss could possibly come.

Yunho is so close to kissing you. His eyes are fixated on your lips and his whisper sends a warm flush all over your body, “If we do this, there’s no going back.” You are in a haze and you whisper, “Yes,” and it barely makes it past your lips before Yunho kisses you.

And suddenly the air is knocked out of you. This was an emergency situation, an uproar went in your head.

Jeong Yunho is kissing you, his lips on yours and you push down all questions in the back of your mind and kiss him back. The kiss becomes impatient almost immediately as he grips your waist and holds your cheek with his other hand manoeuvring the kiss. You kiss him back feverishly, lips clashing harshly against each other and you tangle your hands in his hair tugging at them harshly.

He pulls away for a breath of air and you pant lightly as you look up to his lust-filled eyes and he hoarsely speaks up, “My room.” The walk through the corridor is a blur and you cling onto Yunho’s arms as he quickly opens the door and closes it after you two enter.

Pushing you against the door he kisses you again and swipes his tongue over your lips and you grant him access as a slow, elicit moan leaves your mouth. Fighting for dominance is not useful as Yunho taps your thighs twice and you comply with him jumping and locking your legs along his torso as he carries you to his bed.

Lying you down gently Yunho’s eyes run over your messy figure before he asks, “Are you sure?”

Your heart melts at the sincerity in his tone and you nod a “yes” quickly not wanting to waste any more time as Yunho dives in for your neck. He presses light open-mouth kisses along your jawline before moving his head and sucking harshly on your neck. You moan loudly as he continues nibbling delighted at your response and presses a light kiss adorning his work after.

You start to become impatient and almost rip open his shirt and he chuckles lowly saying, “Slow down, kitten.” You exhale lightly at the nickname and watch him pull your t-shirt over your head and throw it to the other side of the bed. You run your nails through his toned chest drooling over the perfect texture and he chuckles.

“Damn no bra, aren’t you naughty, kitten?” he slurs his words lightly and you throw your head back in pleasure as he takes one of your perked-up nipples and fiddles with it.

“I-I was just-" You try to finish your sentence and he hums bringing his voice lower by an octave and looks at you almost challenging you to finish the sentence. “I was just going to sleep so I had no bra o-oh my fuck Yunho,” you moan loudly as he dips down suddenly sucking your other nipple. You arch your back in pleasure and his hands slide down your waist playing with the hem of your shorts before yanking them off along with your panties.

The cold air hits your clit making you shiver from the sensation and he smirks looking at your state. Arousal drips from your vagina and he places a long finger collecting them and pushes his finger in you. You cry loud at the immense pleasure you feel and you see his pants straining as he moans too and says, “Fuck, you are beautiful.”

He scissors another finger inside you and then adds another and you moan his name loudly as he hits your g-spot frequently and picks up pace and you feel your stomach tightening. You are close, so close when he suddenly pulls out his fingers and pants and you open your eyes at him desperately.

“Need you,” he moans and quickly opens his pants and boxers and you almost gasp at the sight. You knew he was big, but this was a whole new level and you drool at it. Yunho would be proud but right now he was horny and needy and needed to be inside you badly.

He hovers over positioning himself and pushes inside you and you moan his name out loud as he stills himself. When you tap him to move he obeys and picks up his pace, his strong hands holding your hips down as he slams into you. “Fuck faster, Yun,” you scream and he coos at the nickname.

“Fuck baby aren’t you small and tight?” he moans explicitly when he feels the tip of his cock on your stomach, “All for me.” Your eyes roll back and you chant his name feeling your high build up fast at his pace.

His cock slams against your walls making you light-headed as you barely murmur an ‘I’m close’ and you can hear him grunt something along the lines of ‘Me too.’ With one last long-drawn moan you cum, your high getting released rapidly. He pulls himself out before coming all over your stomach.

You pant lightly, slowly returning to reality as Yunho gets up to get some wet tissues from the bedside table. You watch him silently as he cleans you and himself up while you lie and adore his face that was sculpted by the gods. His awkward clearing of throat brings you back from your trance and you look at the shy smile that makes its way into his face.

“Listen urm, I like you, y/n,” he speaks shyly gazing at your fingers which were now intertwined with his and you smile back saying, “I like you too, Yun.”

“Oh good,” he exhales and you laugh at his puppy-like demeanour and run your fingers through his grey hair as he leans into your touch. He brings his lips down to kiss you and you can feel his smile as you kiss him back softly as he holds your hands in his. Pulling back he puts another peck on your lips as you two become a giggling mess under the warm covers.

✸ㅤ ara's notesㅤㅤ───ㅤㅤ i am happy for this one yayay lmao i mean a bit self indulgent but okay ig ㅤㅤ»ㅤ series mlistㅤ ateez mlist ㅤ main mlist ㅤ naviㅤㅤ𠈔

✸ㅤ taglistㅤㅤ───ㅤㅤ @haneagerr @tunaasan @evidive @huachengsbestie01 @philijack @atiny-lizbeth @chxnnii @nakiiko @therealcuppicake ㅤㅤ»ㅤㅤ comment here or in series mlist to be added or removedㅤㅤ𠈔

© arafilez on tumblr. please don't copy and repost my work as your own ▰▰ ✶

[minicountessisme]

So the other day @knightlynight and I were talking and the subject of Pokemon came up. Specifically, we were talking about how the current stories Pokemon games try to tell don't work with a silent protagonist and we brought up Sun and Moon as an example and how much better the games would have been, if we got to play them AS Lillie.

At some point @knightlynight mentioned how we can even keep the player choice between a boy and a girl, by giving them the option to simply switch to play as Gladion. Then that got me thinking that that would mean the Lillie would automatically get Gladion’s role in the game… And I just couldn’t help myself, so here is Edgy Lillie for everyone!

I didn't want her to just straight up be a female Gladion, so I gave her her own aesthetic and her own team.

Gladion's outfit reminds me a lot of Zoroark, one of his signature pokemon (I don't know if that was the intention), so since Lillie is heavily associated with Alolan Vulpix, I decided to change up the colors and shapes and make hers reminiscent of snow storm clouds.

Because of the anime, I was under the impression that Gladion is a Dark Type specialist and I was prepared to make Lillie an Ice Type specialist. So I was very surprised when I realized I was wrong, while making her team, and it threw a wrench at my plans.

So, as stated previously, Lillie is associated with Alolan Vulpix, so she gets to keep it. I also gave her the Zubat line, because it felt fitting with her "new" role in the story. I also gave her the Pancham line, for some reason, with Team Skull and everything, I thought it was fitting. The story requires her to have Type: Null, so she gets that also. I was caught very off guard when I saw Gladion uses a Porygon-Z. I thought it was so out of left field, and, in my attempt to also find something out of left field, I gave her a Kangaskhan. Looking back that one is not THAT out of left field, considering what happens in the story. And of course she also gets the rotating Kanto starter.

[lilith-hazel-mathematics]

Self-referencing functions

Hey mathblr, let me tell you about one of our favorite foundational systems for mathematics! It's designed to allow for unlimited self-reference, which is neat since self-reference is usually thought of as a big no-no in foundational systems. It turns out that it actually doesn't matter at all, because the power of self-reference is completely exhausted by the partial computable functions. The theory ends up being equivalent to Peano Arithmetic.

What are the axioms?

The theory is two-typed: the first type is for the natural numbers, and the second type is for functions between numbers. For convenience, numbers will be represented by lowercase variables, and uppercase variables represent functions. To prevent logical contradictions, we permit that some functions will fail to evaluate, so we include a non-number object ☒ called "null" for such cases. The axioms about numbers are basically what you'd expect, and we only need one axiom about functions.

The < relation is a strict total order between numbers.

Each nonempty class has a minimum: axiomatize the "min" operator with φ(n) ⇒ ∃m,(φ(m) ∧ min{k:φ(k)}=m≤n) for each predicate φ, and relatedly min{k:φ(k)}=☒ ⇔ ∀n, ¬φ(n).

Numbers exist: ∃n,n=n

There's no largest number: ∀n,∃k,n

There's no infinite number: ∀n,n=0 ∨ ∃k,n=S(k)

Every functional expression represents a function object that exists: ∃F, ∀(a,b,c), F(a,b,c)=Ψ for any function term Ψ. The term Ψ may mention F.

To clarify the fifth axiom, we define 0:=min{n : n=n}, and relatedly S(k):=min{n : k<n} is the successor function. The sixth axiom allows us to construct self-referencing functions using any "function term". Basically, a term is any expression which evaluates numerically. Formally, a "function term" is any well-formed formula generated from the following formation rules.

"n" is a term; any number variable.

"F(Θ,Φ,Ψ)" is a term, whenever Θ,Φ,Ψ are terms.

"Φ<Ψ" is a term, whenever Φ,Ψ are terms.

"min{n : Ψ}" is a term, whenever Ψ is a term.

In the third rule, we seem to be using the boolean relation < as if it were a numerical operator. To clarify this, we use the programmer convention that true=1 and false=0, hence (n<k)=1 whenever n<k is true, and otherwise it's zero. Similarly in the fourth rule, when we use the numerical function term Ψ as the argument to the "min" operator, we interpret Ψ as being false whenever it's 0, and true whenever it's positive. Formally, we can use the following definitions.

(n<k) = min{b : k=0 ∨ ((n<k ⇔ b=1) ∧ n≠☒≠k)} min{n : Ψ(n)} = min{n : 0<Ψ(n) ∧ ∀(k<n),Ψ(k)=0}

Okay, what can it do?

The formation rules on functions actually gives us a TON of versatility. For example, the "<" relation can be used to encode literally all boolean logic. Here's how you might do that.

¬x = (x<1) (x≤y) = ¬(y<x) x⇒y = (¬¬x ≤ ¬¬y) x∨y = (¬x ⇒ y) x∧y = ¬(¬x ∨ ¬y) (x=y) = ((x≤y)∧(y≤x)) [p?x:y] = min{z : (p∧(z=x))∨(¬p∧(z=y))}

That last one is the ternary conditional operator, which can be used to implement casewise definitions. If you wanna get really creative, you can implement bounded quantification as an operator, which can then be used to define the supremum/maximum operator!

∃[t<x, F(t)] = (min{t : t=x ∨ ¬F(t)}<x) ∀[t<x, F(t)] = ¬∃[t<x, ¬F(t)] sup{F(t) : t<x} = min{y : ∀[t<x, F(t)≤y]}

Of course, none of this is even taking advantage of the self-reference that our rules permit. For example, we could implement addition and multiplication using their recursive definitions, provided we define the predecessor operation first. Alternatively, we can use the supremum operator as a little shortcut.

x+y = [y ? sup{succ(x+t) : t<y} : x] x*y = sup{(x*t)+x : t<x} x^y = [y ? sup{(x^t)*x : t<y} : 1]

Using the axioms we established, basically as a simple induction, it can be proved that these operations are total and obey their ordinary recursive definitions. So, our theory is at least as strong as Peano Arithmetic. It's not hard to believe that our functions can represent any partial computable function, and it's only a little harder to prove it formally. Conversely, all our axioms are true when restricted to the domain of partial computable functions, so it's consistent that all our functions are computable. In particular, there's a straightforward way to interpret each function term as a computer program. Since PA can quantify over computable functions, our theory is exactly as strong as PA. In fact, it's basically just a definitorial extension of PA. Pretty neat, right?

Set theory jumpscare

Hey didn't you think it was weird how we never asserted the axiom of induction? We asserted wellfoundedness with the minimization operator, which is basically equivalent, but we also had to deny infinite numbers for induction to work. What if we didn't do that? What if we did the opposite? Axiom of finity unfriended, our domain of discourse is now the ordinal numbers. New axioms just dropped.

There's an infinite number: ∃w, 0≠w ∧ ∀k, S(k)≠w

Supremums: (∀(x≤a),∃y,φ(x,y)) ⇒ ∃b,∀(x≤a),∃(y≤b),φ(x,y)

Unlimited Cardinals: ∀a, ∃b, #(a)<#(b), where #(n) denotes the cardinality operation.

Each of the above axioms basically just assert the existence of larger and larger ordinal numbers, continuing the pattern set out by the third and fourth axioms from before. Similar to how the previous theory could represent all computable functions, this theory can represent all the ordinal recursive functions. These are the functions which are representable using an Ordinal Turing Machine (OTM). Conversely, it's consistent that all functions are ordinal recursive, since each function term can be interpreted as a program that's executable by an OTM. Moreover, just like how the previous theory was exactly as strong as PA, this theory is exactly as strong as ZFC.

It takes a lot of work to interpret ZFC, but basically, a set can be represented by its wellfounded and extensional membership graph. The membership graphs can, in turn, be encoded by our ordinal recursive functions. Using the Supremums axiom, it can be shown that the resulting universe of sets obeys a version of the Axiom of Replacement, which can be used to prove the Reflection Theorems, ultimately leading to the Specification Axiom. By adapting similar techniques relative to some regular cardinal, it can then be shown that every set admits a powerset. Lastly, since our functions are basically generated from infinitary computer code, they can be encoded by finite strings having ordinal numbers as symbols. Those finite strings are wellorderable, which induces a global choice function, proving the Axiom of Choice. Excluding a few loose ends, this covers all the ZFC axioms, giving the desired interpretation.

In the finitistic version of this theory, we made the observation that the theory was basically just a definitorial expansion of PA. In the infinitary case however, we unfortunately cannot say the same about ZFC. This ultimately comes down to the fact that our theory provides explicit and definable choice functions, meanwhile ZFC cannot. Although ZFC guarantees that choice functions exist, it cannot prove the existence of a definable choice function. This is because ZFC is an inferior theory has no clue where its sets come from, or what they really look like. Our theory, built from unlimited self-reference, and interpreted under the banner of ordinal recursive functions, is instead equivalent to the theory ZFC+"V=L".

[positively-knotted]

Category theory has made us so accustomed to morphisms that it always feels wrong when a natural map isn't a morphism, at least not in the obvious category.

Like, take a manifold closed surface Σ. Write UTΣ for the "unit tangent bundle" of Σ, ie the space of unit vectors tangent to Σ. A loop γ in Σ gives a canonical loop (γ,γ') in UTΣ. Let's call that the lift of γ. So far so good.

It's natural to ask if this descends to homology. Let's take Z/2-homology to be simple. It actually doesn't, since any null-homotopic loop γ has γ' "do a full loop", so the homology class of the lift of a collection of null-homotopic loops depends on the parity of the number of loops.

But that's fixable. Let ζ be the homology class corresponding to a lift of a single null-homotopic loop. Then we do have a well-defined map φ: H_1(Σ) -> H_1(UTΣ) given by sending [γ] -> [(γ,γ')] - ζ. You can check that this is independent of representatives - you just play around with diagrams. The idea is that you're just measuring the "extra" spinning in γ', and ignoring the full turn that's necessary by yknow, being a circle.

This looks good! It's pretty natural, it sends 0 to 0, it feels very homomorphism like. But it's not! It satisfies φ(a+b) = φ(a) + φ(b) + (a•b)z, where • is the intersection form. This is like, close enough to a homomorphism that you can work with it, but still! It goes against modern mathematical sentiments.

[zenertia]

HOLY CRAP IT'S DR. REFLEX

[yesornopolls]

“Didn't they try to do that a few months back when Houdini got released?” you didn’t get the reference 😭😭😭

https://youtube.com/shorts/W5kuNaM7Qe8?si=8WFEX3ziEhVFV_21

“Listen lil kiddies lemme make this quite clear

This man was around even before you were here

So what you’re all mad cuz that man was a lyricist

While your rappers are all mumbling gibberish

No, go ahead and shut your mouth

Better yet go and sit ur ass in time out

Boy was running laps even fore you could walk

Hell boy was spitting bars even for you could talk

So no, im afraid you’re null and void dear

Im afraid your opinion dont matter here

Cuz one day you’ll grow up and see

How everyone went and forgot about z”

Sorry. My feed shows me FAFO, Kendrick Lamar and crazy as fuck fights that happen at McDonald's.

[lillies-and-honey]

As a Gen Z, here is my take on why so many young people became conservatives or voted red this election.

Warning long. TLDR at the bottom

Conservatives have sold a picture perfect image for a long time. And as kids we grew up seeing our parents struggle like crazy. We watched things get worse while slowly the country got more progressive in values. We went through a pandemic and many of us felt hopeless.

Conservative beliefs claim to offer women

- unconditional love

- freedom of time to have fun hobbies

- not having horrible hours of work

- being cared for

- safety (this is a big selling point for many with the SA statistics and abuse statistics)

What they didn’t say in there speeches was that the love was conditioned on popping out babies for your husband. That your free time actually wasn’t yours. It was to spend with the children, or to please your husband, or MAYBE do a “feminine” hobby if you have already taken care of everything in the house plus more. That not working means not chance to leave if you dislike something. That the care you receive is often the care someone has for a possession, not a living breathing person. And that your safety from the outside world, meant any protection from the inside was null and void.

To men they sold

- a loving wife

- a promise of wealth and no worries

- a family

- job security

- friends

- power

What they didn’t tell the men was that the wife would resent him for her lack of choice in marrige, no matter the circumstances. That the wealth was something they would never see, that very few of them actually made the money to live in the houses put in the newspapers and online. That even if they were wealthy they now had other worries, like if there daughter was safe, or if there gay son was literally going to be hung, and his case buried because no one cares for the hate crimes. That the family he got, would never see him because he would always be working, praying for a promotion only for the promotion to go to the bosses nefew because the corporate ladder is a myth to keep workers complacent. That he would see his friends hitting their wives, and would not be able to say anything because it was their right to domestically disapline a hysterical woman. And that any “power” they gained would not be theirs. It would the person above them. That they would be a puppet because they would never get to the top, despite always feeling so close.

The lists look great. All of those have something for everyone. Sometimes multiple things. And in a time of despair it is easy to fall for propaganda and ideals. To think about all the pros and worry about cons later. But we need to worry about the cons BEFORE we lose the ability to.

TDLR: young people vote red because blue works in realism, and red offers ideals they won’t uphold but look nice from the outside. And Gen Z is desperate for a relief and hope.

[teshadraws]

Nia references Trubbish and Garboder in one of the earlier chapters when counterin Tobias' argument about the oddities of the human world…

How could such a species even exist if humans never naturally came to be in this Pokemon world of Seekers?

One of Trubbish' Pokedex entries says, "... was created when garbage and industrial waste mixed, causing a reaction that generated Trubbish."

Unless you may have an entirely different origin in mind for them, lmao.

Same goes for both forms of Muk and Grimer.

… Do Kantonian Voltorb and Electrode exist in Seekers? I can't remember if either have ever appeared...

And I guess the regional forms directly affected by humankind's actions (i.e. Alolan Ratata and Raticate, Alolan Meowth and Persian, Galarian Weezing, Galarian Meowth and Perrserker, Hisuian Zorua and Zoroark) could technically have unique ways of comin to existence due to certain historical or cultural events in the past.

Apparently the Vanillish and Klink lines came first and are what inspired the creation of ice cream and gears…

What about Golett and Golurk and Baltoy and Claydoll? Both lines were created by ancient civilizations… Same POSSIBLY goes for Bronzong and Bronzor.

And I can see Rotom existin... they jus can't inhabit appliances because those jus don't exist in Seekers' pokeworld.

And what of the Magnemite line? Castform? Castform was shockinly actually artificially created in Hoenn to help predict weather! I could see them existin somehow through natural means (clouds that became sentient through mystical means).

What about Deoxys? Deoxys simply came from space when its virus inside a meteorite mutates in the planet's atmosphere… Not from any manmade means.

Does Spiritomb exist and would it be comprised of 108 Pokemon spirits?

The ones I can def rule out from previous asks and convos are Mewtwo, Porygon line, Genesect, Megearna, Type: Null/Silvally, the Galarian fossilmon, Future Paradox Pokemon… And that would also go for Past Parodox Pokemon as well.

I'm also guessin that rules out Meltan and Melmetal as well (can't remember if you mentioned that).

And ya said Ultrabeasts don't exist purely because of no Ultra Wormholes, so no Lunala, Necrozma, Solgaleo, Cosmog, nor Cosmeon. (Though someone made a point in the server about that tombstone possibly havin a depiction of Lunala on it…) I do like the idea that Lunala and Solgaleo have existed once in this world, but someday jus... vanished.

Eternatus is said to be from another world as well… I'm guessin it doesn't exist, or maybe it does to some compacity? Do Zacian and Zamazenta exist in some shape or form?

And since gimmicks like Z-Moves, Dynamax, Gigantamax, and Mega Evolution also don't exist, it'd only make sense the Terrastalization phenomenon also doesn't exist, so no Teragapos either… (Maybe they did at one time but have all vanished or gone extinct).

Could the Treasures of Ruin (Chien-Pao, Wo-Chien, Chi-Yu, and Ting-Lu) also exist in some capacity? It could've been some long forgotten or scarcely known Legendary crafted the items they possess and planted them as precious artifacts across rhe world that intrepid explorers or passersby found and the resultin avarice of whomever owned the treasures caused their curses to bring them to life and take on their corporeal forms as a form of punishment or some sick pleasure from that Legendary? I dunno, I jus really love this quartet! They're so fascinatin and I myself have actually found a way to incorporate them into my PMD EOS AU lore!!

I know this is an enormously long ask, but thanks tons if ya take the time to comb through this and offer some answers! I know a lot of this is reachin and not really pertinant to Seekers' main plot, but it'd be really cool supplementary material! Sorta like what ya guessed for Zekrom and Reshiram.

Oh dang, this is a beefy ask, haha! Here we go.

The Pokemon in Seekers still create waste, even if most of it isn't nearly as manufactured and toxic as the human world's! Plus, the runoff from natural poison types like the gulpin and clodsire lines contributes to the natural poison waste in the environment. I will say that poison types like trubbish and grimer are much less common in Seekers than in the mainline Pokemon worlds, though!

Kantonian voltorb and electrode exist as a natural steel-type offshoot of the Hisuian variant! They just happen to look a lot like the pokeballs of other Pokemon worlds. :]

Hm...I'm going to say the golett/baltoy/bronzor lines just came from ancient Pokemon civilizations' artifacts, rather than human ones!

Magnemite aren't artificially created, so they're present in the Seekers world! I agree that castform could exist through different means, but it's likely a rare occurrence since they would have to come together through a sort of "freak accident" of weather phenomena.

Deoxys isn't currently present in Seekers, but they would have the potential to show up at some point if the space virus made its way to the planet!

Spiritomb does exist, but it's Pokemon spirits instead of human ones as is usually implied in Pokemon's canon.

The meltan/melmetal line exists, though they're rare! They're not manmade and are born from natural steel components.

Whoops. Forgot that I mentioned Lunala on the crobat's tombstone, haha!!! 😅 Let's say that Lunala and Solgaleo are largely considered legends, then, even more so than other Legendary Pokemon. They were thought to exist once, but have long since returned to their own dimensions and are no longer present in the Seekers canon.

Similar to Deoxys, Eternatus isn't currently present in the Seekers world, but could potentially show up if the meteorite it was born from in canon showed up in the world!

Zacian and Zamazenta exist, just without the same lore from Sword and Shield (so no Darkest Day). Instead, they simply guard their territory from threats. I don't think they'll be considered Legendary in Seekers, though. They feel more like regular (albeit powerful) Pokemon to me. I don't have an area in mind for where they dwell, though! 

Terapagos probably exists, but its ambient power isn't enough to cause terrastalization in other Pokemon. No game gimmicks here.

The Treasures of Ruin might exist, but that's another quartet that I wouldn't really consider "Legendaries" in Seekers canon! I'd say they're lying dormant in their shrines throughout the Seekers world, but I don't have any lore currently on who sealed them away. They were sealed away due to being dangerous, though, since they were created from negative emotions! Not that that nixes the possibility for redemption down the line. 👀

Hope that satisfies some of your curiosity!

[holydramon]

Thought these looked fun so decided to do one myself!

Used the favorite pokemon picker to narrow down favorites and this Pokemon home team builder to get the pictures :3

[thegoldfisharmy]

Pokemon Teams for Invader Zim characters pt 2. Dib

Absol: It's pokedex entries describe how it runs from it's mountain homes to warn human settlements of incoming disaster (which is actually really similar to the mythology surrounding mothman in our real world) Also: Scythe.

Blipbug: It's a little scientist bug that evolves into a UFO ladybug. And come on, just look at it. They've got matching glasses.

Iron Moth: Absol wasn't enough, I had to get Agent Mothman here an actual moth pokemon. There are a surprising amount of moth pokemon. Ended up going with this one because it's "wings" are like a satellite dish and it's pokedex entries draw some connections to UFOs.

Yamask: Representing the more mystic side of Dib's obsession with the paranormal. It's a little ghost with a runestone, which I think encapsulates ghosts and magic fairly well.

Type: Null: A failed science experiment that just needs a little friendship to reach it's full potential. In short, a disappointment. Dib probably got it from his dad.

Porygon2: Look, by this point, I'd already decided to give Porygon to Gaz and Porygon-Z to Zim so why not give the remaining "human" character the last stage in the evolution line. Porygon2 is specifically designed for surfing the internet, so maybe it has some connection with the Swollen Eyeball network? idk, it's definitely the weakest one.

[zenertia]

Twitter's Fun

You guys should check it out sometime, there's lots of cool people over there that have way too much patience for my bullshit

[Maetan's Original Twitter Post, 7:32 AM · Oct 7, 2024, My Original Twitter Post, 10:45 PM · Oct 8, 2024]