serious-discussion

[timid bronze]

yup

[deep mango]

sometimes that communication is a little manipulative because sometimes it hurts peoples feelings / isnt productive to be fully direct and honest

and the better path is "i need to learn, so i will learn for them, but for now they dont need to know im learning"

[timid bronze]

Sure but when you said manipulation i took it seriously and got worried since i wasnt sure if you were joking

bc altho u can communicate, manipulation is no joke

it's a terrible trait to have

but now that i understand your undertone i get where you were going

[deep mango]

i dont really think so

a lot of manipulation is about showing compassion and understanding

[timid bronze]

what is your definiton of manipulation

im referring to guilt tripping, playing the victim, gaslighting, twisting words, etc

[deep mango]

being deceptive / dishonest to get someone to think or do what you want

like if someone gets a new haircut and you think its ugly as hell but you want to be a good friend, its manipulative to tell them you love it because youre lying to preserve your friendship

it affects their thoughts and actions in a way that does something you want instead of representing the truth

[timid bronze]

i dont agree that kind of lie is manipulation in the same way harmful deception is

you are not actively trying to control or exploit the person in question

what youre saying is more of a white lie in my eyes

you are simply being polite

[deep mango]

i think you are

politeness is manipulative especially when you want something out of it and arent just doing it cuz its normal

lots of people will tell you they never lie but they lie all the time

[timid bronze]

by definition, it for sure can be manipulative, but im drawing the line at intention here

[deep mango]

and good and bad lies arent a strict dichotomy. every lie has positive and negative effects and spiraling consequences

[timid bronze]

i'm calling manipulation with the intention to control or exploit terrible

[deep mango]

i think politeness is manipulation with the intention to control or exploit

also, i think its worse when you make someone feel bad just for the hell of it instead of having an intention of control

[timid bronze]

i was next going to say i think that's an interesting take

i don't agree with it though

[deep mango]

so i dont really get that either

[velvet dagger]

I feel like "control' is a word that has a tricky connotation here

[timid bronze]

most people arent trying to control or exploit just by being nice

theyre trying to be considerate or avoid hurting feelings

sure politeness can be manipulative at times but that shouldn't be the default

i would think that masks it as a weapon and i would not like to refer to it as one

[velvet dagger]

Like, officially "Wanting you to feel better" can be referred to as a form of control, but colloquially this is not the same type of thing as when people refer to controlling someone in the sense of, trying to extract concessions

[timid bronze]

Exactly

[velvet dagger]

Like are you changing the circumstances from "This would be an unpleasant interaction" to "This would be a pleasant interaction", or are you trying to go from "This is the type of thing that the person would not be willing to do" to "This type of person will be doing what you want"

If you're being nice to someone and they're nice back, you're not somehow taking someone who would not otherwise consent to being a nice person and manipulating them into being a nice person

[timid bronze]

well said

[latent edge]

人(￣ω￣;)

[deep mango]

i guess i agree with that

[cyan goblet]

how was the flight

[deep mango]

i will tear your head off

[cyan goblet]

cheers

[deep mango]

im ABOUT TO GO ON IT

[cyan goblet]

oh

[deep mango]

We got deplaned due to an issue

[cyan goblet]

ah

[deep mango]

then bounced around from gate to gate to gate

[cyan goblet]

which airline

[deep mango]

and now are about to fly

american

[cyan goblet]

american sucks

[deep mango]

every airline sucks

[cyan goblet]

delta is nice

[timid bronze]

i love qatar airways

[cyan goblet]

but pricy

[deep mango]

delta is fine

[timid bronze]

delta is also good

[deep mango]

delta has issues

[cyan goblet]

yeah

[timid bronze]

Delta has always communicated with my family and i

ab anything

what issues does it have..

[timid bronze]

Ong

same with southwest

[cyan goblet]

southwest used to be good

but now they're shit because of all the changes

[deep mango]

idk all the airlines seem the same to me, have the same cancelations and changes as with any airline

southwest was useful for 2 free checked bags

[cyan goblet]

yeah

[deep mango]

now it is useless

[cyan goblet]

and seats were just first come first serve

now they're assigned

[deep mango]

i transported all my shit to and from college by southwest

[deep mango]

idk why they are advertising this as a plus

like

literally made ads about it

!?!?!?

[timid bronze]

As long as i. get the window seat im happy 😌

[deep mango]

i have an aisle seat tonight

[cyan goblet]

yeah idrk

[deep mango]

next to 2 people i thought were twjns

[timid bronze]

ryc would u get my luggage for me if i asked u for help

[deep mango]

bht then they started kissing

[timid bronze]

.

LMFAO

[deep mango]

nothings grosser than that

[cyan goblet]

they could still be twins

[deep mango]

idk why youd ever date someone who looks exactly like you

[timid bronze]

Please dont imply..

[deep mango]

at least theyre boy and girl

[timid bronze]

I would

What's wrong with that

As long as they arent actually my sibling

[deep mango]

it drives me crazy seeing gay couples that look exactly the same

[cyan goblet]

true thank god they're not gay or anything like that

[deep mango]

idk it would just FEEL weird to me

like do it if you want

but for me i need the person to be sufficiently different

[timid bronze]

Fair but idc as long as theyre attractive XD

[deep mango]

physically

[cyan goblet]

i mean i blush every time i look in the mirror

[deep mango]

okay well unfortunately im super hot so i need to date down

[timid bronze]

Shut tf up

U and ur ego

[deep mango]

no i dont date down

i date up

but like

different ppl

idk

no math nerds

[cyan goblet]

i wouldnt be able to date someone who does math

[deep mango]

i dated one math nerd

[cyan goblet]

because i want my future spouse to make money

[deep mango]

d4

it was not ideal

[cyan goblet]

because lord knows if i become a mathematician i wont

[timid bronze]

crazy

[cyan goblet]

okay i didnt mean it like gold digger

[deep mango]

anamono has house husband energy

[cyan goblet]

i'd love to be one

if my wife made enough to sustain both of us

[velvet dagger]

"Future spouse" do I need to call Cheryl?

[timid bronze]

ryc would u be a stay at home husband

and dami would u be too

[cyan goblet]

i'd greet her every day in a damn apron and the house clean and clothes washed and errands ran and food ready

[deep mango]

just scratched my shoulder that shit is def a little sunburned

fuck

[errant zenith]

Hi

[cyan goblet]

i'm talking in the past tense yk

[deep mango]

i mean yeah but i would still want to do SOMETHING

[timid bronze]

Ngl id love for someone to cook for me

Idm cleaning

But omg yes cook for me.

[deep mango]

ill run my etsy shop and call myself a small business owner

[cyan goblet]

ahhh yes etsy

[timid bronze]

hi

[deep mango]

i love cooking

ill cook for my husband

[timid bronze]

Work remote

[cyan goblet]

buy something off of shitty chinese amazon and resell for $10

[deep mango]

i want to be a personal chef

[cyan goblet]

and call it "handmade"

[velvet dagger]

Wouldn't be too inclined? I feel like I've def centered a lot of my identity on the idea of a career

[deep mango]

i like touching grass

ill work at a garden store part time

[cyan goblet]

yep

that's the dream life

ryc gets it

[deep mango]

or ill live on the shore and repair peoples boats

[cyan goblet]

it's a shame garden centers dont hire for the summer because i wanted to work at one as a summer job

[errant zenith]

Hi

[deep mango]

or take tourists on boat tours

im a great tour guide

someone smells like weed

[errant zenith]

Why

[cyan goblet]

classic chicago

[deep mango]

oh maybe thats me

oops

[cyan goblet]

the train i was on smelled like piss all the way from oak park to ohare

did you smoke a blunt before dropping the butt in the cannabis amnesty box

[deep mango]

no

i did smoke twice while here

with others

[cyan goblet]

fun

[deep mango]

the first blunt was extremely high quality

that was great

the second one was just fine

the first was followed by an incredible meal and then cuddles

[cyan goblet]

i haven't had weed since like last december

[timid bronze]

ryc when he sees a single guy https://youtube.com/shorts/46zekydKbb4?si=ICV3PZcpGMd5ibpK

[cyan goblet]

idrk if i miss it or not

[deep mango]

the second was followed by cuddles and then falling asleep together

both very nice

[cyan goblet]

holy shit

idgaf about the cuddles part

incredible meal would be awesome

[deep mango]

yeah the meal was crazy

[cyan goblet]

my roommates last year were major stoners

so i would smoke like almost every other day with them

last year as in 23-24 school year

[deep mango]

that guy was so cool

omg

[cyan goblet]

and my "meals" were just like a tub of ice cream

i'd sit down on the floor with a spoon and my half gallon of ice cream and just dig in

[deep mango]

his snake tattoo 💞

[cyan goblet]

christ

today for dinner i had leftover chipotle

[deep mango]

tbat meal was 200$ for 2

lol

[cyan goblet]

i can't fathom that

oh

[deep mango]

oh well

[cyan goblet]

yeah one time i took a girl out on a date to some fancy place

[deep mango]

tbe cocktails were like 18 bucks each

thats why

[cyan goblet]

it was like $350 or so for the two of us

oh

[deep mango]

we got 2 drinks each

[cyan goblet]

$18 for a cocktail is crazy

but i guess it's chicago

[deep mango]

other ridonkadonk chicago meals

[deep mango]

similar in nyc these days at a nice place

sad

[cyan goblet]

yeah

holy hell that food looks good

[timid bronze]

that looks too expensive

that probs cost more than my medical bills

[cyan goblet]

did your per diem cover it all

[timid bronze]

those tacos tho holy shit

i want them

[deep mango]

idk

we'll see

cest la vie

the burger was the best thing there

that shit was mind blowing

[cyan goblet]

were you inspired by my burger story

[deep mango]

middle tacos were also amazing

[deep mango]

no.

[cyan goblet]

yeah you were inspired

as i am inspired by your photos

see i wasn't really hungry but now i really want a burger

[deep mango]

okay, i am about to take odd

off

[cyan goblet]

have a safe flight

[deep mango]

#nyc

the guy next to me needs a lobotomy

bye

[cyan goblet]

you sure that's not just a mirror?

cya

[serene vault]

safe travels!

[errant zenith]

Safe travels

[timid bronze]

fly safe dont fart on the plane

[deep mango]

phbbbbt

[cyan goblet]

turn your phone on damn airplane mode

the plane is gonna blow up if you dont

[errant zenith]

Yh follow the safety rules

[fresh comet]

travel safely!

and enjoy the flight!

[deep mango]

i landed

[cyan goblet]

How was it

I’m in drive thru for burgwr

Got inspired

By you

[deep mango]

it was fine

i watched some futurama

and then an episode of Monk

Monk isnt as good as i remember

[cyan goblet]

Who’s ur fav character in futurama

[deep mango]

i havent seen that much of it. so hard to say. but probably normie take and say bender

[cyan goblet]

Yeah he’s my fav

I binged it for a while but idk it got stale

[tender heron]

[timid bronze]

@velvet dagger @errant zenith @fresh comet astro already knows but i relocated villages and mightve abandoned yall sorry i forgot to bring u with me now idk where u all r and ill have to find u someday..

Got a new cat to keep me company in the mean time

I need a name for it

ill name it suremark

[errant zenith]

Wow

[velvet dagger]

[errant zenith]

We’ve been replaced

XD

[timid bronze]

Bro im sorry

[errant zenith]

Not even 24 hours

XD it’s okay

[timid bronze]

Maybe yall shouldve gotten ur asses up Smh

instead of sitting all day

[errant zenith]

You the one who controls us

[timid bronze]

No

[errant zenith]

We followed ur instructions

[timid bronze]

Well skill issue

Yall r math and physics majors

Use ur brains when im ab to leave the area

xD

[deep mango]

🤣

[timid bronze]

Ugh why r u here now

have u showered yet

u prob smells like a cockroaches ass

[deep mango]

i showered right before the flight

im going to sleep

[timid bronze]

wait where r u rn

[deep mango]

jellycat is owning some noob in discussion

[deep mango]

at my parents house i got home from my flight

[timid bronze]

u shoulda seen what jellycat said to dami earlier

[deep mango]

theyre related

[timid bronze]

Ohh

[timid bronze]

@velvet dagger r u gonna take that?

[velvet dagger]

Nah disowned

[timid bronze]

i fear ryc is jellycat

He seems to be a big supporter for jellycat

[deep mango]

fear or hear

[timid bronze]

I FEAR

[deep mango]

bear?

sear

[timid bronze]

Shut your bitch ass up

[deep mango]

not anymore. i respect from a distance these days

it hasnt been the same since the day when esca and i-

[timid bronze]

?

[deep mango]

oh well, i always look ahead

[timid bronze]

Okay

then I shall fear u r jellycat

We all fear

💔

[velvet dagger]

Had to step away for a sec but yeah if this were true that'd be game over for ryc

[timid bronze]

bros a simp

☠️

Ryc you know u can just confess directly on ur main right?!?!

[deep mango]

me and my alt Jellycat were dating, until one day when Jellycat walked in on me feeding Esca grapes from the vine. Jellycat stormed off. I knew I screwed up big time but I was prepared to apologize to my partner. Unfortunately that night, Jellycat collected his belongings and fled into the town without a trace. These days I catch a glimpse of Jellycat from across the town square, walking in and out of the grocery, or even depositing wads of cash at the bank. But not once has Jellycat looked back my way

[timid bronze]

This shit cracks me up

[deep mango]

confess to... myself!?

[timid bronze]

To dami

[raven plaza]

Finding Grass (1/69)

[errant zenith]

Where

[timid bronze]

Dang u r attracted to urself then

[deep mango]

yes, its known in the fanfiction business as selfcest

[neon garnet]

[deep mango]

ok that big lug of a dog finally got out of my bed

and onto the couch

[timid bronze]

hi cleoo

[neon garnet]

oh

[neon garnet]

hi ally

[timid bronze]

Ryc pls sto p th eself obsession.

Its weird

[neon garnet]

[timid bronze]

How ru

[raven plaza]

This is why men can't practice self-love in this society

[deep mango]

one day, i was fetching cookies from the bakery when i passed cleo and ally looking at fresh sourdough loaves. "have either of you seen jellycat?" i asked. "wait, arent you jellycat?" cleo asked. "well, no, jellycat is his alt, so they're the same but also different" explained ally

[timid bronze]

Ok but he has an alt he says is his bf

This is not self love this is Crazy

[neon garnet]

im okay! a bit sleepy

[neon garnet]

ryc fanfic era

[timid bronze]

Sleep nowwww

[deep mango]

in the end, they directed ryc to jellycat. ryc brought jellycat a chocolate chip cookie from the bakery but jellycat crumbled it into pieces and then dropped it on the ground. ryc cried, slapped jellycat, and ran out of the bakery plotting his revenge

[neon garnet]

im still settling after a nightmare

[timid bronze]

Bro is infatuated with jellycat

[timid bronze]

awe im sorry :(

[neon garnet]

whats jellycat?

[deep mango]

its fine cause its me

[timid bronze]

ryc's alt

[neon garnet]

it's okay ^^ it happens

[neon garnet]

oic

[neon garnet]

i woke up confused and thought i was covered in beetles

which now that im more awake i feel grateful that i am in fact not covered in beetles

[serene vault]

rip

to those left behind

[timid bronze]

nightmares can be so scaryy sometimes 😭

[neon garnet]

https://tenor.com/view/kitten-cat-baby-cat-sleepy-dead-gif-2196520660398809357

[deep mango]

cute buggos

[neon garnet]

she babbyyyyy 🥺

[neon garnet]

yepp

im sure one day i'll eventually stop having them

like i feel like i have a lot of time left and i probably wont have them the entire rest of my life

[velvet dagger]

Wordle 1495 6/6

🟦⬛⬛⬛⬛
🟦🟧⬛🟧⬛
⬛🟧🟧🟧🟧
⬛🟧🟧🟧🟧
⬛🟧🟧🟧🟧
🟧🟧🟧🟧🟧

Oh my God

[neon garnet]

that makes sense to me

[neon garnet]

oop

[neon garnet]

dami i heard order matters for those

jk

[velvet dagger]

LMAO this is high contrast mode

[neon garnet]

im not sure what that means

[velvet dagger]

Orange = right letter in the right spot

[neon garnet]

oh so you got it ^^

[velvet dagger]

Yeah this was just evil because of how many words share that ending

[neon garnet]

valid

maybe i could play it sometime

[velvet dagger]

||Could've been eater and I would've been toast||

[neon garnet]

ok it bedtime

gn everyone

[velvet dagger]

Good night!

[timid bronze]

wait

is this the wordle

noo

[velvet dagger]

ALLY NO

[timid bronze]

im too curious ;-;

Das my bad

[velvet dagger]

Hopefully you forget by the time you do it

[timid bronze]

Should work i have small brain of memory anyway

[errant zenith]

Gn!!

[restive salmon]

||Pater gater fater water jater hater I hate it I hate it ||

I’m crying

I tried a filler word

Now I either lose

Or get it

[restive salmon]

I learned my lesson

Didnt lose tho it was close

Wordle 1495 6/6

⬜⬜🟨🟩⬜
⬜⬜⬜🟩🟩
🟨🟩⬜🟩🟩
⬜⬜⬜⬜⬜
⬜🟩🟩🟩🟩
🟩🟩🟩🟩🟩

[latent edge]

https://tenor.com/view/touhou-fumo-touhou-aya-shameimaru-flip-gif-23524306

[solid yarrow]

:O

[latent edge]

peak flip

[solid yarrow]

Me if I pass all my exams haha

Though I would more likely end in the hospitla

[pulsar pagoda]

im literally dying from doing all this fucking corpo BS

[solid yarrow]

[latent edge]

I learned today (not really) that a field called arithmetic statistics exist

[solid yarrow]

corpo BS?

[solid yarrow]

hm?

[latent edge]

what type of corpo

[pulsar pagoda]

its my courses

[solid yarrow]

hm

[latent edge]

arithmetic statistics
looks inside
we use tools from analytic number theory

[pulsar pagoda]

present a canva of a finance dashboard with its KPI's for a tech product

[solid yarrow]

:3

[pulsar pagoda]

fucking braindead shit

[latent edge]

The only difference is arithmetic statistics is more broad

Instead of sticking to prime distributions like a maniac you can talk about other things

[latent edge]

:3

[solid yarrow]

Anything that you interested in?

[latent edge]

I'm interested in all

[solid yarrow]

[latent edge]

But I guess

I care about class numbers the most

[solid yarrow]

What makes them more special?

[latent edge]

Well it's good to know what is UFD or not

For context

[solid yarrow]

Uniformly distributed?

[latent edge]

If class number is 1 => UFD

Unique factorization domain

[solid yarrow]

The what now

[latent edge]

its oke me explain :3

So you know how in the integers you can factor integers into primes?

[solid yarrow]

Not really no

Wait

Yes nvm

[latent edge]

Like 4 =2^2

oke

So you can play similar story for higher integers

By higher integers I mean Z[alpha] for an algebraic integer alpha

For example Z[i] ={a+ib| a,b in Z}

Z[sqrt(2)]

etc

so far so good?

[solid yarrow]

So basically a set of translation?

[latent edge]

You can think of it as copying Z in some way yeah

[solid yarrow]

Mhm.

[latent edge]

Are you familiar with field extensions?

[solid yarrow]

I think I get the idea.

[latent edge]

Great

Yeah so in the classical case we have Q as a field

And the integers in Q are Z

We do the same task in Q(i) and it turns out the integers are Z[i]

But it's worth noting it's not always Q(alpha) => Z[alpha]

We take the maximal such set of "integers"

[solid yarrow]

I am not sure what you mean by this

[latent edge]

Z[alpha] might not be the whole integers

[solid yarrow]

They are the same set?

[latent edge]

No we are just trying to make sense of integers in general

[solid yarrow]

So the integers in Q[i] are the same as in Z[i]?

[latent edge]

The "integers" in Q(i) is the whole set Z[i]

[solid yarrow]

Hm

Oke

[latent edge]

yeah but note that it's not always true

so finding the whole set of integers inside a field extension requires a bit more work

[solid yarrow]

Mhm

[latent edge]

Okay let's make stuff more precise

These Q(alpha)'s are called number fields

Just a finite field extension of the rationals

so far so good? :3

[solid yarrow]

Mhm

[latent edge]

Okay and corresponding to any number field K we have the ring of integers O_K

And these come from some monic polynomial of integer coefficients

So all in all we have a ring O_K. It's a dedekind domain (it behaves similar to Z as in it has prime elements and so on)

But the catch is we don't always have unique factorization

[solid yarrow]

Okay o.O

[latent edge]

yeah and that's where class number (ideal class group) business come from

it's a group that measures how bad is O_K from unique factorization

so now this naturally makes you question how often do you get UFD for some field extension

now this becomes statistical

Fun fact: for imaginary quadratic extensions you have finitely many. There are 9 exactly

But for real quadratic case it's open

But conjecturally there are infinitely many

[solid yarrow]

?

9 =/= infty

Wait

Mksread

Lmao

[latent edge]

lmao

tfw reading is hard

[solid yarrow]

Yeah writng, reading and walking is even harder

[latent edge]

multitasking be like

[solid yarrow]

Fr though

[latent edge]

but yeah that's it

that's why i care about class numbers

[solid yarrow]

But does that mean that in this way C is possibly "worse"

[latent edge]

The whole C?

Well you want to look at the closure of the rationals right

that's the "big boy"

[solid yarrow]

[latent edge]

Yeah that's quite literally

All of number theory

[solid yarrow]

And I thought rationals are easy

[latent edge]

lmao

But instead of looking at the closure

Just look at the galois group

[solid yarrow]

Now wr go down the algebra root

[latent edge]

Spoilers: even the Galois group is hard to think about

[solid yarrow]

[latent edge]

So instead of take representations of this big group

Maps from this Galois group to GL(n)

At least we know the n=1 case

[solid yarrow]

So... ermm... what was a Galois group again

Me not know algebra ._.

Aside from abit od group stuff from linear algebrs

[latent edge]

It has info regarding automorphisms of your field extension

[solid yarrow]

Ah

[latent edge]

For example

Q(sqrt(2))

How many automorphims do you have up to isomorphism

Well you have the identity map that sends sqrt(2) -> sqrt(2)

then you have one that sends sqrt(2) -> - sqrt(2)

so in total you have 2 elements

[solid yarrow]

[latent edge]

yeah

So what is Gal(Q(sqrt(2))/Q) isomorphic to?

[solid yarrow]

Well Q cup {± sqrt(2)} no?

Or am me confus

[latent edge]

The automorphisms I just described

We have

1. Identity i: sqrt(2) -> sqrt(2)
2. tau: sqrt(2) -> - sqrt(2)

[solid yarrow]

._.

I misunderstood the question

[latent edge]

it's okay galois theory is hard

[solid yarrow]

I thought we map Q and sqrt(2)

Because then you'd have many options

[latent edge]

yeah a lot

[solid yarrow]

[latent edge]

so what happens when you compose tau twice?

:3

[solid yarrow]

Big pwobem

-sqrt(2) not defined

[latent edge]

uh

remember tau is a homomorphism :3

so one time you do it you land at - sqrt(2)

You do it again and you pick up another sign

they both cancel and now it's positive

so this has the same effect of taking the identity map i

tau^2= i

so the galois group is cyclic of order 2 :3

[serene vault]

i wish i knew what this means

[latent edge]

Do you know group theory?

[rain vale]

What is CA in ur name

?

[latent edge]

Complex analysis

[rain vale]

Oh I thought chartered accountant

[rain vale]

You doing real analysis?

[latent edge]

Now? No

I did do real analysis though

[rain vale]

What now then

[latent edge]

The analysis I touch nowadays is harmonic

[rain vale]

Oh

[serene vault]

i'm just starting in abstract and linear alg

i'm admittedly not very much familiar with most terms in those fields, sorry

[latent edge]

Well roughly speaking what I said is "symmetries in Q(sqrt(2))" and "cycles of order 2" are the same thing

as a group

Admittedly this makes no sense if you haven't seen what's the point of algebra

[serene vault]

that's a fair point. i'm trying to get there

probably too early to be going there, but i'll try to get there anyway

[rain vale]

There was someone called deltoid in server

[latent edge]

One common question to ask is if you are working with an algebraic object, can you relate to other familiar objects?

[serene vault]

i don't think i am deep enough into abstract algebra to be able to confidently and accurately answer this question yet

so no would be the answer

[latent edge]

this question depending on what math you do can either be really easy or open problem

[serene vault]

i see

i hope i can catch up by the time i get into university then

[latent edge]

Do you know modular arithmetic?

[serene vault]

i have an idea of the general concept and a bit of the calculations

but i won't claim to know every last detail

[latent edge]

yeah this should be enough to get my point across

take mod 2

so you only have the numbers {0,1}

Because everything else will collapse to these two guys right

3 mod 2 = 1 etc

[serene vault]

yup

[latent edge]

okay let's take + to be our operation

[serene vault]

by any chance, is this what i heard called a Galois field?

[latent edge]

yes

[serene vault]

i see. sorry to interrupt, please continue

[latent edge]

alright

so in the integers with + we have the element 0 that satisfies a+0 = 0+a = a for all a in the integers

This 0 is called the identity element

it's the thing that you do stuff with it and has no effect on the result whatsoever

[serene vault]

so the additive identity

[latent edge]

yep

Now similarly the additive identity in integers modulo 2 is 0 as well

you still get a+0=0+a=a right

[serene vault]

yup

[latent edge]

Alright cool

okay the elements are {0,1} as we said

what happens when you add 0 twice?

[serene vault]

you mean 0+0?

[latent edge]

Yes

[serene vault]

that would be 0, i suppose?

[latent edge]

Yep

Let's ask the same question for 1

[serene vault]

also 0

[latent edge]

yep

So somehow the elements have the property that if you add them twice you get the identity element back

[serene vault]

that's why it's cyclic, correct?

[latent edge]

Yeah that's why they are cyclic

[serene vault]

i see

[latent edge]

Same thing goes for modulo in general

it's going to be cyclic of order n

order here means you spam the element n times and you get the identity element back

[serene vault]

and the term isomorphism is because we are adding the same elements, not different ones, i am guessing?

[latent edge]

isomorphism here means if we have two groups A and B and if we say A is isomorphic to B then we mean they have the same structure

Just like how integers modulo 2 vs cyclic group order 2 are the same thing

[serene vault]

ahh

got it!

[junior veldt]

isomorphism!

[latent edge]

good job!

[serene vault]

thanks for the super deep explanation (and your time and effort)!

[junior veldt]

also hiiii delteto

[serene vault]

i actually wasn't expecting to get an explanation after i said i was just starting abstract alg

[latent edge]

I like to think of cyclic as having an n gon and you rotate it

[serene vault]

but thank you!

i'm going to try to research what you said more when i'm free later

[latent edge]

So for cyclic of order 4 you have a square. Fix a vertex a. Now rotating 90 degrees 4 times will land you on the same vertex

[serene vault]

understood! maybe i'll get around to trying to understand it algebraically by proving

not sure what this high schooling brain can achieve, but i'll give it a shot

[latent edge]

yeah and the thingy I was talking about

Namely the galois group

for the case Q(sqrt(2))

It happens to be cyclic of order 2

which is also isomorphic to integers modulo 2

[serene vault]

i see

i have much to learn then, but thanks for the headstart!

[latent edge]

No problem I'm glad you understand it

Makes me happy genuinely

[serene vault]

i will say i understand currently at a moderate level

but i will study this more later

[errant zenith]

meow

[serene vault]

though school is already calling me crazy for studying all this at my age so hahah

[errant zenith]

keep it up! youre doing great

[latent edge]

Relatable lmao

[errant zenith]

dont overwork yourself but you have the freedom to learn and study whatever you want

[latent edge]

My prof told me I should just do my phd at this point

[serene vault]

you know, same!

i got told to just go uni at this point

[errant zenith]

see if u can do that lol

[serene vault]

i'm technically 2.5 years away from uni

[errant zenith]

if u can skip credits by like

doing exams

[serene vault]

why bother

[errant zenith]

ask ur school

[errant zenith]

so u can uni earlier

[serene vault]

stay in school, gather more knowledge

go to uni being more overpowered

[latent edge]

I would stay in school

[serene vault]

plus, i prefer studying alone tbh

[latent edge]

Not because of learning or anything

[serene vault]

and i also have teachers to help understand uni material

[errant zenith]

[latent edge]

It's helpful staying in school to establish friendship or whatever

[serene vault]

social, basically

[latent edge]

Yeah you get better socially

[serene vault]

that's true as well

[latent edge]

Also you don't have responsibilities

[errant zenith]

oh

what that

[latent edge]

I wonder who is this person

[errant zenith]

oh yeah what happened to deltoid

hope theyre okay

[solid yarrow]

but tau o tau (sqrt(2)) = tau (- sqrt(2)) which is only defined for the inverse function? Am I missing something

[vivid halo]

You are yes

[latent edge]

pick an element a+sqrt(2)b. Apply tau twice

[solid yarrow]

but tau:{sqrt(2)} -> {-sqrt(2)}, no?

me really getting confus now

[latent edge]

Yes

What's the issue

[solid yarrow]

you can't apply tau on a+sqrt(2)b

[latent edge]

huh

Wait when you say {sqrt(2)} do you mean this as a set?

tau just looks at a+sqrt(2) b and changes the sign

tau(a+ sqrt(2) b) = tau(a) + b tau(sqrt(2)) = a - sqrt(2) b

@solid yarrow

Hope this helps

tau here is a field automorphism

[fresh comet]

abandoned…

[brittle socket]

https://tenor.com/view/lolol-dummy-laughing-pointing-on-you-gif-15125641

https://tenor.com/view/count-dooku-christopher-lee-star-wars-gif-23719747

[vast wraith]

tikz-cd my beloved

[narrow carbon]

Oh, thank you so much for clearing everything

[fresh comet]

dw btw, ally and I are good friends

[latent edge]

https://tenor.com/view/touhou-melm-frog-it-is-wednesday-suwako-gif-5995973774230341762

[empty mirage]

Higher!

And delt

[timid bronze]

wait so probably actually think im srs

Bruh ;-;

[ocean robin]

hiii

[verbal turret]

yo

[fresh comet]

I didn’t!

I know you’re just messing around

[latent edge]

https://tenor.com/view/touhou-fumo-touhou-aya-shameimaru-flip-gif-23524306

[fresh comet]

hi Bushy!

[fresh comet]

hi Tabby!

[fresh comet]

ello!

[timid bronze]

Hi tabs

[timid bronze]

Well ik u didnt

[junior veldt]

hi higher

[fresh comet]

I just had pho

[timid bronze]

but some r taking it so serious ;-;

[junior veldt]

looks yum

[empty mirage]

Hello higher!

[timid bronze]

Makes think ppl think of me low

If someone genuineky hated me im not making them my profile thats like the definition of harassment

[timid bronze]

So good

[empty mirage]

I made tahin noodles once

best damn meal I ever made

was really easy to make too

[fresh comet]

some people don’t know

[empty mirage]

Reminds me I should do that again

[fresh comet]

hey Pseudo!

[latent edge]

I did eat chicken pho once

[timid bronze]

Ya but if u think of someone more highly u wouldnt think :p

Ima take it down anyway

[latent edge]

tfw i went to a restaurant near my uni and i saw my prof

[ocean robin]

how are we al today :3

[latent edge]

We both ate together :3

[ocean robin]

i LOVE pho

[timid bronze]

Just came back from the store

and its raining sm

So glad we got bakc before it started raining hard

[ocean robin]

nice! and yay?

oh rain bad

[timid bronze]

No i love rain

But not when im outside

._.

[ocean robin]

well i'm glad you got home before it rained hard :D

[ocean robin]

thats so fair

[timid bronze]

one time on campus i was exiting a building w a friend while it was raining hard and

there were also sprinklers that were nearly hitting us

[ocean robin]

oop

[timid bronze]

Its ok i was smelling like @deep mango that time aka a cockroaches ass after a long day so idm the shower

[ocean robin]

PFFT

[fresh comet]

I think it’s just that some people aren’t familiar with our dynamic, and I want to avoid giving the implication that we’re mortal enemies

either way, I’ll say that I personally found it pretty funny

[fresh comet]

genuinely amazing food

[timid bronze]

We r enemies

[fresh comet]

[ocean robin]

right!!

[timid bronze]

i wanna try shaking beef

I never had

[ocean robin]

i need to eat pho again

[timid bronze]

it looks rly food

food

food

food

good

god damnit

[ocean robin]

food

[solid yarrow]

pho = rice soup?

also nice bowl

looks pretty fancy

:3

[ocean robin]

rice noodle soup!

[solid yarrow]

rice noddle soup?

[ocean robin]

yea they use rice noodles :]

[solid yarrow]

that's a carb festival

:3

[ocean robin]

[solid yarrow]

gonna fall into food coma afterwards

[ocean robin]

as long as its yummy

[solid yarrow]

fair

might even try supplementing it with something a little more "fatty"

then the energy levels might not drop to harshly

[latent edge]

Chicken pho is great

[ocean robin]

デルテト

(delteto)

[ocean robin]

fairrrrrr

[solid yarrow]

deltoid having knowledge in da cuisine

i see

[ocean robin]

i like beef pho

[solid yarrow]

so... f0xy-deltoid-cooking-show when?

[solid yarrow]

now i wanna eat pho too :(

[latent edge]

We'd win

:3

[solid yarrow]

someone need to gib me good recipe

[solid yarrow]

for sure

:3

[ocean robin]

you should try it if you can :]

[solid yarrow]

is it expenso to make?

[latent edge]

Deru tetotetotetoris

[ocean robin]

i love adding an absurd amount of jalepeños to mine

[ocean robin]

to make, yes from what i remember

[solid yarrow]

mhm

[ocean robin]

i have never made it tho

[solid yarrow]

oh

:(

[ocean robin]

yea :(

[solid yarrow]

i thought it was some low-pricey food that just tastes good

but pricey = bad

:(

now me sad

time to lay down on my bed

and

stare at the wall

[latent edge]

Wait

How dare you do my daily activity

That's my expertise

[solid yarrow]

By identity principle you and me are basically the same :3

[latent edge]

:3

[vital niche]

ratataaltata

[fresh comet]

that’s what I just had

[vital niche]

hi guys

[solid yarrow]

hello

[fresh comet]

hello battery

[solid yarrow]

gib me pho recipe :(

[latent edge]

https://tenor.com/view/touhou-fumo-touhou-aya-shameimaru-flip-gif-23524306

[vital niche]

hi foxy and higher!

[solid yarrow]

and why pho expensive

me getting sad-angry

[vital niche]

i’ve never had pho

i wan

[solid yarrow]

same

yes

me too

[ocean robin]

hello!!

[vital niche]

pho 🍲

mm

[ocean robin]

pho is very yummy i highly recommend

[vital niche]

hiya!

[latent edge]

Kinda unrelated but shit got expensive here I decided to plant my vegetables instead of buying

And it works

[vital niche]

ayyy

[solid yarrow]

crazy

[vital niche]

https://discord.gg/epicgardening

[solid yarrow]

i don't have the room for it tbh

could probably hold basil or something similar though

[latent edge]

basil .

[vital niche]

basil is nice

[solid yarrow]

does this work for weed too? asking for a friend ._.

[solid yarrow]

mhm

[ocean robin]

basil yummy

[vital niche]

idk vro 💔🥀 i think yes

[solid yarrow]

hm

[latent edge]

I have tomato and cucumber

:3

The tomatoes are tiny and sour :3

[vital niche]

i have lettuce, onion, potato, stawb

dry

[ocean robin]

onions!! my beloved

[vital niche]

strawberry

[solid yarrow]

i never really liked tomato raw. though i like it when used in other dishes, i.e. soup or sauce

cucumber is okie

[vital niche]

yes the texture when it’s raw is just…. bad

i love cucumber 🚨

[latent edge]

My cucumber has spikes in it

cucumber the hedgehog

[vital niche]

ayy wild cucumber

[solid yarrow]

what

did you try eating nails again?

👀

[vital niche]

it’s wild cucumber i think

[latent edge]

it has a nice taste to it

Better than plastic cucumber you buy here

[solid yarrow]

show picture of cucumber growth place :3

[ocean robin]

same

one of my least favorite things ever

[vital niche]

how to get perms for uploading photos 😥

[ocean robin]

get the active role!

[latent edge]

Old photo

[solid yarrow]

🤝

[solid yarrow]

you have an actual garden :O

[vital niche]

h o w

[latent edge]

Yeah

[vital niche]

just be active?

[solid yarrow]

meanwhile me rotting away in my one-room apartement ._.

[ocean robin]

you talk a lot basically, you gain more experience in the math channels i heard

[latent edge]

The transition from mathematician to farmer in my 40s is going to be crazy

[ocean robin]

same!!

[solid yarrow]

🤝 ^2

[vital niche]

ahhh

[ocean robin]

i have a doctors appointment in about 3 hrs 35 minutes

and im anxious

[vital niche]

[solid yarrow]

you'll be fine

[latent edge]

https://tenor.com/view/touhou-remilia-scarlet-tea-smile-gif-25413091

[vital niche]

[ocean robin]

but thankfully i dont have anything else to do today after that

[solid yarrow]

what's your fav tea?

[vital niche]

yay!

[solid yarrow]

maths

[latent edge]

Matcha

[ocean robin]

oolong milk tea is the best tea imo :3c

[ocean robin]

yes!!!

[vital niche]

chai straight from the motherlands

[latent edge]

Maths and chill

[ocean robin]

need to study more topology and abs alg

[solid yarrow]

you also have one of those fancy drinking glasses with the metal straw?

[latent edge]

Chai is also great

[solid yarrow]

wait

did i confus

mate

[latent edge]

metal straw LOL

[solid yarrow]

with matcha

[latent edge]

yeah i think u did

[solid yarrow]

._.

[vital niche]

i love chai my parents 5 servings of it everyday!

[solid yarrow]

sorry

[latent edge]

i rarely drink mate

[solid yarrow]

i only drink the glass drink thingy

though i always wanted to try it

but me don't have that drinking apparatus

so i can't try :(

[vital niche]

average south asian household vro 🥀💔

[solid yarrow]

as of now rooibos-vanille is my fav

[ocean robin]

[solid yarrow]

from teekanne

[vital niche]

what does matcha taste like?

[ocean robin]

grass

[solid yarrow]

haha

[vital niche]

grass

is it nice grass

[latent edge]

The more matcha you drink the more girlboss you are

[ocean robin]

i personally dont like it

[vital niche]

diva alert 🚨

[latent edge]

And the more your japanese sounds like ojousama

[ocean robin]

unfortunately

[solid yarrow]

btw deltoid do you know anyone in mathcord that is in-to-deep in complex analysis? i am looking for a textbook rec for ug->masters

[latent edge]

Yes

[ocean robin]

PFFT

[latent edge]

Me

[solid yarrow]

hi ryc

[timid bronze]

am i missing out ive never had chai

[deep mango]

low as Higher when hes lower

[timid bronze]

SOO SOO GOOD

[ocean robin]

i need to learn more complex analysis

[solid yarrow]

i thought you were da number theory expert?

[ocean robin]

it was so fun

[solid yarrow]

YES

[timid bronze]

Shut your bitch ass up

[solid yarrow]

Today was the last lecture of the course

[latent edge]

I need advanced complex analysis

:3

[solid yarrow]

upcoming wednesday exam

[vital niche]

yes! chai just refers to tea, so it’s just normal tea ingreadients cooked in the traditional way!

[ocean robin]

same

[deep mango]

youre always sticking your nose up roach butts no one else knows wtf that smells like

[timid bronze]

Ya im aware

i just meant like

[solid yarrow]

i was oogling at conway

but vol. 1 seems like ug

though we couldn't cover everything

[latent edge]

Kindaa depends what flavor you want

[solid yarrow]

true

[vital niche]

ally you changed ur name back lmaoo

[latent edge]

I wanted more contour integration

[solid yarrow]

i haven't really thought too much about that ._.

[timid bronze]

with the masala flavor

[deep mango]

nothing makes me more pmo than "chai is just tea!!!!"

[timid bronze]

ngl i barely drink tea

om more coffee person

[deep mango]

obv anyone means masala chai with the standard spicing

[timid bronze]

Yea pinging me with arabic is hard

[solid yarrow]

same. though tea can be great sometimes

[latent edge]

There's a flavor of it that goes deep into complex geometry. Idk that stuff well

[timid bronze]

Coffee so good

i need coffee

[vital niche]

oh nice your aware 😮‍💨 good because some people think it’s some whole ass diffent concuction

[timid bronze]

for the taste

[deep mango]

its like if youre like "hand me a tissue" and the person goes "um these are puffs"

[solid yarrow]

coffee meetup :3

[timid bronze]

Omg no im not uncultured

[latent edge]

What kind of coffee

[timid bronze]

And plus i season my food

unlike dami

[vital niche]

ayyy

[latent edge]

yall making me want to drink coffee rn

AHHHHHHHHH

[solid yarrow]

yeah... i am not really sure how to find my direction though ._:

just try i guess?

[vital niche]

ally where r u from? if ur comfortable sharing ofc

[timid bronze]

theres this good coffee shop on my campus that mskes it fresh

But itsj so expensive

[solid yarrow]

no ba

*d

you need to eep later

[timid bronze]

Me bornand raised in the US