serious-discussion

[bright hill]

,av strongest

[fathom swallow]

PTYamin#8224's Avatar

Click here to view the image.

[tender tulip]

I can't think of a counterexample nor a way to prove the converse

[bright hill]

No

[frozen merlin]

what's stopping K=F

[bright hill]

Take Q and Q^+ viewed as a field

[tender tulip]

for any subfield, sorry for the confusion

let me rephrase it

[bright hill]

And the automorphism phi(x)=-x

[frozen merlin]

and also if K<F, then the automorphism of Q(root 2, root 3) sending root 2 to -root 2 obviously does not fix Q(root 2)<Q(root 2, root 3)

[bright hill]

Wait that's not a field lol

[tender tulip]

For any field $F$, and subfield $K$, is the image of $K$ under an automorphism of $F$ always $K$

[fathom swallow]

Mizalign

[frozen merlin]

oh wait its not pointwise fixing

[tender tulip]

which I don’t think is trye

*true

[bronze pelican]

ay thats a cute pfp

[frozen merlin]

yeah, switch x and y in F(x,y)

[tender tulip]

But I’ve never heard of an analogue of characteristic subgroups for fields

[frozen merlin]

then F(x) not fixed, right? (F a field)

[bronze pelican]

how are you applying sigma to x?

[tender tulip]

What do you mean

it’s just the field of all sigma-x

[bronze pelican]

how are you applying sigma to x

[tender tulip]

Functionally?

[bronze pelican]

oh K is a subfield

[tender tulip]

yeah, good point. Thanks

[bronze pelican]

yeah its not always true

[tender tulip]

apparently if for some field $F$ and some subfield $K$, if the stabilizer of $K$ is normal in $Aut(F)$, and the extension is algebraic, then the extension is normal

[fathom swallow]

Mizalign

[tender tulip]

as per what I was told yesterday

i just don’t see how algebraic-ness has anything to do with automorphisms

i’m trying to use resources (artin and d&f) to find what I’m looking for but all of them are considering intermediate fields of a galois extension which is uber-specific

namely

1. Every intermediate ring is a field
2. No intermediate field is fixed by the same fixing automorphisms of the base field, and the extension is finite

[pure sun]

This is not true

Take K = Q and F = Q(cbrt(2))

Aut(F) is trivial, and hence so is its subgroup Aut(F/K) (which you like to call the “stabilizer of K”)

So it’s a normal subgroup

The extension is algebraic

However not normal

[tender tulip]

ah, thanks

[pure sun]

I think that youre not writing down what yoh wantto though

I think what you are trying to write down is

If you have an (algebraic) tower of fields F / K / L and if Aut(F/K) is normal in Aut(F/L) then K/L is normal

As opposed to saying that F/K is normal

[tender tulip]

that was a part of it

[pure sun]

What do you mean “a part”?

[tender tulip]

Why does algebraicity matter here

[pure sun]

Idk you were the one who had that as an assumption

[tender tulip]

Also Aut(F/K) being normal (and algebraic) in Aut(F) does not garuntee it’s galois, correct

[pure sun]

Also fwiw my second statement also isnt true. Take L = Q, K = Q(3^(1/4)) and F = Q(3^(1/8)). Aut(F/L) = Aut(F) = Z/2Z and all subgroups are normal

In particular Aut(F/K) is normal

But K/L is not a normal extension

My second statement is closer to correct though — if you assume the large extension is galois then it is

Actually maybe normality suffices

[pure sun]

I.e. if F/L is normal then this is true

[tender tulip]

hm

[tender tulip]

this was what I was gonna ask later

[pure sun]

“Normal” doesnt even make sense if youre doing transcendental extensions

So if you want to talk about things being normal you should limit yourself tk algebraic extensions

[tender tulip]

I’ll be back in 20

[pure sun]

Ok i might be gone then

You might be interested in thinking about this, though. You can directly link the non-normality of the lower extension to the non-normality of the subgroup Aut(L/K) in Aut(L/F). Try to show that if sigma(K) is a subset of K for all sigma in Aut(L/F) then Aut(L/K) is a normal subgroup of Aut(L/F). Therefore if it’s not a normal subgroup then there must be some sigma in Aut(L/F) which doesnt take K to itself

Now let sigma be as above and let x be an element in K for which sigma(x) is not in K

Sigma(x) is a conjugate of x and they are roots of the same min poly (over F) but x is in K and sigma(x) isnt, so the min poly of x over F has one root in K but doesnt split, so K isnt normal

In order to prove the other direction, that normal subgroup implies normal extension, you need to assume that L/F is normal

And i gave an example earlier to show why that’s a necessary assumption

[tender tulip]

i just want to understand how automorphisms and algebraicity combine into the notion of galois extensions and their beautiful properties

A Galois extension F/K is an algebraic extension such that
Fix(Orb(K)) = K

Where Fix(X) maps subgroups of Aut(F) to sets that it fixes, and Stab(G) maps subsets to subgroups that fix it (lattice morphisms)

but not much I can think of comes from this, and why is algebraicity so important

ESPECIALLY when finiteness becomes involved.

i wish there was a way to phrase finite extensions with automorphisms instead of going on a side tangent to “determine” it via vector spaces

[vivid halo]

[tender tulip]

algebraicity just says every intermediate ring is a FIELD which ofc has it’s own implications

For some transcendential extension A/B, with transcendential element x, then we can map A[X] to B which fixes A but maps X to x, but because the kernel is trivial (epimorphic) this new ring image is isomorphic to a subring of B that contains A, which the implications of which I haven’t worked out more of

oh wait yeah

that’s fairly intuitive, it’s just the ring generated by powers of the transcendential element

[vivid halo]

yeah

the algebraic extensions are natural here since they have connection to quotients of polynomial rings and you can talk about minimal polynomials of algebraic elements and so on

[tender tulip]

yeah

[vivid halo]

transcendental extensions don't really have an interesting relation to these same things

like it's the same as adjoining variables

which is important, it just behaves very differently

[tender tulip]

why is this important in conjunction with the “stabilizer-fixation” def of galois extensions

gtg

[fathom swallow]

gmod

[cold needle]

are you using the sub notation to mean "in base n"

1010_10 meaning 1010 in base 10 ?

i am in confusion

[zealous garden]

do you have your bases reversed?

[ancient flame]

yes

[ancient flame]

what

oh right

LOL

whoops

[deep bridge]

hi guys I’m perperaing for grade 9 math entire test with all units and stuff does anyone have like a link with example tests or etc to help me prepare?

[ripe wasp]

picked up a new book today

[tender tulip]

lets say we have two complete lattices A and B with a heterogenous relation between their elements R. Can we technically define functions between them that essentially map any element to the minimal element that is related to it in the opposite lattice

it technically maps joins to meets and vice versa

and inverts order

[tight comet]

Why 3e? Was it cheap?

[ripe wasp]

yeah, it was second hand so i got it for really cheap

cheap for a math textbook at least

[tight comet]

good enough, since 4e is out. not too sure on the edition differences

[full isle]

Are you poor?

I can help you out

[ripe wasp]

i mean i'm not necessarily poor, but i'm just a high school student

like i can usually ask my parents and they'd usually say yes, but i feel guilty whenever i buy a textbook that's expensive

[full isle]

I get it now

[errant ridge]

but I am

[mint canopy]

Have you considered the wonders of the internet

Without naming names, there are websites that host books

[errant ridge]

you can name them in dms

[mint canopy]

Had to check the rules just in case

Look at this crazy wikipedia page! https://en.wikipedia.org/wiki/Library_Genesis

[full isle]

Something is wrong with you idiots

We really cant have nice things

[mint canopy]

Definitely haven't engaged in any of this "piracy" nonsense, no sir

[full isle]

The more you spread awareness the more chances it wont exist later on

[mint canopy]

It has an entire wikipedia page are u being funny

[full isle]

You are dumb as hell if you think wikipedia page equates to popular knowledge

[mint canopy]

🙄

[full isle]

Just keep it at DMs

[mint canopy]

Publishers are v much aware of libgen, but libgen has legal ways to get around it

It won't be going anywhere soon.

And certainly any academic knows about libgen lmao

[full isle]

This is most possibly the most privileged argument I ever heard

I wont change your mind and I dont plan to

all I ask is to keep things at DMs

[mint canopy]

Christ jass, can you please be a bit more polite at least

[full isle]

no because its an actual problem

[mint canopy]

It's really quite simple. Libgen is going to be fine.

[full isle]

In the possibility that it isnt

Realize you are a contributor

[mint canopy]

I'd love to contribute to libgen, but I haven't got any books! 🤓

[full isle]

Its copywright infringement and books have been removed for this

[tight comet]

High school students reading Grimmett and Stirzaker........

[full isle]

Also the site has gone down in the past

[mint canopy]

Great stuff. While we're at it, should we get the TeXromancers to stop posting their project that reproduces copyrighted material on this server?

Wait it is just "copyrighted" isn't it

[full isle]

it shouldnt be advertised

thats the point

[tight comet]

You can also write original non-copyrighted mathematical books

[full isle]

The whole point is you arent supposed to share it

[deep mango]

No matter how much I completely disagree with jass are, please stop jokingly working around the discord tos policy about piracy stuff

[mint canopy]

Ooer

[deep mango]

Thanks

[tight comet]

There is a growing body of creative commons licensed books

[full isle]

disagree?

[mint canopy]

Forgor about the discord policy

[full isle]

you say disagree

and do just that

agree

[deep mango]

So that the server doesn't run into issues

Not for any other reason

[mint canopy]

Checked the server rules but not discord's rules 💀

[full isle]

lost manga scanning websites hheaven and other similar websites

[tight comet]

Although there probably isn't anything that is libre-licensed on the level of Grimmett yet

[errant ridge]

cut off one head, and two more shall take its place

[trim vessel]

Yo if anyones interested in using about 3 minutes guessing fictional characters names who have NOT read percy jackson/heroes olympus pls tell me in dms. sorry if i dont reply right away/are offline when dmed

[full isle]

this already happens with libgen

they site gets shut down and they host in more areas

worst case scenario we will need to spoof location by using virtual network to access it

[errant ridge]

[full isle]

afaik the site should still be fine though but access will be harder

[ripe wasp]

guys i already knew about the library lol

i just like having physical books better

that’s why i feel a bit guilty

because i already technically have a pdf of everything

and i don’t exactly need the physical book

[open aspen]

just talked to my new roommate about math a bit

hes a physicist

im not convinced we agree on a single definition

[unborn trellis]

what was his answer for what a tensor is

[bronze wedge]

Physoids be like: infinity minus infinity = 0

[open aspen]

"basically a vector"

which is pretty based

[bronze wedge]

Definition of a vector

[open aspen]

I asked what a manifold is, he said locally flat and is a topological space
I asked what a topological space is, he said has a manifold in it

Their books go hard though

like wtf is a world line

[unborn trellis]

they're not too worried about the specifics

Really annoying though when relativists use technical facts from Riemannian geometry without elaborating at all

[open aspen]

they're applied mathematicians, they dont need to care about the details, I get it

[unborn trellis]

The edges of the light cone I believe

[open aspen]

I dont worry for a second when I use results from #foundations

because that shit scares me

[hollow sundial]

Me IRL

[bronze wedge]

Physicists arent applied mathematicians

[odd narwhal]

Next ask them what "locally" means

[open aspen]

ill add that to the list for banter topics

[hollow sundial]

Interesting take. I think it's hot but correct

[open aspen]

close enough to true for what i am attempting to conclude

im not really an applied foundationalist either

[zealous garden]

within a monad of course

[open aspen]

im gonna ask what a field is next

[bronze wedge]

imo the litmus test for applied mathematics is "are you on the math faculty"

[open aspen]

well that seems incredibly unfair

[hollow sundial]

Basically haha

[open aspen]

plenty of applied mathematicians arent affiliated with a university at all

[odd narwhal]

Imagine applying your math outside of academia

How impure

[open aspen]

the horror

where's that xkcd of <blank> is just applied <blank>

https://xkcd.com/435/

xkcd: Purity

On the other hand, physicists like to say physics is to math as sex is to masturbation.

[zealous garden]

anyone here into computational geometry

[neat frost]

Lmfaoo that footnote

[open aspen]

the footnotes are always incredible

[hollow sundial]

Petition to rename applied math "impure math"

[chilly hull]

what even is "pure"

[open aspen]

the fewer the numbers, the more pure the math

[peak tide]

for some reason that brings to mind this recollection from TA'ing first semester calculus once upon a time:
professor: [explains some simple concept]
student: can you show a numerical example?
professor: this is a numerical example, x is a number
student: #$*(&#@$

[storm sage]

LOL

[open aspen]

gradschool has led me to he discovery that i know nothing

[full isle]

what do you study

[zealous garden]

This fills me with excitement for the many holes I get to fill

[open aspen]

topology/geometry

[full isle]

what specifically

[open aspen]

nothing really yet, just a second year. i have more knowledge in partiuclar areas obviously but it isnt really worth mentioning, i may or may not end up doing stuff in those areas

[full isle]

what favorite topic as of 2022

[open aspen]

Hyperbolic geometry

[full isle]

then you definitely know something

[sinful mica]

Hyperbolic geometry is rad

Or at least it looks cool

[arctic lagoon]

Assume I am about to study in the library, and that I will be reading a specific book. In case both the library and I own a copy of it, should I bring my own copy instead of using the one from the library?

[toxic gale]

I mean, you can jot notes down on your own copy so you might prefer that. But if it's heavy and you have to lug it there then maybe considering not bringing it.

[peak tide]

it there a nonzero chance that someone else will check out or be otherwise using the library copy?

[arctic lagoon]

It’s certainly possible that someone else would be needing it, and not every book has more than one copy available there.
I don’t write much on the books so that is less of a worry for me.

Well I guess I’ll just bring mine with me then. They are not of the size of dictionaries anyway.

[young rain]

@neat lintel dude join

Plz if u can

I’m so high right now it’s actualtm insane

The vc @neat lintel

I need math help

Jk dude I’m just really extremely high and it’s actually crazy

[high kite]

what is abstract alegbra about?

[arctic lagoon]

A general treatment of similar structures occurring ubiquitously in mathematics

[young rain]

Me neither

It doesn’t feel like I actually did it

Like it’s not real

[high kite]

what do you mean by tteatment like a covid vacine?

[young rain]

If i wasn’t high I wouldn’t have pinged u too

Cuz I already know that sh look stupid

But idc bc

This is is unbelievably insane rn

[high kite]

no one cares that your high

[arctic lagoon]

Well I guess you could also ignore the first four words from my previous reply.

[high kite]

oohh i get it now

now what do you mean by structures like lines , grpaphs shapes?

[arctic grove]

not really?

algebra deals with how these structures behave/how they become what they are

and more

[high kite]

how they become .. thats a cool way of phrasing it!!

[arctic grove]

yeah!

algebra itself is cool 😌

[high kite]

so i asked im what is abstract algebra and he said ::

A general treatment of similar structures occurring ubiquitously in mathematics

we can rephrase that:

a general discusiion or exploration os structure that are vecoming or , have becom e

https://tenor.com/view/fancy-as-fuck-present-fabukous-murder-she-wrote-angela-lansbury-gif-16434223

[arctic grove]

yeah

you start off by studying about groups, rings and fields

u see what makes them what they are, seeing how they behave when compared with other things of the same kind

its very cool

[young rain]

@high kite stfu

I only @ him here bc dms closed

[high kite]

ewwwwwwww

https://tenor.com/view/whet-what-ew-can-you-not-stop-gif-9908266

[errant ridge]

it's like high school algebra but far far far more general

and then there's universal algbera

[fathom flint]

Can anyone suggest to me how can I improve myself in trigonometry? Or like in Pure mathematics ....

[errant ridge]

practice

[fathom flint]

I'm trying my best. I do all the h.w.from book and question paper but I feel like I'm not improving... Most of the time doing maths I stuck, there is always a problem and I need help! Which I don't like so much. Later I realise that was easy🙂💔 then why I couldn't do that math by myself!!

[errant ridge]

make sure you really understand why you're doing what you're doing when you're solving

like "why this step and not that"

and make sure you understand and have an intuition behind trig

[fathom flint]

I will try to keep your advice🤎. But can you explain to me what you mean by having an intuition behind trigonometry?

[errant ridge]

like do you know why sin^2 (x) + cos^2 (x) = 1?

[fathom flint]

To be honest noooo! I asked the teacher, he said you don't need to know this how this comes from now just memorize it, you will know it later in your A'levels.

[errant ridge]

Lol im just saying knowing how the unit circle works helps a lot while doing trig problems

[fathom flint]

Um, okay!?!

[solid snow]

Bruh the explanation isn’t even that hard

The unit circles radius is always 1, therefore any right triangle you construct from that radius has a hypotenuse of 1

If cosine is one side and sine is the other

You do pythagorean theorem where c^2=1

And there you go

[toxic gale]

Yeah pretty much. If a teacher is unwilling to explain, you might wanna consider looking up more resources online appropriate for your level. Khan Academy is frequently recommended for the middle/high school level, so maybe give it a go. Having an understanding of why some identity is true helps a lot in remembering it and knowing when to use it.

[brittle socket]

Imagine your teacher is unwilling to mark or actually do something useful for English

Saying this from experience

[alpine vessel]

Dang..... there's a lot of occupied math help

[bright hill]

noiree?

what does that mean?

[alpine vessel]

It's a name

[bright hill]

oh

[dusty compass]

Semester began

[open aspen]

You should see at the end of the semester

[dusty compass]

Lol

[plain path]

Sorry, I’m new here but I have a math problem and I’m not sure where to post it lol. Basically I’m wondering what f(x) is if it’s conditions are f(x) + f(1/x) = 4 * pi, and it goes through points (0, 0), (1/5.002, pi), (1, 2 * pi), (5.002, 3 * pi), and it approaches 4 * pi as x -> infinity. It has to be continuous, and the range is [0, 4 * pi] between [0, infinity]

Where would I even post a question like that? Lol

[sick burrow]

If it's a homework type question read #❓how-to-get-help

[plain path]

Ah, ok, thanks

[neat lintel]

if there are 100 ppl and 40% of them have eaten chocolate , and 30 % of them have eaten mint, (they can eat both ) (the 30% can overlap with the choco eaters)

what's the probability that one person picked has eaten both

[sick burrow]

https://tenor.com/view/crazy-no-one-cares-who-asked-who-asked-meme-gif-24508192

#❓how-to-get-help

[neat lintel]

is ther a way to know who has helper role

[sick burrow]

[dry gust]

A = eats chocolate
B = eats mint
A intersection B = eats both
independent contingencies =>
P(A intersection B) = P(A)P(B) = 40% * 30%

[ancient flame]

orrrrrr just use latex and you dont have to pay for an annual subscription for shitty font

[full isle]

user handwriting argueably better

[arctic grove]

it looks cuter

[ancient flame]

yeah

[arctic lagoon]

Either Latex or Handwriting. I’m at the two extremes about this.

[neat frost]

What two extremes

Like you basically only have those two options

[deep mango]

What about microsoft word

[eager reef]

[bright hill]

you guys are all weak

I write in ms paint

[zealous garden]

I use my phone keyboard

[arctic lagoon]

There are people occasionally typing TeX code as plain text.

[neat frost]

Haha funny joke

[arctic lagoon]

Presumably as @zealous garden intended in his reply

[neat frost]

Yeah you could also carve it into a rock, but I mean an actual alternative. You wouldn’t submit a plain text file for a math paper

[arctic lagoon]

Or you can do what people used to do for typesetting before Tex was invented. Reading old publication really is a pain in the the for me

monospace everything

[zealous garden]

Oh no I do that but I meant lim ₓ→ₐ f(x) = L ⇔ f(μ(a)) ⊂ μ(L)

∀x∈∅(∃y(y*x=0/0))

And such

[vocal roost]

i still wondered why i call it a closed loop integral

[storm sage]

Because it's an integral over a closed loop

[bright hill]

[muted tide]

Do you guys know any good volunteer opportunities or websites that can help me find volunteer opportunities? I am looking for something related to business/finance. If you know some other opportunities/organizations you can let me know and I will check if they a operate locally. Thanks.

[brave wraith]

why is there no thumbs down cat _ _:'(

i need it

[high kite]

https://tenor.com/view/cat-thumbs-down-tongue-out-cute-kitten-gif-16279168

[ancient flame]

classes start today 😬😬

[deep mango]

what will you have today?

[cyan goblet]

thanks for asking. today i had a cobb salad, chobani greek yogurt, and a naked blue machine

for lunch i will have a wrap

[deep mango]

you had that for breakast?!

[cyan goblet]

yea

[deep mango]

a cobb salad

[cyan goblet]

yea

ikr? i cant believe i forgot some carbs

[storm sage]

GOOD LUCK

[ancient flame]

Ty!!!

[cyan goblet]

ok i got an uncrustable for my carbs

[storm sage]

Remember, only stop showing up to class after the first week so that the professor knows who you are /s

[cyan goblet]

TRUE!

i’ve introduced myself already to all my professors

i’m basically done with sandwich

[deep mango]

i'm stuck on the last few clues of this crossword

[cyan goblet]

what’s the crossword

[cyan goblet]

with the school year *

lmao im thinking about my sandwich rn

[deep mango]

oh fuck i finished it and now it hasn't solved

tghhh

[deep mango]

nyt tuesday

[cyan goblet]

i should hop onto crosswords

i just dont understand a lot of hints

[deep mango]

ok i finished it

[cyan goblet]

congratulations

i am so proud of you for finishing nyt tuesday

[deep mango]

we can organize some here, downforacross is a great collaborative crossword site

[cyan goblet]

sounds fun

[deep mango]

nyt = new york times

[cyan goblet]

ik

im so bogged down with hw and classes that i dont do much other than study

and its only the third day of classes

[deep mango]

yes

[cyan goblet]

but i like it

homework is fun because classes r fun

[odd narwhal]

Cobb salad is gross

[deep mango]

Agreed

[odd narwhal]

You have hw on the first week? Damn

I have physics and genetics hw 🤢

@ancient flame r u starting uni

[ancient flame]

yeee

[odd narwhal]

What do u have today

In terms of classes

[ancient flame]

microecon online, intro to business in-person, marketing online, and stats in-person

in that order

[odd narwhal]

R u a business major?

[ancient flame]

yep

[odd narwhal]

Inch resting

[arctic grove]

yeah

[ancient flame]

lol

[odd narwhal]

Why did u choose business

[arctic grove]

coz he is greedy

[ancient flame]

im very interested in it and I think it is a good opportunity for financial success

I love things like marketing & HR

[odd narwhal]

Well.good luck

[ancient flame]

tyyyy

[odd narwhal]

Having online and in person classes interspersed like that seems like a bit of a pain

[deep mango]

gmod like "i love HR"

[arctic grove]

cant u take a math minor gmod

[ancient flame]

a bit but eh

[ancient flame]

LMAO

[deep mango]

i kinda like it

since ur not just at home where you can like

[ancient flame]

I will probably do an information systems minor

[deep mango]

find excuses to not attend the online lectures

[ancient flame]

lol

[deep mango]

wow shyshu is so sad

??

[ancient flame]

ikr

[deep mango]

he probably wants to live vicariously through you

[odd narwhal]

Motion to ban non-integral domains

[arctic grove]

[arctic grove]

wut

[ancient flame]

lol

[wooden flax]

Good or bad stats

[ancient flame]

havent gone yet

[wooden flax]

Motion to ban non noetherian ring

[ancient flame]

that's at 3 pm

[wooden flax]

I mean Cale based or not

[ancient flame]

oh

no

that's probably stats 2

[surreal sapphire]

i remember reading this post that noetherian is unnatural and actually one should work with some other notion of ring that is more general and more natural

[wooden flax]

Aid what is that notion

And

[surreal sapphire]

i dont remember, i use noetherian

it was shared by chmonkey

[wooden flax]

Lol based

[wooden flax]

Makes sense

[ancient flame]

when will gmod lose active role

[vivid halo]

When you stop posting

[ancient flame]

lol

which is kinda happening now

[hollow sundial]

when will @rough beacon stop posting

[sick burrow]

lmfao @mortal igloo

found in a list of GRE practice problems

clearly the problem author never took your calc class

[alpine kindle]

ew reusing variables

but also this does not seem complicated

[sick burrow]

no the problem doesn't look hard

it's just funny that it's technically incoherent

anyways I should get back to studying

[mortal igloo]

👀

[alpine kindle]

$g(x) = \sin(\sin(x))$ so $g'(x) = \cos(x)\cos(\sin(x))$ so $g'(0) = 1$

[fathom swallow]

ally 🌈

[sick burrow]

wow I solved it in a completely different way

[alpine kindle]

how

it's like

hm

yeah I'm dumb

[sick burrow]

fundamental theorem of calculus + chain rule

[alpine kindle]

chain rule?

oh

I'm not sure how I'd use that

like did you sub

[sick burrow]

$$f(x) = \int_0^x \cos(t) \ dt \quad f'(x) = \cos(x)$$
$$g'(x) = \frac{d}{dx} f(\sin(x)) = \cos(x)\cos(\sin(x))$$

[fathom swallow]

Poppy Lascelles

[sick burrow]

found the technique in my GRE prep book

[deep mango]

not using leibniz integral rule

[sick burrow]

the what now

[tall badge]

rip dummy var

[sick burrow]

oh it's just the general form of that

[deep mango]

oh yeah my brain immediately went to leibniz integral rule cause i saw x in the bound and in the integrand

i didn't even realize it was a dummy variable fuckup 😭

https://en.wikipedia.org/wiki/Leibniz_integral_rule

so useful

[sick burrow]

oh yeah that seems kinda pog

[deep mango]

i have never actually proven this

which is silly

[sick burrow]

shouldn't be that hard to prove

[untold sapphire]

Noetherianity is a disease from which the human race will soon recover.

[eager reef]

Lmao

[errant ridge]

the proof in the wikipage of the leibniz rule is pretty understandable

[errant ridge]

i thought you had to use the leibniz rule for dummy variables until yesterday

[rancid topaz]

What did I do wrong here? For #2

I feel like this integral has 2 answers

either -2arcsin(x) + c

or 2arccos(x) + c

bc u can leave the 1 or -1 inside the integral and take out either -2 or 2

My teacher said that I was wrong here though so I’m confused as to why I got the question wrong

[storm sage]

Your teacher is wrong, -2arcsin x + C is valid

,w derivative of -2arcsin(x)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Eric Tao#5735

[storm sage]

they were probably just grading by an answer key and going through it fast so they made an error, -2arcsin x + C and 2arccos x + C are both valid here

[hollow sundial]

smh bad teacher

[storm sage]

imagine ever making a mistake

couldn't be me

[hollow sundial]

you only make epik fails

[storm sage]

LOL

[pure sun]

i love these kinds of problems hahaha

like, where two very "different" looking functions are really the same

[hollow sundial]

,w plot -arcsin(x)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[hollow sundial]

,w plot arccos(x)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[pure sun]

i do this activity in my calc classes at the start of the class after we do u-substitution. i ask them to integrate 2sin(x)cos(x). i tell half the room to use u = sin(x) and the other half to use u = cos(x)

one half gets sin^2(x) + C and the other half gets -cos^2(x) + C and then I prompt them to "argue about it until you figure out which side was actually correct"

[storm sage]

LOL

genius

[pure sun]

someone usually figures out the trick after a minute or so and then we talk about it

[odd narwhal]

Oh that's cute

[pure sun]

oh here's another weird calc trick eric, idk if youve seen this before but it always freaks calc students out. it uses integration by parts. here's how it goes:

[eager reef]

Buncho do you mind looking into #groups-rings-fields really quick

It’s 2am and I’m not sure if I’m lying to yamin rn

[pure sun]

let's find $\int \frac{1}{x} dx$ using integration by parts. Choose $u = \frac{1}{x}$ and $dv = dx$. Then $du = -\frac{1}{x^2}$ and we can take $v = x$. Then, using $\int u dv = uv - \int v du$ we find that our original integral is equal to

$\frac{1}{x} \cdot x - \int x \cdot -\frac{1}{x^2},dx$

simplify everything and we get that our original integral $\int \frac{1}{x} dx$ is equal to

$1 + \int \frac{1}{x} dx$

now subtract $\int \frac{1}{x} dx$ from both sides and conclude that $0 = 1$.

[fathom swallow]

Buncho Bananas

[storm sage]

LOL yea I've seen that

so good

[pure sun]

I like to do that example after I do the integration by parts example that's like, integral of e^x sin(x)

where you do it twice and then add the original integral over

and so this is a similar "trick" where you subtract the original integral from both sides

except it cancels out

[storm sage]

Love it

[dapper badge]

made chicken for the first time today

think I ate too much 😵‍💫

[deep mango]

wow

well done

hope it was good!

[dapper badge]

yeah my friend helped me to make sure I didn't get food poisoning

and it ended up pretty tasty

but now I think I got the food sleepies

[tall badge]

pics

[open aspen]

That's the first proof of something like 1=0 I've seen that didn't involve dividing by 0

Very nice

[arctic grove]

is the mistake here that u took dx as the second function?
I cant figure out what went wrong here

[neat frost]

Integration constant

[arctic grove]

oh its indefinite integration

lmaoo

[fading moon]

how do you pronounce $(\frac{7}{10})^5$ in English?
Sorry I'm from a non-English country.
is it seven-tenths to the fifth power?

[fathom swallow]

runoob

[odd narwhal]

Yes that's fine

[brittle socket]

Latex tip (if you didn't know alr)

You can use \left( \right) to size the brackets properly so that they loook nice

Like

[ \left( \frac{7}{10} \right)^e ]

[fathom swallow]

grass

[jaunty stag]

I say it as
"7 upon 10 whole to the power 5"

[frozen merlin]

I say "7 over 10 to the power of 5"

but what you wrote is equally fine

[fading moon]

so you prefer to say 7 upon/over 10 rather than seven tenths?

[frozen merlin]

I'll say "a half" instead of "1/2" but I'll say "207 over 95" instead of "207 95ths"

depends on the size of the numbers I think

[neat frost]

Objectively, sincerely, honestly, wholeheartedly, completely, absolutely not

[sleek wing]

in a rare turn of events I completely agree with slurp

no human in the history of history has said it like that

[dapper badge]

Oops I ate it so fast that I forgot to take a picture. But I think I will make more tonight so I'll see if I can remember

[gritty copper]

7 by 10 whole raised to the power of 5

[errant ridge]

I read (7/10)^5

[arctic grove]

u are very wrong

[sleek wing]

I am incredibly correct

[arctic grove]

not at all

[sleek wing]

as per usual, I am

[arctic grove]

considering thats how i say it a lot of times

[sleek wing]

you are an idiot

[arctic grove]

and a lot of people do

[arctic grove]

no you are an idiot

[sleek wing]

does it make more sense in hindi or something

because that's one of the most clunky, verbose ways I've ever heard someone phrase "7 over 10 all to the power of 5"

[bright hill]

good morning slurp!

[arctic grove]

not really?

[sleek wing]

damn hittin my mans slurp up with the reversal

[arctic grove]

its just a lot of people say it like that

i never found it fun but it became a habit so a bit hard to get rid of it

[bright hill]

can't let him be first every time

[arctic grove]

Good morning Darq!

[bright hill]

good morning shushy!

[fading zealot]

Is it mathematically correct to say that “nothing” is a part of everything?

[errant ridge]

define "nothing" and "everything"

rigorously

[bright hill]

the empty set is a subset of every set

soooo

ig?

[neat frost]

Good morning DarQ!

[fading zealot]

That's more like “you can always choose to take nothing”

[arctic grove]

this should be a sticker here

but with higher readability

hmm

[fading zealot]

Maybe split it into like three stickers

[arctic grove]

hmmmm

that sounds like a lot of work
and stickers dont work as nicely as emojis do

[eager reef]

we have new stickers

[golden pendant]

how to calculate length of a cord covering a 1/3 of a circle, any resources for the whole cords lengths vs angles shit in a circle i learned in school?

[sleek wing]

trig

[golden pendant]

oh yeah

makes sense

[bright hill]

this is nami's doing, isn't it?

[errant ridge]

I'm gonna dumb all over this place

it's dumbin' time

[neat lintel]

Hi where can I ask about lambda calculus?

[storm sage]

#foundations possibly?

That's my first guess

[deep mango]

That's probably what I would say, or #proofs-and-logic

[sturdy lava]

Hey guys, which topic discussion does a question like this belong in?

[leaden finch]

Math

[past stone]

currently obsessed with map projections. are there any digital tools to visually make your own projections? like adjust equations to define mappings from a sphere to a plane?

[uncut pilot]

Anyone have the ti nspire cas 2

[tall badge]

ok heres ur reminder, dont disappoint 🙂

[wooden flax]

^^

[fervent pebble]

german music is so good

well

the german pop i like

at least

[dapper badge]

Haha what if I forgot to put the chicken in the fridge to defrost? That would be such a silly thing to do ahaha

[tall badge]

man

u can quickly defrost by putting it in cold water

[dapper badge]

Oh bet

[eager reef]

[dapper badge]

Dinnies!

[deep mango]

nice, looks good

[dapper badge]

Lots more for the weekend

[deep mango]

jesus

[tall badge]

yoooooooooo looks delish

[neat lintel]

why do people like college parties?

It’s honestly more boring, no good food, everyone sharing the same drink

Going to the bar is more fun, they have good food

Also the chicken looks amazing

[deep mango]

bars are expensive and loud and full of obnoxious people

big college parties suck

but small parties with close friends are great

the food is an issue

[neat lintel]

Definitely I agree with u

[neat lintel]

Quick question bars == clubs right?

[deep mango]

not necessarily

there are plenty of normal bars

most of them blast music and make it impossible to talk

[neat lintel]

Ok the club is where I went and actually enjoyed me time

*my

[deep mango]

and it's way way cheaper to buy a couple kinds of alcohol for a party than it is to get 2 or 3 drinks at a bar

like 10 or so bucks

[neat lintel]

Yeah

Alright next week am back to math

Tired of trying new stuff

[deep mango]

haven't been to a proper club, i think i'd probably like that a lot more

since i like dancing a lot

[neat lintel]

Yeah

One thing about clubs is the music, my music taste is trash but I love it

[deep mango]

lol

yeah i like a lot of very "refined" music but i also definitely don't mind club music

[neat lintel]

nice talking to u ryc see u around

[deep mango]

good night!

[errant ridge]

m

[brittle socket]

Good Afternoon Chalk

[errant ridge]

good afternoon grass, have you touched grass?

[brittle socket]

Yes I have touched myself

[errant ridge]

[brittle socket]

Why the stare? How do you shower without touching yourself

[dreamy heath]

Hi discussion 2

[brittle socket]

Guess why I lost 2 marks in a practice paper I was doing

[errant ridge]

Lol fair enough

[brittle socket]

What were you thinking

[vapid sentinel]

Do anyone attend the Oxford MAT livestream?

[severe swallow]

yo, does anybody know for linkedin.
does the "courses" section on your profile represent what courses you teach or which ones you actually took

[neat lintel]

i think took because what u teach only applies to "teachers" lol

[neat lintel]

how would you prove an existence of something without giving an example

[brittle socket]

Axiom of Choice

[bronze wedge]

Axiom of choice

[brittle socket]

Seems like you had the same idea as me

[bronze wedge]

Tensor product is always done this way

[surreal sapphire]

hm? the tensor product is constructed

[bronze wedge]

Universal property + other construction method proves existence of the tensor product

[surreal sapphire]

you prove it exists by constructing it, yes

[eager reef]

that proof was kinda hard to read

constructive proofs in general

[full isle]

What they do is they make an object with desired properties

so it exists

[peak tide]

in some contexts, you can prove existence by showing that the set of such objects has positive measure

[smoky verge]

can i post something on here

[tender tulip]

choice

[slim parrot]

How do people self-learn from math textbooks?

1. Do you take notes when reading them?
2. Do you try to derive proofs yourself before learning the topic (or seeing the way they proved something)?
3. Do you solve all the problems at the end of a chapter? How much should problems one solve to be satisfied of the understanding of a chapter if they are short on time?

[river moon]

yes, yes and no

in general for any school or first/second year in university topic you'll easily find tons of practice problems, so you'd want to solve most of them

but more advanced books don't always even have exercises and when they do there isn't a whole lot of them plus they can be quite difficult

[alpine kindle]

i usually do a few exercises for each subchapter

some people like Moth do most of them

[fading moon]

How do you pronounce P(A|B)?
P A line B? or P A with regard to B? or conditional probability of A with regard to B?

[manic ginkgo]

I think

I usually read it as Probability of event A occurring given B

the last

[neon silo]

I would say "probability of A given/assuming B"

leaning towards given

[fading moon]

Thank you!

[untold sage]

"P of A given B"

[wooden flax]

like you should 😌

i get so much anxiety if i dont complete most of the excercises

literally have trouble sleeping

[bright hill]

I go by vibes

I just make sure to leave a few for review

[storm sage]

"Do I feel like doing these? Nah, moving on to next section"

[bright hill]

especially when you're just itching to move on to that section you've been looking forward to

[storm sage]

I only do them if I'm having trouble understanding the concept

And then if there's some reason where I really need to have that concept down then I do them

[chilly hull]

i dont get why integrating factors work

[storm sage]

is this for a differential equation of the form y' + p(x) y = q(x)

[chilly hull]

yes

[neon silo]

It would be great if we could write y' + p(x)y = q(x) in the form (M(x)y)' = Q(x) because then the equation would be separable and thus easily solvable (assuming the integral on the RHS is doable), this is what integrating factors help us to do

[tall badge]

i wrote smth on it if ur interested #multivariable-calculus message

[chilly hull]

yoo

[chilly hull]

interesting

thank you

[velvet dagger]

You are correct

[fathom swallow]

runoob

[brittle socket]

[fathom swallow]

runoob

runoob

[fading zealot]

The professor teaching project management (It's called “software engineering” but it's actually PM) in the upcoming semester is notorious for just reading the texts in a very flat tone and answering questions by “I would say yes/no”
Looks like we've got ourselves some sleep aid here

[delicate panther]

For me,

1. Depends on the book. Good books that has a clear line of logic shouldn't need notes, only page # of specific concepts. Books that jump from concepts to concepts leaving you confused af is a sign that you need a better book 💀
2. Some proofs that you can immediately visualize the logic doesn't hurt to try; proofs that are very basic can be skipped due to triviality; proofs that are core concepts of the subject you are learning are usually too hard for you to derive/prove in a time-efficient manner (that's why the author wrote the book, to present you with this "new" concept) and should be read and studied carefully instead of trying to prove it from a vacuum.
3. Try to understand what each problems are trying to teach you. If you see 20 pages of calculus exercises may be a good hint it's written for engineers and usually prepped for failing them in courses 💀; overall try to solve the problems that pose new concepts and things you are not familiar with

biggest lesson: never self-teach Rudin's Principle of mathematical analysis as a first course to real analysis 💀

[bronze wedge]

What's wrong w/ Rudin lmao

The measure theory part is bad

But that's it

[delicate panther]

as a first course to real analysis

[bronze wedge]

I took it as a first course

[delicate panther]

it took me way more time than worth it to understand the first few chapters

maybe you have a solid foundation and all the prerequisites for it

i couldn't understand what a topology is, what compactness means

[bronze wedge]

Its usually recommended to have a background in proofs b4 starting baby Rudin

[zealous garden]

I'm still working on compactness myself

[delicate panther]

even then I still wouldn't recommend it because the concepts are too big of a leap

the book is known for being terse

is a good reference book

[bronze wedge]

Idk about that - it's an undergrad text so it doesn't have many of the results you'd like it to have

[delicate panther]

besides, you are self-teaching it, meaning any questions you had would go unanswered most of the time

ya my point is still just to use a better text on analysis

[bronze wedge]

Pugh is a good suggestion, there is also Abott or Tao

[delicate panther]

maybe I'm dumb but I really had a hard time reading Rudin, I'd agree on Tao being good

[bronze wedge]

You're not dumb! There's nothing wrong w/ not understanding a math text first try

[delicate panther]

it took me 2 years to finish 2nd chapter in rudin, that's why I never would recommend that book to any self-teachers

you need at least a strong set-theory foundation

and i studied more logic for it

[brittle socket]

Dami: Where's my Schroder

Hi Phenom

[bronze wedge]

Schroder is good, but so is Kolmogorov Fomin

Those are books of a different level than rudin

[toxic gale]

I self-taught out of Bartle and found it pretty doable. Bartle writes quite well. Though it doesn't touch topology until last chapter I think.

[toxic gale]

Ayo!

[brittle socket]

Geography memorisation is cancer

[velvet dagger]

Lmao grass

[neat lintel]

Is it still possible to do original research on the gamma function?

Or has everything been discovered yet?

[solid snow]

We can’t tell if everything’s been discovered

[dense belfry]

It seems like a pretty shallow topic to try to do original research in, especially considering the fact that there is likely 100+ years of research on that function which you don't know about

And especially if you don't have someone giving you a problem to work on that you know is approachable for you and means something

[bronze wedge]

Probably better to find another area of research

[flat scarab]

Is it possible to algebraically solve a^x = x in terms of a?

Or do we need a value for a?

Or is it a case for Newton Raphson/cobweb diagrams?

[bronze pelican]

I tried to look into the history of research surrounding the Gamma function and found this quote by Phillip Davis: "each generation has found something of interest to say about the gamma function. Perhaps the next generation will also."

Forget special values of zeta, let's talk about special values of products of Gamma functions

[ancient flame]

ew

why is it written 2^4 and not 16?

[vivid halo]

oh god yeah I played around with these recently

[tender tulip]

let F/K be an algebraic field extension,

If Aut(F/K) is finite (nontrivial), then is the extension a finite extension?

this does not extend to transcendential extensions, correct.

[odd narwhal]

Wait my bad

I had the inequality the other way around

[tender tulip]

Or is any extension with a finite auto group necessarily finite

[odd narwhal]

It's actually |Aut(F/K)|<= [F:K] so I'm not sure if that means the extension is finite

https://math.stackexchange.com/questions/3748042/finite-automorphism-group-of-infinite-extension-of-field-of-positive-characteris

Seems to be false

[tender tulip]

i intend to comprehend the fund theorem of galois theory without comparing orders because that method seems insufficient to me

the best alternative I’ve seen is via primitive element and using the group quotients

[tender tulip]

what I want to understand is what specifically about finite galois extensions creates the bijection

For example:
Let A/B/C be a sequence of infinite algebraic extensions.
if A/C is galois, (defined via automorphiams), then is A/B?

[queen crown]

Yoyo

2nd line

Correct?

[blazing pawn]

#❓how-to-get-help

[queen crown]

Ik how to get help

oh

Wrong channel lmso

Lmfao

[blazing pawn]

[blazing pawn]

What does this mean

[tender tulip]

without using inequalities on the degree of the extension or order of the galois group/subgroups

[blazing pawn]

So you want a reformulation of "given a finite Galois extension E/F there is an order preserving bijection from intermediate extensions K to subgroups of Gal(E/F) sending degree n subextensions to index n subgroups"

that does not mention the order/index of the subgroup or the degree of the corresponding field...?

[tender tulip]

i want to prove it without using such

[blazing pawn]

so you want to prove the existence of the order preserving bijection without making reference to the specific degree of the extension?

[tender tulip]

yes

what property of finiteness

induces the bijection

[blazing pawn]

getting a proof of that is not particularly hard

explaining how the infinite case works is harder and involves talking a lot about topological groups

[tender tulip]

The topological group explanation seems like it piggybacks off of intermediate finite extensions

[blazing pawn]

What

[tender tulip]

I read a little into it but it didn’t make a whole lot of sense

[blazing pawn]

you probably frankly dont have the prerequisites to understand it

I dont think you know much about topology

[tender tulip]

no, not really besides what a topology is

[blazing pawn]

But the point at which finiteness is utilized isnt hard to see in the proof of the finite case i dont think

[tender tulip]

and the basic ideas of hausdorf-ness and compactness

all of the proofs I’ve seen use inequalities on orders and degrees

[blazing pawn]

the point of the bijection is basically to say that if you have some finite galois extension E/F with galois group G

[rocky oak]

Quick question before I get in a help channel, is boolean algebra considered maths?

id say yes but ya know, dont want to sound dumb lol

[zealous garden]

what's a hausdorff space

[tender tulip]

every two elements of the set the topology is over have a pair of disjoint neighborhoods

[blazing pawn]

suppose we have H with fixed field L and let K = Gal(E/L). we wish to show that H = K, yes?

[tender tulip]

yes, and the other way around

[blazing pawn]

The point here is that you can easily directly see that H is contained in K and that the degree of H is [E : L]

[zealous garden]

yes I know that

[blazing pawn]

and K is the group of automorphisms of E/L

[zealous garden]

but what is it

[blazing pawn]

and by definition there are at most [E : L] automorphisms of E/L

hence |K| <= [E : L] = |H|

and since G is finite and H and K are two subgroups of the same order with one containing the other, they are equal

[tender tulip]

my interpretation of it was that it improves your ability to compare elements by the open sets that contain them. Hausdorff Spaces essentially allow you to “isolate” points from eachother

i forget specifically what I wrote down for the justification and did a little drawing

i used an analogy of a city

[blazing pawn]

if your extension was infinite and G was infinite then these sorts of cardinality comparisons wouldnt imply anything

[tender tulip]

but I’m trying to avoid that

[blazing pawn]

You literally cant

this theorem is literally not true for infinite extensions

you are going to have to make reference to the key properties of finiteness

[tender tulip]

is there a way to prove it without referencing the degree of the extension besides knowing it’s finite

or what properties are equivalent to a finite extension

[blazing pawn]

what does that even mean?

[tender tulip]

i’m trying to think of a better way to explain it

I’m really trying to avoid touching on polynomials

[blazing pawn]

it sounds like what your asking is "is there some theorem about finite extensions which we can reference here without explicitly comparing the cardinalities of various subgroups" but the proof of said theorem is going to rely on that so

No

[tender tulip]

which the proofs of the inequalities between subgroup order and field extension degree are determined by in all the sources I’ve seen

[blazing pawn]

like the literal key content of what is going on here is that in the finite case two things of the same degree related by containment are in fact the same

whereas in the infinite case they are instead related by closure

i dont really understand where this preoccupation is coming from but if you find this unsatisfying i suggest you step back and work through this stuff again until it feels more intuitive

[wooden flax]

this book series is amazing https://en.wikipedia.org/wiki/Great_Books_of_the_Western_World

I went to my local library and they had half of the books in stock

checked out like 5!!

got descartes, fourier, hegel, and a couple more i forgot

[onyx idol]

how do you determine the midpoint of collision between 3 particles

[brisk briar]

Hi guys random but I'm trying to make a joke, when $a^2 + b^2 < c^2$ that means that the triangle is acute right?

[fathom swallow]

Not Trout

[full isle]

a squared plus b squared equals c squared plus two a b cosine theta

so 2ab cosine theta is positive

[brisk briar]

hm?

[brisk briar]

wait isn't a^2 + b^2 = c^2

OHHH

[open aspen]

for a right triangle

[brisk briar]

okay i get it

this accounts for any other triangle

and a^2 + b^2 is less than c^2 when cos theta is positive

because for 0 < theta < 90 its positive

then for 90 < theta < 180 its negative

[unreal epoch]

AYO

[brittle socket]

Lol didn't notice that that got so many reactions

[stone ferry]

@potent plume Get in here, post your question so we can all look at it some more

[potent plume]

Ok i understand

[stone ferry]

Alright I'm gonna drop this instead

Can anyone solve this

With no other information

Just 2 equations on a section of masking tape

This was posted in a help channel by another person, we have no idea what to do and it's funny, so I'm putting it here

[neat frost]

Wrong

That’s not masking tape

Unless it is

It looks more like the margins of a piece of paper

[stone ferry]

That really looks like green masking tape / painting tape

[rapid trench]

Again, the problem we had before is that the don't have enough information from the question by itself, and just An=n²+4 or An=n-4 are not questions by themselves; not only that, they don't mean anything specific like that.

[potent plume]

You know i fold it the paper

And

[neat frost]

Though the blue line at the bottom looks like the rule in a piece of paper

Could be masking tape tho

[stone ferry]

Hmm maybe

Okay

[potent plume]

Do you think this is the wrong or correct

@stone ferry

[stone ferry]

So you already knew the answer?

Read help-4

[potent plume]

You know im dumb I don't know

[stone ferry]

You're right, but it's funny

Because it was funny

[potent plume]

Im telling that my answer is correct or not

[potent plume]

I beginning rn in this server don't you ever think this is funny

[stone ferry]

I got laughed at in my first help channel too

It's tradition

[potent plume]

What kind of tradition

[stone ferry]

Hazing

[leaden torrent]

yeah no

first off this is in incredibly bad taste

airing out someone's shit to make fun of them

but also you know that posting questions outside of help channels is against the rules

the fact that you think its "funny" doesnt change shit

[potent plume]

Is the an= n² +4 = n-4 is correct

[leaden torrent]

especially since the apparent "humour" comes from mocking them

[stone ferry]

That's fair

[potent plume]

2+2

Equal

[leaden torrent]

sigh

[delicate panther]

tfw u have a question about a question you are not sure what the question is and it develops into a series of questions and eventually you question your sanity

me rn

[bright hill]

I'm dying lmaoooo

[full isle]

lol

arent they okay with this behavior

i dont see the issue

they both having fun with it

[wooden flax]

@stone ferry im pretty sure the person was talking about a series a_n

where they defined what a_n is

[open aspen]

why do we even care so much lol

another day another poorly phrased help question

[full isle]

@open aspen

[untold sapphire]

This is annoying to read.

[deep mango]

lmao

so bad

[neat lintel]

do we even use the term "imaginary numbers" anymore?

[open aspen]

What is the OP to this?

[stone ferry]

Better question: can you call 1+2i an imaginary number or is it just a complex number

[open aspen]

It's a complex number

I feel $z$ is imaginary iff $z = Im(z)*i$

[stone ferry]

Just multiples of i

[fathom swallow]

Migillope

[open aspen]

Yeah

Otherwise 1 + 2i is also a real number by similar logic

[zealous garden]

$z$ is imaginary $\iff z + z* = 0$

[fathom swallow]

wraithlord_koto

[zealous garden]

Where z* is the complex conjugate

[full isle]

its fax tho

god bless dick boechards

[storm sage]

why not just write re z = 0 lol

am I missing something

[zealous garden]

Because Re(z) is magic

Z* is not

[storm sage]

Lol what

how

[zealous garden]

Re(z) is a Blackbox

The complex conjugate is basic

[bronze pelican]

Re(z) = (z +Conj[z])/2

[untold sapphire]

No, I think I probably agree with Borcherds. I'm annoyed at the whining saying the question should be shut down

Give it a rest. just let people ask questions

What do you call a discussion site where nobody can discuss anything

[full isle]

thats what i mean

i agree with the third person

[solid snow]

Stack exchange when you dont write up a 300 page pdf detailing the context of the questions, it’s implications, the history of math related to it, and an autobiography

[untold sapphire]

Hahahah

[solid snow]

They just shut down questions for no reason I don’t understand

[neat lintel]

what is the name of the operation where u invert the digits of in binary

[zealous garden]

xor -1

Bit twiddle

[wild lantern]

Bitwise complement/bitwise negation.

[neat lintel]

Hi

[leaden finch]

OMG SWEAR

[sinful mica]

https://www.youtube.com/watch?v=Sp9B7raW_O4

sorry for the poor resolution on the equations

[uncut socket]

@hollow sundial Did you know that greatest integer function is abbreviated GIF, so then is it pronounced as gif or jif?

[hollow sundial]

haaaaaahaaaaaaaaaaaahaaaaaaaaaaaaa

it's pronounced fleur

because i'm @themateo713#5303

[winter hinge]

What

[winter hinge]

Anything that requires my presence ?

[hollow sundial]

no! meant to wrap it in backticks

[uncut socket]

Your presence is always needed

[tame breach]

Hi can someone help me in #prealg-and-algebra

[light needle]

yall should read me new blog: https://aareyanmanzoor.github.io/2022/08/26/Stone-Čech-Compactification-and-Multiplier-Algebras.html

[wooden flax]

whats unfortunate about az

[light needle]

many, many things

[wooden flax]

:((

ill read your post tmrw

[eager trout]

John's saying he's unfortunately alive on earth right now

[wooden flax]

where?

oh

LOL

john model theory arc is over

[light needle]

oof dw ill get backon to it when AWS roles around

[wooden flax]

amazon web services?

[light needle]

https://swc-math.github.io/

[hollow sundial]

Arizona Web Services

[eager trout]

Speedy web compiler?