#serious-discussion
1 messages · Page 412 of 1
yuS
i think think x think
Thonk fractal, thonk!
in the comic it was think mark think
was it really!

^^^
Y’all should read the comics, it’s 144 issues long and p good imo
I honestly agree
@ moderators
Man of culture liquid
give back
why did you lose it
nah I just left for a while
oh
then yeah lol u could get it back
it's up to u
no presure
oh
idk if it's automatci or not
yeah sure I'd like it back
okay cool liquid
welcome back
it's concentrated in specifically xenoblade chronicles
i am a closet weeb
we do not speak of this 😌
i mean your a mod on a math channel aint nothing closeted about it
really? I think this server seems pretty popping
best server in this network i have been in
wheres the data collection
i was comparing it to real life traffic situations which sometimes go like this
what metric we using
they make a new lane to reduce traffic, but it ends up being clogged anyways
i guess here it worked fine though
from my inspection
yeah but more car anyways tho right
🤔
if anything more people are being directed to #❓how-to-get-help
we figured
if #discussion is so good
why isnt there #serious-discussion
so we made it
discussion-2 is 2-good
the mods actually wanted to make discussion-0 through discussion-9
petition for discussion-3
one discussion for each help channel
nah next up is #serious-discussion-2
nested discussions 
but we convinced them that was a bad idea
discussion-4: the search for discussion-3
you shouldnt be
no bulli 😠
sideurk has been banned.
Namington = sideurk = jacobian = waldo
waldo
We finally found waldo
what's waldo was my favorite puzzle in elementary
yes and after this, we take the warp pipe to discussion 4-2
inb4 fast 4-2
@deep mango Thank you for the ping - I slept fairly shortly after 🤣

remarkable
how will they charge a transcendental amount of money from your account
sometimes CIBC randomly charges me $60+ service fees and then refunds in within a day
thats an irrational fee

they gave me a nice phone call yesterday saying I should move my money into a real savings account
Does it?
I've already got a savings account, so just move it in there and then you won't have to hassle with setting one up!
Isn't it just 1. make appointment at bank 2. go to bank 3. "Hi can I move my money into a real savings account" 4. do some paperwork
Well, I thought I had a savings account but it turns out its just a chequing account thats called "savings"
surprisingly this wasn't a scam Ultra
does this not seem like a lot of work to you
Suprised pikachu face
Lots of social interaction
It might be a significant amount of mental energy
But from like
Time
It's an hour max
thats true
I did this earlier this summer
I think my barometer for this stuff has become wonky since covid lmao
I'm pretty much of the opinion that if I need to do anything besides make a phonecall it's too much work
I'll get over that soon enough


Similarly
Anyone who calls a meeting
For something that could have been an email
I hate them instantly

u gotta learn Vietnamese now
weird question
why does quantum physics specifically have a reputation of being like, impossibly hard and counterintuitive
at least among laymen
all the physics undergrads i know struggled way more in their PDEs or geometric relativity courses
pop sci
is it just because those subjects are more amenable to cutesy youtube video visualizations of phase diagrams and rubber sheets?
Yes
maybe that doesn't explain it fully because string theory has that same reputation I think but I don't know if thats due to popsci stuff as much
well string theory is just fucked in general
"trust me guys, E x ℝ⁸ for E an elliptic curve is definitely a natural setting for the universe's physics to be based off, we didnt just add copies of ℝ until it matched experiments"
does relativity not sound cool
i told someone i studied math
stuff like Schrodingers cat also feeds into it
relativity is a boring word compared to quantum
quantum representation theory
topologgical quantum field theories
etc
the jargon comes up
still a dumb question
mathematicians just wanted in on the cool fancy word
good way to get research grants

lol
Sheeeesh

yes
Special relativity requires less math than QM?
"philosophically exciting" - a bit dubious
Eh he's not wrong
hmmm... dubious.... strokes goatee
how exciting
fluid dynamics near the bottom
I’m blocking xkcd
Like sure, "philosophically exciting" is tricky to formalize, and one could perhaps make a case that QM shouldn't be so philosophically exiting, but it's hard to deny that it is
QM says a lot of weird counterintuitive shit
Physics is bad applied mathematics is good
Like?
i like physics tho
"Particles can be in 'multiple places' at the same time", "observing something changes its state", "P(A or B) < P(A)", quantum entanglement, quantum tunneling, etc
Fluid dynamics is just "water go swoosh"
"P(A or B) < P(A)" ???
😡
Like sure, it's extremely fucking hard to describe exactly how water goes swoosh, but at the end of the day, that's all you're doing
Double slit experiment
I don't believe in reality really so who cares about the rest of those but "P(A or B) < P(A)" doesnt make sense
Some locations see less light when both slits are open then when only one is

Union of two sets must always be greater than or equal to the cardinality of the larger set
Even though that makes absolutely no fucking sense
ow my scroll finger
Middle mouse, mouse to the bottom of the screen, afk, win
press page up key
just too much philosophy for my finger to handle
But yeah you can roughly have P(A or B) < P(A) in QM
no
Is that not true?
I have no clue but I have a visceral reaction to it
I'm talking about some specific point in the double slit
Yeah I know
Not the overall distribution
The probability of anything happening is 1/2 because it either happens or it doesn't
The light at that point is determined by the distribution
Like that's how superpositions add is it not
ban this joke
Measure theory btfo’d

Wtaf
What is this new universe
Is this some weird non-ZFC system or something
Where I say weird unintuitive shit, people disagree with me, and then I turn out to actually be right
Truly insane
Sullying a man for asking a question is bad form
i dislike this
I immensely dislike this
i never said you were wrong I merely disagree with the idea that its true
Jesse btfo
I’m going back to algebra where things make sense
Probability in QM is weird as fuck
You can have P(A) = P(B) = 50%, but P(A or B) = 0
iirc
Oh ok now it makes sense


Fr I actually get why just from that
It’s like if you had a polarised filter at a 45 degree angle, there’s a 50% chance a horizontal wave will pass through, same for a vertical, but the composite of both will never pass through
That’s how I’m thinking about it anyway
That's P(A and B) is it not?
Hmm
this is why MP is a failure
Well no cause even if just one component goes through it would “pass” so it’s A or B??? I think???
this feels like the result of an extreme abuse of notation rather than an actual difference in ideas or anything
Just take 2 qubits in states \
$\sqrt{2}/2 |0\rangle + \sqrt{2}/2 |1\rangle, \quad
\sqrt{2}/2 |0\rangle - \sqrt{2}/2 |1\rangle$
Gamma Once More
I believe here the probability of observing any one of them in state 1 is 50%, but in the composite system, both are guaranteed to be 0
Just take 2 qubits in states
$\frac{\sqrt{2}}{2} |0\rangle + \frac{sqrt{2}}{2} |1\rangle, \quad
\frac{\sqrt{2}}{2 }|0\rangle - \frac{\sqrt{2}}{2} |1\rangle$
Buncho Dragons
Thank you for cleaning that up for me Buncho
Was too lazy to type the fracs out on my phone
I mean the thing about QM is that it's been confirmed experimentally, right?
sqrt
Like many many times
doesn't mean its not crankery
sqrt sqrrrrt
So we've actually seen physical examples of P(A or B)<P(B)
Such as double slit
Where P(X) literally means "the proportion of the time the experimenters observed X"
Literally the most indisputable definition of probability there is
I'm cryin in the club rn
Literally just look at the results from double slit
I think you need to put a big asterisk on that "or"
I feel like the issue there is it's easy to miss just how fucking weird double slit is at first glance
Do I?
Is it not?
nooooooooo it's a different way of doing probablity, as ultra said
This is literally the proportion of the time that the experimenters observed an event
"""""""true""""""""
A discrete event
whatever, I stand by the fact that applying anything related to logic to reality is stupid
yeah yeah I'm not saying it's a wrong way, but under the normal methods of doing probability it won't work due to the way cardinality behaves under union
doesn't this like
If not "the proportion of the time something happens"
I'm pretty sure this reasoning is actually what's behind Bell's theorem
In some sense

Maybe this is when I finally cross the line and say something wrong
in the wrong sense
Featuring 3Blue1Brown
Watch the 2nd video on 3Blue1Brown here: https://www.youtube.com/watch?v=MzRCDLre1b4
Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics
Link to Patreon Supporters: http://www.minutephysics.com/supporters/
This video is about Bell's Theorem, one of the most fascinating results in 20th century physics. E...
this just means that trying to axiomatize natural systems is silly 

Jesse is trying so hard to cope rn
ive been saying this
Based take from Ultra
I mean the thing is, we have a pretty good formalization of QM that we can apply to the real world and make pretty accurate predictions with
almost a brofibration
Probability behaves in a perfectly logical way in QM, it's just also a completely bullshit way
The universe should not work like this, but we still understand it kinda
I get that QM is like ""accurate"" and ""applicable"" but I am coping and think its dumb
P(A or** B) < P(A).
**Not really or
solved
I get that QM is like ""accurate"" and ""applicable"" but I am coping and think its dumb
Yeah not really
Based on my very limited understanding of QM, the asterisk would go on the "or" if it went anywhere
got it
(^^)
^O^

凸(¬‿¬)
cope

quantum demagogy arc, i see
I am not angry I just think that the thousands of people that have dedicated their lives to this subject are objectively wrong.

I mean how do you keep a straight face and write down P(A or B) < P(A)
Clearly I was born in the wrong century
Should have been born in the early 20th century when it was still in fashion to call Cantor a crank and spend your time trying to disprove QM
cantor is a hack fraud
what do people have against Cantor?
beard
theyre just jealous
Dear Cantor: you claim the natural numbers are "countable." Ok then count them, I'll wait

who even wants local realism 
I've just be talking to myself for the past hour
Edd merely doesnt understand the depth of the subject that me and Gamma are discussing
What if Gamma is actually jesse's alt
What if this entire server is just all Hank's alts
yes but edd banned morza and got dmeoted
edd was never mod
what
you set yourself up for this one

You can't estimate my level of thinking if you don't know even elementary terminology, so this is just emotions.
I only speak the truth
Yes
Wait what happened
Are y’all talking about physics
Concern
no
i just drew it
or actually I didnt draw this one but
I drew the original
this is the 5th iteration
what's the convergence rate?
im still waiting for my pfp to become an emote.




Who has the best pfp on this server
me.
namington put a lot of effort into it
My pfp is not the best
Can't vote yourself
Me
Ultra
Nami
Brofib
...
...
Slim
I vote brofibration
PiCrew 
I beat Slim!

i still haven't made a picrew ><
woog has a nice pfp and so does mniip

I remember when Namington's pfp was a bird or something
Mine is usually a cross, and therefore is the best
I like Faye's alot too 

mine is a cookie cat from steven universe, so its goodness is bounded from below
shamrock
absolutely not
ultraproduct
it's literally carseat headrest
ultra and sham
no
it's a wizard
oh right
good shit
I remember the tweet
shoulder width
god bless lime soup
it's called "swag" you wouldn't get it
Wimdth
wait is that not your actual face
weird tongue
was my pfp for a bit

when the phi^2A hits
based arnold
I think I finally have a pfp I actually like
what is it supposed to be lol
Yeah mine is a cat
,av Gamma Once More

it's a stork
Clearly a cat as you can tell

,av arnold
4 members found matching arnold!
1. arnoldfini#0410
2. Arnold Berbunger#0688
3. arab arnold#9017
4. Arnold Schwarzenegger#8180 ```
Please type the number corresponding to your selection, or type `c` now to cancel.
will be my new pfp
5
Member selection timed out.
"Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap."
we lost fone?
damn i have never seen a more based intro
rip


pepe emotes were removed
tteppa here
no
yesterday
was it discord copyright or racism tterra
definitely not tos

they clearly didnt have any negative connotations on here lmao
we've got the important ones
just make jesse honorable so he can read the #「ivory-tower-emeritus」 discussion and we don't have to repeat it
to be clear about what slim is saying, it's not pepe emotes. it's groyper emotes (don't look up groyper unless you want to go on a list) and the physically defomed pepe emotes.
that should probably be removed
we still have to sort out the rest

there are quite a few of them
sure you can
metal, why isn't jesse honorable yet?
i don't think im at liberty to say
etaleneenya
politics
it's gonna put you on my list
gpa
I think it means Im a bad user
Wait what emotes got removed?
lmao
read up
do they keep scores
only for jesse


i am putting the mod on the spot 
also,
demote ryc to trusted
he will say he was memeing
or that
i remember when i was added to honorable and the first thing that was said was tterra going "before jesse and poros? really?"
ryc for owner
Demote ryc to owner
(which i agree with of course)

look ryc i like you but they;ve been here for like 20x the time you have
Wait mniip keeps scores on us?
yes.
yeah but tterra its clearly not based on time lol
Based on what?
that's how mafia works

Is it automated or
based on your DN score
what's deez nuts
It's based on how quickly you can suck dic
we're talking about the magic numbers that make the active role go
it's based on scores. i have an extremely high score due to helping out in the highest value channel, #advanced-analysis
im very quick
formula: (messages in question channels/messages in discussion channels) - (chill messages)
What's my score mniip
yes slim
hear that, jesse? better reach 20k messages in a month
I am very active
Gamma your name is confusing
Why
wait why is jesse not cool?
Oh huh Liquid is honorable again
I asked.
You don't have the required permissions to ban members here!
don't forget that there's nepotism involved here. ange is my blood relative.
Idk I just get confused by it lol
jesse helpers role arc
Well I wasn't Gamma for like half a year
dark green 
Maybe a bit more
yeah true. I like pink tho 
And now I'm back
adv helper
BIG ME PINK COLOUR
adv helper 
Because Lagrange was an annoying name
big me
,whohas advanced helper
Couldn't find a role matching advanced helper!
,whohas adv helper
Members in Adv Helper*
======================
1. Namington#1983
2. doubledual#2930
3. Daminark#6041
4. 88ddda#7872```
ill take adv helper over honourable 
I think you need to help people for that
lmfao
what is the difference between helper and adv helper*?
adv
adv helper is dark green
Wasn't adv helper a failed experiment
I'll take admin over advanced
oh, advanced helper?
That didn't go anywhere
You can't ping advanced helpers
this is the reason I am not yellow name as well
Actually I should probably change my name to Gamma Once Again
We need to make honourables pingable.
adventure helper
There was some ideas about separating helpers for higher math from lower math (whatever that means)
And a couple of ideas were tried
advecting helper
@honorable

You should be able to ping honorables but you get auto muted for 3 hours if you do
@bronze pelican they disabled that a while ago
@tteppa

yeah I will just go with adventure helper, sounds cool lmao
How often are honorable added
moldi is trusted
@polar panther for honorable
What is trusted
trusting moldi 
i still dont know what trusted means
do people trust me
who are you
no
I trust u xt1
what is the banach-alg thing?
i don't trust a single person here

Lol asking who are you on discord is pretty funny

but like what does it mean for someone to have it?
I trust everyone in 
Does that include you
people do have reputations around here 
absolutely nothing
🦶
this is haram
I wouldn't mind #suggestions access lol

🦶
🦶
¯_(ツ)_/¯
suggestions is dead
What even gets talked about in the ivory tower
The private feet channel is honorables+ only
slim there is a deep state conspiracy to keep me white name
how do i get honorable
whether pepes shall be removed or not 0.0
Ping Daminark
OKAY WHO WANT'S HELP
meeeee
Wait you need to help people to get honorable?
No
someone pick a textbook and we'll all alternate helping each other with questions
someone plz ask what 1+1 is
Involving considerable delays
then I will help
Waig there's actually a proper nomination system?
and get honorable
well the way you get nominated is by being somewhat helpful i would argue
if I have been nominated this is not true
Who gets to nominate
yellow names
Why is natural log called ln and not nl?
Honorable can nominate for honorable and trusted
I am curious what the mods talk about
french
So it is your fault that jesse doesn't have honourable? 0.0
I suppose they want yellow names to be role models or something lmao
"ln" "le natural"
Also why was a new notation created for logarithms, why not just say a^c = b?
Jesse has been nominated many times
I'm pretty sure I've been nominated by quite a few people actually
it is ange's fault
integrallllsssssssss
I'm not joking when I say its a deep state conspiracy 
Nominations can happen whenever
going to start using nl, i refuse to speak french 😤
Also why didn't they just make a symbol for log instead of have it be log?
I remember last year
the final judgement comes from the mod team
it's like three variables being multiplied
that sounds confusing
can you tell me how many times Ive been rejected 
The decision comes from the mod team with considerable delay
i've been here for like 2 months
Dami was holding back on giving Max honorable just to mess with him
for ryc it was genuinely just delay
rip sin, tan, cot, csc, arg, img, ker, lim, cos, sec, abs, Hom
what
exactly, they could've made symbols for all of those
same with Loch right
would've looked better too
but why would they
it feels like you've been here for like 10 years lmao
Loch should have got it like 6 months ago lmao
i actually didn't know loch was proposed maybe i forgot
Have I ever been nominated 
yes, it does feel like that, doesn't it?
or maybe i wasn't mod then
Yeah the mod team doesn't tell anyone anything
nominations are handled with considerable delay
it is sadge
Hey if I ask a question and someone asks a question on top of it like 5 minutes after I post it, should I say something? I just don't want to be rude or anything.
you can tell them the channel is taken
Are there logarithms which use imaginary numbers?
yes, there are
jesse and I stay forever oppressed by the mod team
Yes, logarithms use imaginary numbers.
see the issue is like if we say no, then what happens after a while when the mods do feel like said person should have honorable

Okay cool. Thanks ^^
is my concern

what do you mean?
do you guys not reconsider people lmao
are you ever able to have an answer to logarithm of a negative number?
one rejection and its over 
yes, the complex log works fine for that
oh shit i'm about to beat jesse LOOOOL
i guess i will ask then
like Log(-1) = i*pi on the principle branch
Full name: ranyakumoschalkboard#7228
Nickname: ryc
Presence:
Online
Activity: Nothing
Device: Active on desktop
Seen in: 1 guild
Joined at: 07:22 PM, 01/04/2021
(67 days 0 hours and 1 minute ago)
Created at: 05:24 AM, 13/01/2019
(876 days 13 hours and 59 minutes ago)
ℌonorable, Advanced, Very Active, , Analysis
38019. Alkizar#3476
38020. Mulberry#6976
38021. stewSquared#7231
38022. > ranyakumoschalkboard#7228
38023. Jay14641#7662
38024. matthew#5876
38025. girantinas#8133
Full name: jesse#3659
Nickname: jesse
Presence:
Online
Activity: Status:
P → Q, P ⊢ Q
Device: Active on desktop
Seen in: 1 guild
Joined at: 05:31 AM, 24/08/2020
(287 days 13 hours and 52 minutes ago)
Created at: 02:14 AM, 03/09/2019
(643 days 17 hours and 9 minutes ago)
Not very ppl, Advanced, Talks, Talk Announcements, Streamer, Very Active, Logic
20576. Prince Lux Grey#0001
20577. The-Elite#9627
20578. jtay_313#8299
20579. > jesse#3659
20580. Mega Euler#9607
20581. power#7555
20582. Vvhisper#7166
Lollllll


They don't teach this in algebra
For some reason
I thought I talked a lot on here 
probably because it's analysis
This is what ryc does instead of calculating lattices of subgroups
you learn this in complex analysis
this is all your fault
Is it?
i wonder how many of my posts are one word
Why do they teach imaginary numbers in algebra than but not logarithms of negative numbers
probably a number of them
they're poorly behaved
the complex log is an incredibly weird function
Holy shit Namington had 220k
because you need more stuff. complex numbers require special care
wow
I wonder where sloth is on the leaderboard now
I'm sitting at a chill 5,022 messages
t!top
Viewing server rankings • [ Angetenar#4727 ]
that's not enough to understand the complex log
omg field extensions 
epic win
anyway complex log is related to euler's formula, which says e^(ix) = cos(x) + i*sin(x)
i have more than 2k results on this account i need to go outside
,ui Gamma Once
Full name: Gamma Once More#2735
Nickname: Gamma Once More
Presence:
Online
Activity: Nothing
Device: Active on desktop and mobile
Seen in: 1 guild
Joined at: 03:50 AM, 19/04/2021
(49 days 15 hours and 35 minutes ago)
Created at: 08:12 PM, 17/11/2017
(1297 days 23 hours and 12 minutes ago)
Advanced
39918. Zac#4811
39919. Positivityy1#4540
39920. ionPie#2941
39921. > Gamma Once More#2735
39922. Frog guy Peep...#6415
39923. Foodcoloredfruitypebbles#2527
39924. georgcantorbfam#6442
BRUH
so you can understand complex log after understanding euler's formula
stop spamming that here
did you change your name or something
oh okay thank you ryc
I've never seen you before today
but it's still kind of hard to understand
and thank you to everyone else
np
Damn I've been here longer than Jesse
phd student in what?

math
If you count when I first joined
yes i am 
phd student in weeb culture
pretty huge dolphin
What so you study ryc?
I feel like I've been here for way too long lol
PDEs and dynamics
,ui Namington
Full name: Namington#1983
Nickname: Namington
Presence:
Away
Activity: Status: 8620
Device: Active on desktop
Seen in: 1 guild
Joined at: 08:19 AM, 25/02/2019
(833 days 11 hours and 7 minutes ago)
Created at: 04:04 AM, 20/10/2015
(2057 days 15 hours and 22 minutes ago)
Administrators, Moderators, ℌonorable, Adv Helper*, Advanced, Very Active, 
6559. Paris#2855
6560. AD#0021
6561. Gemma#8894
6562. > Namington#1983
6563. goodgue#3769
6564. Onthemoon#6524
6565. Triseth#0262
so what chance do i have of understanding it considering i'm in high school
so
I want to be a phd student 
rip
No.
these ppl
I am a phd student
smh my head
What do you study ange?
yes I'm doing algebra for my thesis
Applied fluids
i'm a pretty huge dolphin myself
Judging from this, moth should have honourable 0.0

Moth does have honorable
what is your thesis
here's what i get about complex log. uhhh, it's got a spinny riemann surface that looks like a spiral staircase. and, you always have to branch cut by some path from the origin out to infinity if you want to use it. and, the argument principle is a thing
that's all i know
Monodromy
nope, don't know that

and this happens because e^(2pi*n+x)i = e^xi
google "R/Z ring" for more info on that one
yes
i understand more than i'm letting on
why are these thijngs called correspondences
why is natural logarithm base in exponential formulas?
are they literally from like private letters
i'm trying to hide my knowledge about complex log so that in the future people will underestimate me

this is kind of hard to understand until you see calculus
Cause e is swag
the reason ends up being that e^x is the function whose derivative is itself
we should use pi instead.
and ln(x) is the function whose derivative is 1/x
that's why you want e and not something else
-ln(1-x) has a nice power series
and that's why e is the "natural" base
Well I guess I'll go learn calculus
because of the power series
You can look at the Taylor expansion
depends on what you mean by 'why'
Or at least not remember
Also that’s the definition of e
just take the power series and differentiate term by term
because of swag

Is analytic geometry, such as conic sections important to know for calculus because I forgot it all?
Alrighty, I'm going to go learn calculus and come back once I've learned it all
Have a nice life people, untili next time
Oh right and then you define e^x by its power series
farewell
goodbye

all of calculus...
e^x defined by its power series >>>> defining it by compound interest limits
It's tricky when everything in analysis has like 5 equivalent definitions
Don’t do it analysis is a scammmm
define e^x as the sum of hyperbolic sine and cosine

For example I have no clue what trig functions are
Wtf
They go spin spin
they go spin spin
It’s the real and imaginary parts of e^ix
They go spin spin
Yeah I know that
Sine's just a function that models our heart beat.
This that is
They spin at the correct speed
And I know the properties they have
set me back several years in my career in mathematics. However, it had a redeeming feature: it
led me to realize that I had no idea what a differential equation is. ```
But like how are they defined
u guys rn
How long does it take to completely learn calculus? I have the entire summer
about 30 minutes
"completely"
i mean it totally depends
Calculus has an ill-defined upper boundary
I have an ill defined idea of what this means
no one knows calculus of variations so
use khan academy or pauls online notes + 3blue1brown essence of calculus or sylvanus thompson calculus made easy
In a sense, all of math is just fancy calculus
There is no “all” of calc
Calc 1 and 2 can be done in like a few weeks, I guess?
Wrong
I don't think so
I was planning on using khan academy
You could probably learn highschool calculus over the summer if you went very very fast
Algebraic geometry is only useful for algebraic analysis which is just fancy d-modules
in the wrong sense, sure
I already did some of the limits part in khan academy
So I know some calculus
It was effortless
that's good
Who gon tell im
continue along there
Arithmetic derivative
I'll be back when I learn the entire limits section
Bye
Wait so how are trig functions defined
We do study discrete limits
Derivative on polynomial rings
In analysis
Differential galois theory
Is it just through e^x
Power series
Oh yeah that would make sense
Or through e^ix
Differential galois theory is something I will have to know eventually actually
both are pretty much equivalent
computability theory is just numerical analysis
As well as differential algebra

Stop
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Yes
Saying x is only useful for y is pretty gross tbh
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Wait is the derivative a homomorphism of a polynomial ring to itself
Even if it's just a joke
hi liquid
Hmmm
Product rule
Yup doesn’t map 1 to 1 got it
Im confused as to what this question means
derivative of a homomorphism...
yeah, algebraic geometry isn't useful for anything how dare you say it's useful for y!

The derivative is a vector space homomorphism








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