like sigmas are written simultaneously
#serious-discussion
neat lintel
Like
leaden torrent
if you're familiar with programming, nested Sigmas behave the exact same way as nested loops
neat lintel
leaden torrent
you just take a sum in your sum
neat lintel
Incidental i read this the other time
olive kayak
if you're familiar with programming, nested Sigmas behave the exact same way as ...
sadly im not
neat lintel
Maybe look up like double summations idk
olive kayak
it gets really confusing if its entries are indexed
leaden torrent
[\sum_{i=1}^{m}\sum_{j=1}^{n} f(i, j) = \sum_{j=1}^{n} f(1, j) + \sum_{j=1}^{n} f(2, j) + \dots + \sum_{j=1}^{n} f(m, j)]
fathom swallowBOT
Namington
olive kayak
like this one
leaden torrent
[= f(1, 1) + f(1, 2) + \dots + f(1, n) + f(2, 1) + f(2, 2) + \dots + f(2, n) + \dots + f(m, 1) + f(m, 2) + \dots + f(m, n)]
olive kayak
from hubbard hubbard
fathom swallowBOT
Namington
olive kayak
it's not that I don't understand
i just get confused
and it takes long time to decipher what it means
like I have to write down some entries to get it
leaden torrent
it might help to write out some concrete examples
take some matrices A, B, C and see what these sums correspond to
neat lintel
backslash will stop discord from killing your messages
leaden torrent
backslashes \, not forward slashes /
neat lintel
Noted
ancient flame
I have my business exam today!
after today I can officially say that my summer has started
wooden flax
This seems obvious, but in R^1, the set a<x<b is open but the set a<=x<=b isnt right?
dense belfry
Yes, the second one is closed
Not open
Do you know a formal definition of open in R?
wooden flax
Do you know a formal definition of open in R?
Yeah, it is open if for every point p, there is an epsilon such that all points within epsilon from p is in the set
thats why i thought that was obvious but wanted to make sure i didnt have some misconception
dense belfry
Yeah the reason it's not open is because if you consider the endpoints, only half of an interval around the endpoints are in the set
Does that make sense?
wooden flax
Yeah the reason it's not open is because if you consider the endpoints, only hal...
this was exactly my thought lmao
dense belfry
Okay good
gloomy spruce
that looks like my uni notes
neat lintel
Abbott!
dusty compass
New Yorker on Grothendick: https://www.newyorker.com/magazine/2022/05/16/the-mysterious-disappearance-of-a-revolutionary-mathematician
sick burrow
Alexander Grothendieck was born in March, 1928, in Berlin, to Alexander Shapiro and Hanka Grothendieck.
So you're telling me that if he hadn't taken his mother's name he'd have been Alexander Shapiro?
That we'd be hearing about the great algebraic geometer Shapiro
deep mango
Based matrilineal naming tbh
wild tree
How do I tell a teacher I spilt water on my assignment and i need to have a extra day to do it
swift sinew
“I spilt water on my assignment and I need to have an extra day to do it”
chilly hull
you get a scratch paper stapled onto your assignment with those questions answered
wild tree
thank you SO MUCH
chilly hull
im sure your teacher will be fine with that
fair estuary
How do you get access to the advanced math voice chat?
next schooner
vivid halo
New Yorker on Grothendick: https://www.newyorker.com/magazine/2022/05/16/the-mys...
Research was still ongoing in mathematical domains termed “Grothendieck universes,”
ugh
this is what happens when non-mathematicians try to write pop math articles
dense belfry
Oof
fair estuary
>Research was still ongoing in mathematical domains termed “Grothendieck univers...
What is that?
warm chasm
chilly hull
wdym
if you're looking for when you learn about functions for your first time probably #prealg-and-algebra
functions are used literally everywhere in math
sick burrow
>Research was still ongoing in mathematical domains termed “Grothendieck univers...
Also the example of a category they give being "the category of triangles and uhh... things that relate triangles to each other"
sick burrow
Does it?
vivid halo
I mean to the extent that they completely misrepresent stuff in the field, yes
sick burrow
Sure the math in it seems questionable but does it give an inaccurate history of Grothendieck's life?
That seemed to be more the point from glancing at it
And does it misrepresent the scale of his contributions? Or just the contributions themselves
Also tf is this definition
According to Wikipedia you need inaccessible cardinals to get a model of this?
An uncountable model rather
mortal igloo
One has to think, this journalist probably had a lecture from a mathematician he interviewed and took notes from it in order to write this article
vivid halo
Grothendieck universes are equivalent to inaccessible cardinals
sick burrow
But why?
mortal igloo
The power set property looks very stronk
vivid halo
I mean that's just what the statement is equivalent to
sick burrow
Isn't that just "transitive set plus pairing powerset and union"?
vivid halo
also it's not just uncountable
they're larger than anything you can produce in standard ZFC set theory
sick burrow
I guess powerset gives you the "true" powerset
vivid halo
it's not the powerset that gives you most of the size here, it's the arbitrary unions
sick burrow
Well the union needs to be indexed by an element of your set
vivid halo
sure
but you can just keep going larger
the power sets give you successor cardinals
the unions give you limit cardinals
sick burrow
Oh I see you can take the union of things indexed by a set in your universe not just a union of things in a set in your universe
vivid halo
yeah
sick burrow
Wait no I might just be stupid
Because you can get limit cardinals in ZFC
Just not the regular ones
vivid halo
right
sick burrow
So Grothendieck universes have the same power there
But also ZFC can't build a model of ZFC either
vivid halo
the existence of one Grothendieck universe is equivalent to the existence of an inaccessible cardinal \kappa, since the set of sets with cardinality <\kappa forms a Grothendieck universe
sick burrow
Is a Grothendieck universe not just a set theory
I guess your power sets look different
vivid halo
the power set is the same
everything is the same
it's just equivalent to saying you have an inaccessible
vivid halo
sure if you have a Grothendieck universe/an inaccessible then you can build a model of ZFC
mortal igloo
According to Wikipedia, a Grothendieck universe's purpose is to provide a single set in which you can do math without Russell's paradox happening and having to talk about proper classes
vivid halo
yeah it's just a way of avoiding these things
again I think it's easier to think about this in terms of inaccessibles
since you're just looking at sets of size <\kappa
mortal igloo
My Lean experience tells me that this is compared to universes in Lean
where you have Type 0's, Type 1's, Type 2's, and so on
you can think of Type 1's as proper classes, Type 2's as the next level up
vivid halo
\kappa is large enough that all the usual operations in ZFC will not hit this limit
sick burrow
but yeah I guess what I'm asking is if ZFC + there exists a Grothendieck universe of cardinality kappa equivalent to with ZFC + there exists a model of ZFC with cardinality kappa
sick burrow
My Lean experience tells me that this is compared to universes in Lean
LEAN???????
vivid halo
essentially yes
mortal igloo
Lean 4, to be exact
sick burrow
🟪 🟪 🟪 🟪 🟪 🟪 🟪 🟪 🟪 🟪
mortal igloo
Trying to think about what purple square means
vivid halo
lean
sick burrow
lean
mortal igloo
Never saw that before
vivid halo
like once you have an inaccessible \kappa, everything smaller than \kappa is a "set" and everything larger than \kappa is a "class"
but you can just keep iterating this
vivid halo
yeah
mortal igloo
basic -> easy -> elementary?!?!!
sick burrow
Oh I see you can take the union of things *indexed* by a set in your universe no...
also isn't this statement just stupid
like
replacement axiom
vivid halo
yeah
sick burrow
why did you say "yeah" then 
sick burrow
yeah I do
I just was initially confused because I was like "this just looks like a weaker version of the ZFC axioms"
but then I remembered that ZFC can't model itself without an inaccessible
sick burrow
but then I remembered that ZFC can't model itself without an inaccessible
actually is this true?
vivid halo
that's true yes
sick burrow
so ZFC + Con(ZFC) + there are no inaccessible cardinals is actually inconsistent?
vivid halo
errr
maybe not quite that
main thing is Con(ZFC) doesn't follow from ZFC obviously
I think maybe inaccessibles is equivalent to Con(ZFC) but don't quote me on this
one direction of the implication is obvious
sick burrow
I know that and I know that the existence of an inaccessible gives you an easy model of ZFC
sick burrow
I think maybe inaccessibles is equivalent to Con(ZFC) but don't quote me on this
this is what I was wondering about
cyan goblet
Never saw that before
lean is a drink made from cough syrup + sprite
it takes on a purple color
hence I LOVE LEAN! 💜 and stuff
mortal igloo
Oh wow that's pretty interesting
deep mango
Did you just graduate?
swift sinew
About a week ago yup
deep mango
Hope you get some time to chill out before whatever comes next
I just finished my semester today
I gave a talk in a class
It went well
And I got back grades for my other two final assignments, both good
So the semester ended well even though this was the last of several crazy waves of work this sem
swift sinew
Hey that’s awesome. Sounds like a really nice way to end it
swift sinew
I’m proud of you!
deep mango
Very rewarding
All these finals made me way more excited about doing more math in the areas I was trying to explore this sem
which were a little less immediate to my intended research focus
But might well become my research focus at this point
swift sinew
Which area is that again?
deep mango
I mostly liked PDEs, specifically fluid PDEs and dispersive PDEs (like the schrodinger equation)
But I'm finding that I really like probability theory and its interactions with PDEs more than just PDEs themselves
So not a huge shift
Little from the outside but big from the perspective of someone who has spent all their time learning PDE stuff
swift sinew
Ah gotcha. (I’m a little bit of a probability slut too lol)
Well that’s awesome! Sounds like things are starting to fall in line a good bit
I’m happy for ya!
deep mango
Fokker Planck?
Yes, exactly. Things along those lines
There's a lot of ways to do this ofc
next schooner
Dope
deep mango
But in particular I want to learn more about fokker planck
deep mango
I don't know much about that
I have a lot of vocabulary to learn now
I never was around any probability at all in undergrad
Spending this whole year learning gradually
deep mango
Interesting
yeah at berkeley the math dept and stats dept are separate
So in undergrad I really was isolated from any probabilistic language
and was around a lot of the microlocal analysis / semiclassical analysis people
(sorry gomez)
I thought I liked that and I don't
next schooner
Haha my experience was similar
Ended up going down the percolation theory route then bailed
deep mango
Cool
next schooner
So are you doing a phd?
deep mango
I am in my first year of a PhD
In the US
So I just finished my bachelors last year
And will be getting a masters at the end of next year, and then the PhD goes on for another 3 years for a total of 5.
next schooner
Neat neat
deep mango
So this year and next year, still primarily just doing coursework / seminar stuff.
next schooner
First year of my PhD was similar
deep mango
NYU is a bit odd in that they really have a high coursework requirement for phd students
next schooner
Interesting. Think that kind of thing is more common here in the UK
deep mango
Over the 5 years, one needs to take 3 years worth of full schedules of courses (4 per semester)
So most people do full courseloads for 2 years, then spread out the last batch over the last 3 years.
At NYU at least.
next schooner
Pff that is a lot
deep mango
It's quite nice IMO, since NYU is so dead focused on analysis/PDEs/probability/numerics
Like
It's not like I'll ever run out of relevant topics courses
Basically everything is relevant
next schooner
That's good, yeah
deep mango
it's good that I was forced to explore broadly this year because it led to a slight interest shift
And next year I'll plan to learn some numerics stuff
We'll see
next schooner
Yeah first year of my PhD was similar. Good to spend some time being forced into other stuff
deep mango
Yeah
deep mango
I did a project with a friend (who was on this server for a while actually) in undergrad lasting through the end of last year that was about optimizing certain numerical linear algebra operations
It was pretty cool
next schooner
Oh yeah? Which ones?
deep mango
I was handling the theory side, proving lower bounds for how good they could get
next schooner
Dense field that
My wife's PhD was on optimising numerical solutions for certain eigenvalue problems
deep mango
We were looking at reorderings of loop nests for matrix algorithms. so the most basic example is multiplication, you can also do all the usual matrix algorithms - we used convolution (as in, conv layers of neural networks) as a tool to demonstrate the methods.
the idea was to find reorderings with the best cache behavior, essentially. So I worked on proving lower bounds on the number of loads/stores to memory (the best reordering is no better than this big formula depending on the parameters, etc)
And then my friend was looking for algorithms to meet the lower bounds. We got the asymptotics to meet but not quite the constants.
next schooner
Huh, sounds really interesting actually
deep mango
This was submitted in November, we got accepted recently and will be presenting at a conference in june
It's very cool
next schooner
Oh awesome
deep mango
I'm hoping to do a talk about it here soon
The techniques are really weird and seem magical
Like
The core theorem is a hardcore abstract functional analysis / group theory theorem
which generalizes Holder's inequality somehow
But as much as I was involved in this project, I didn't get a ton of numerical linear algebra knowledge out of it. I focused on my side of it.
next schooner
A lot of my simulations are run on supercomputer environments so I'm pretty interested in large-scale high-performance operations
next schooner
Not that I really make much use of them lmao
deep mango
Cache management and data movement are massive massive things for these huge operations, as well as managing parallelism correctly
next schooner
I only really have scope to optimise to the point I can get the data required for publication
Yeah memory use and allocation is absolutely CRITICAL
deep mango
So e.g. one of our results provides lower bounds and algorithms for optimizing the amount of data that needs to be moved between nodes in a distributed system, to compute a large convolution.
next schooner
VERY cool
deep mango
Thank you!
It was a fun project
I'll probably do a talk about it soon here
(people give talks occasionally, see #events)
deep mango
In particular I've given a talk on another research project I did (after introducing the basic ideas) and I also gave a LaTeX workshop. Those are both recorded
But yeah this would be nice to do
I have to like
Figure out how to give these talks without making them super easy to dox me with
next schooner
fair
deep mango
Yeah
Well
Spend enough time here and I'm sure I'll post some things that I wouldn't want connected to my real name 
next schooner
lmao fair fair
deep mango
something something attractive postdoc guys
cyan goblet
yeah ok ricky
deep mango
Shut
cyan goblet
the door behind you
deep mango
Stop calling me ricky
cyan goblet
😉
deep mango
You're giving people the impression that it's pronounced that way
next schooner
attractive postdoc guys?
deep mango
I came out as gay in January after a really long time in the closet so I've basically spent the whole spring being thirsty. Lmao
deep mango
thank you
cyan goblet
ive been straight since birth and ive been thirsty all my life
deep mango
So true anamono
next schooner
fair fair
deep mango
But it's been fun to be able to be silly about it for the first time in my life
next schooner
yeah i can imagine
can't imagine being in the closet is particularly fulfilling lol
dunno why that still has to be a thing
it's literally CURRENT YEAR guys get over it
deep mango
I didn't think about it very much for a long time, then I did think about it a lot at the beginning of undergrad, came out to a few friends, had a very very weird experience and went back in, and was essentially forced out this winter by an urge that came out of nowhere
No bad reactions or anything
Just like
cyan goblet
if that's the worldview that was engrained into you as a child, it's not really your fault if it's hard to separate from
deep mango
A long time of hoping it would go away
cyan goblet
then there's just modern day people who still believe it's wrong
next schooner
eh i disagree
"oh i was just raised to believe that" isn't really a sufficient excuse to deny people their basic human rights
no mercy for bigots
cyan goblet
i guess i should be more clear
my intent was like
it's difficult to separate yourself from your ingrained worldview
but the point is that you're making an effort to do so
next schooner
right
next schooner
idk I guess I'm from a pretty "woke" place in the UK so homophobia is kinda alien to me
cyan goblet
im from glorious old kansas
deep mango
Mostly I've been in super supportive communities
It's just like
A mental thing more so than an external thing
That made it take a long time to accept and make part of my expression / outward identity
next schooner
some kind of internalised repression?
next schooner
Yeah brains ain't simple
deep mango
For example when I came out I realized that I had a very large number of contradictions / cognitive dissonances that I just hadn't ever allowed to communicate
Like
Literal contradictory beliefs in my brain
Which I know happens and is totally reasonable, but it was weird to start to see all of them all at once.
next schooner
Huh, interesting. I guess it's not that surprising if you don't permit yourself to examine those kinds of thoughts
next schooner
What kind of beliefs? If that isn't too personal
deep mango
Hmmm
mortal igloo
Literal contradictory beliefs in my brain
I'd be interested in hearing some of these
as well
next schooner
yeah tell us your deepest darkest secrets rn
deep mango
Like for example, I find tattoos very attractive on people but for a long time I was very very opposed to the idea of tattoos (despite always finding them attractive)
that's probably the least like
intense example
mortal igloo
That actually makes a lot of sense to me
next schooner
HAHA I had exactly the same thing
no kidding
same with like, facial piercings
which confused my wife a bit, given she has them
deep mango
More intense stuff is about relationships / intimacy / things people do to relax or enjoy themselves I geuss
That's interesting to hear haha
next schooner
yeah i haven't a clue where it came from
Just some weird prejudice I picked up from my childhood, I assume
deep mango
Yeah
deep mango
Yeah
Its lateish here (it must be very late for you!) but this is stuff im happy to talk about a lot more.
It's good practice
next schooner
lmao its 5am
deep mango
Lol
next schooner
i'm nocturnal atm
happens sometimes idk
good practice for what? always happy to chat big shit haha
deep mango
Good to keep trying to dig at things going on in my head and figure out why they're there and how I can wield them properly instead of letting them screw with me
Somehow this feels like a very adversarial process
next schooner
Yeah I know what you mean
I mean I've a long history of mental illness so I know the feeling of being at war with my own thoughts
Certainly it can be alarming to confront how little control one has over them, much of the time
inner finch
inner finch
rename channel to homosexuality
next schooner
Meh, that's just life init
deep mango
Did you have a nice sleep?
next schooner
can't believe this server is so gay
deep mango
Oh I was trying to troll you
coarse grotto
Healthy conversations in discussion-2
Sure beats discussion
deep mango
Ok good
inner finch
im doing this thing where i sleep at 9 and wake up at 4:30
deep mango
Im glad your sleep was weird. Troll successful
inner finch
for the sigma grindset
deep mango
I see
inner finch
Im glad your sleep was weird. Troll successful
lol
deep mango
Lmao
inner finch
im doing this thing where i sleep at 9 and wake up at 4:30
but these days im so tired i go back to sleep and wake up at 8 🗿
weird beard
inner finch
i have an exam today 
also i hate the way these guys set up these exams
the timings are there to fuck me over
deep mango
Its ANOTHER NIGHT where im going to sleep past midnight just in time for another morning where ill wake up before 6 for no reason
brittle socket
Hi Chalk boi
inner finch
Its ANOTHER NIGHT where im going to sleep past midnight just in time for another...
lol
coarse grotto
I should really get some sleep, I’m getting my wisdom teeth out tomorrow morning
inner finch
pane
deep mango
Hello Grass
coarse grotto
deep mango
It's Kirby's milkshake era
next schooner
dentistry 
inner finch
milfshake
deep mango
I loved having my wisdom teeth out. I had milkshakes and soup for like 3 days
coarse grotto
I had a dentist appointment today, so having these back to back 
deep mango
Ugh
coarse grotto
Milkshakes sound nice
deep mango
Over time my dentist tolerance has dropped
But i am still a good boy who goes twice a year
next schooner
if a dentist so much as looks at my teeth i will literally SCREAM
deep mango
It just is more and more painful every time
coarse grotto
I have very big anxiety about my teeth, but it’s nice going to the dentist when they don’t lecture me on flossing
forest jackal
I am super overdue for a dentist visit
coarse grotto
No cavities this time 
forest jackal
not that my teeth are in bad shape, but it has just been forever
coarse grotto
deep mango
GO to the DENTIST
next schooner
how overdue are we talking
forest jackal
5-10 years
inner finch
yummy yummy
inner finch
5-10 years
same
deep mango
That is a truly disgusting gif
next schooner
same
next schooner
who can afford dentists
inner finch
cars
deep mango
next schooner
cheaper to just let the teeth fall out on their own yanno
forest jackal
Like I take quite good care of them, but professional cleaning and warnings of likely issues is important.
coarse grotto
Almost tempted me to post my old car to cry about it again
inner finch
post old car 🚙
coarse grotto
My dental insurance is nice enough that it doesn’t cost too much
deep mango
Blushy sully for emote for ryc
Havent you gotten tired of that name
Imagine
mirzathecutiepie
Doesnt that look so nice and simple
inner finch
nice area tbh
coarse grotto
Yeah, parts of this city are nice like that, it’s hit or miss
neat lintel
Miss as the car parks
Additionally the driver is somewhere else
Beyond that, the wheels don't seem rotating
coarse grotto
It’s kind of hard to take a picture of your car while you’re driving it
wild lantern
Cop out
coarse grotto
Smh
wild lantern
Smh my head to be tbh
(Pls don't try to take photos of ur car while you are driving though.)
coarse grotto
Clearly, I’ve seen people doing stuff like that, it’s ridiculous
wild lantern
I hate driving around people
Driving makes me wonder how more people don't accidentally drown themselves in the shower.
naive bolt
What's with the single | ?
deep mango
This usually means the restriction
So you think of H just as a function on cell k, not on the whole domain.
naive bolt
Alright, from what I'm reading on the paper H is referred as a property of a cell so why wouldn't they just write Hk without |?
H_sl is a predefined value
deep mango
I think writing either is reasonable
But if H represents like, the collection of all the H|_k's over all the cells, then the rigorous way to do this is by restriction to k as above.
naive bolt
Ahh okay that makes sense given the context actually
same goes for the second part below?
brittle socket
Hi Chalk Bird
stray kite
can inner products be defined for any vector space over an arbitrary field?
can we extend the definition from only being for R and C?
sleek wing
inner product spaces are a wide class of spaces
you can define one for any vector space iirc
neat lintel
inner product spaces are a wide class of spaces
how do you translate conjugate symmetry to something that isn't R or C
do you mean like the dual pair or however it was called
sleek wing
ah yeah good point
maybe you can extend it to any field with a funny order 2 automorphism then ;)
normal sparrow
clever knot
Like I take quite good care of them, but professional cleaning and warnings of l...
isn't the actually cost of examinations and cleaning relatively cheap once you get anything treated
and assuming you have insurance or whatever it normal covers such procedures. Beyond this, the tools they use will be able to remove any build up that normal brushing cant (plaque that turns into tarter).
tender tulip
Can you prove induction is a valid proofing strategy (possibly by contradiction) through set theoretic axioms
sleek wing
tender tulip
does induction work for any well founded-order set, without the restriction of a successor (element such that there doesn't exist an element before it or after its precursor) for each element
w a i t
idea
stark charm
does induction work for any well founded-order set, without the restriction of a...
what is founded-order set?
I think you only need well ordering property
tender tulip
well founded
stark charm
But I am no logician
tender tulip
aka with a minima
stark charm
Oh yeah
stark charm
does induction work for any well founded-order set, without the restriction of a...
I wish I knew more about these things
swift sinew
You might wanna make sure your relation is connected
stark charm
I do not know why induction works either
tender tulip
You might wanna make sure your relation is connected
total.
tender tulip
well founded sets are total, so two elements are never unrelated
stark charm
but i cant prove what settings induction proofs are valid
tender tulip
just thought about this for a sec
we could say,
[whatever] is true for x if it's true for base m, and all y < x
but with induction, there exists a UNIQUE element that is a predecessor for x
so instead of considering ALL of the elements before, we consider a unique one
this might help tackle the self-reference, maybe
clever knot
well founded sets are total, so two elements are never unrelated
I would imagine the set would have to be totally ordered or else you might be making a comparsion of 2 elements that are not comparable
tender tulip
Yeah
clever knot
or just show it holds for maybe a subset of the set
tender tulip
self referential.
I = {x in S: (for all y < x in S) y is an element of I} union {m}
it's a self referential set
tender tulip
why not just use the <= symbol?
No, elements being in I depends on I itself
Self referential sets are not friendly (e.g. Russel's Paradox)
... w a i t
i wonder if induction is dependent on the existence of elements prior to a given element, down to the minima
primal seal
It depends upon the empty set being a member of every inductive set
(Set-theoretically)
lean sinew
Does this discord server help with homework kinda scared to post the homework because i haven't got directions on how to solve it and i dont wanna get banned because i didnt show my work
and why im stuck
hushed turret
we don't do it for you, but you can ask for help
sick burrow
yeah #❓how-to-get-help is primarily for homework questions
lean sinew
Thanks alot
one more thing will you still be able to help me if it is in another langue
but i have translated the questions
neat lintel
https://tenor.com/view/bh187-the-grinch-jim-carrey-grinch-smile-gif-19288903
WA-HY!?!!?!?
mint patio
one more thing will you still be able to help me if it is in another langue
Yeah!
The people here are really relaxed, don't worry Han :) if you do something wrong I'm sure someone will correct you and help you figure out where to go
So long as you want to follow the rules you won't get in trouble for making a mistake lol
Read #❓how-to-get-help and post your question in an empty help channel
Remember that help is voluntary though so it may take some time to get a response
forest jackal
and assuming you have insurance or whatever it normal covers such procedures. Be...
Yeah, I never said it was expensive or inaccessible to me, I have just been slack.
clever knot
Yeah, I never said it was expensive or inaccessible to me, I have just been slac...
Is it easy to get into dentist offices or are they normal really busy?
forest jackal
They are quite busy, but not so busy that it is a good excuse
woven granite
hi
ancient flame
I was writing notes about finite abelian groups and I was like "ugh this is long, let me abbreviate this" but I immediately decided not to
deep mango
Abelian is often abbreviated as ab :)
tender tulip
It depends upon the empty set being a member of every inductive set
Mind elaborating?
next schooner
Mind elaborating?
$\emptyset \subset \emptyset$
fathom swallowBOT
josh 🐀
tender tulip
I know, it’s more about the fact that, how can we prove transfinite induction
primal seal
An inductive set exists axiomatically in standard set theory, from my understanding. So I’m not sure you can “prove” induction.
Intuitively, it’s agreeable though
swift sinew
I know, it’s more about the fact that, how can we prove transfinite induction
Supposedly Theorem 1.19 is a proof of Ordinal (transfinite) induction
https://jjsch.github.io/output/oa.pdf
hollow flame
hey quick question
why is this not a bijection
like i understand how definitionally the power set has greater cardinality but like
deep mango
Your images are all sets with only finitely many elements
What's the integer that maps to the set of all even numbers?
hollow flame
oh it isnt surjective
deep mango
Yeah
hollow flame
duh ok thanks
mortal igloo
Put 2-adic integers on the left hand side instead of N 😏
hollow flame
not epic enough 😔
plucky zodiac
I want to be good at calculus 3 but feel like I am horrible as last time I did math was in 2017 and so am reteaching myself as want to do a career in mechanical engineering. Any advice. Want to be good at this so can pass the class
hollow flame
calc 3 as in multivariable?
plucky zodiac
Yes
plucky zodiac
Memorizing the formulas and trying to remmeber which equations to use them like turning polar coordinate into spherical coordonates or finding the volume using triple integrals
hollow flame
tbh when i took calculus i would rederive everything on tests, formulas wouldnt stick in my head
now teaching calculus i see the same thing in my students, formulas just suck
even if you practice at them there are too many
i would say really focus on where they come from
plucky zodiac
Okay as thank you as for me think would need formula sheet to help solve problems but hard to stick which formulas can go to which one. Using krista king to help me out
hollow flame
i really fundamentally disagree with formula sheets
maybe to cram with lol but not for independent problem solving
plucky zodiac
Okay as do get the idea but for me there is so many formulas to look over
vivid halo
There’s not that many, you don’t have to memorize everything
plucky zodiac
Okay as from her sheet there is 49 pages
vivid halo
It’s usually better to know how to rederive them and not rely on memory for everything
That’s ridiculous
hollow flame
Okay as from her sheet there is 49 pages
???
plucky zodiac
Sorry 49 pages of formulas
vivid halo
That’s still completely excessive
plucky zodiac
Okay as that does make sense
hollow flame
best thing is to go through and not try to memorize but see if you understand what theyre saying
plucky zodiac
Okay
hollow flame
if not then go back and study that material
if the original material was just a formula presented without any context? drop the class
i mean im kidding there are other resources online
but if she is teaching calculus like its just a bunch of memorizing then maybe she is not a very good teacher
what a waste of your time, that isnt learning
hollow flame
as a calc teacher, do not blindly memorize the formulas. use the videos & notes to really try to understand
ooh
plucky zodiac
Okay and also suggest this to your class in case
hollow flame
i wouldnt suggest something without looking at it first
there are a lot of free resources online
plucky zodiac
do see it khan academy andf all
hollow flame
yeah of course
also word of warning about differential equations its really easy to get wrapped up in how fun it is to solve the problems
plucky zodiac
Okay
hollow flame
knowing why the methods work is 100x more valuable than being able to solve the problems
usually there is a lot of subtlety
hollow flame
high school AB/BC
velvet dagger
Nice
plucky zodiac
Okay as that is good and thanks for the help
Had a teacher one time name Mr. Boop who taught that
velvet dagger
inb4 ost is Mr. Boop
hollow flame
or i will be next year, at least. this year im teaching a transitional class
plucky zodiac
Do agreed
plucky zodiac
Okay
wooden flax
Today I saw the Pizza application of Theorema Egregrium! Its great!
bronze pelican
Whsts that
wooden flax
okay so like if you pick up a pizza normally
its possible toppings will fall off
but if you like bend the crust
horizontally
one principal curvature is nonzero
gaussian curvature is still 0
so tip cant flop if you roll the pizza
forest jackal
so tip cant flop if you roll the pizza
unfortunately some pizzas are quite thin and of questionable structural integrity, their metric changes when you fold them / pick them up! 🙀
deep mango
🤨
dire mulch
lol
forest jackal
But it is a great application, I had seen that one before and am a big fan.
dire mulch
wdym by their metric changes?
forest jackal
like the crust and toppings stretch
deep mango
Come to new york and i'll show you an inextensible pizza.
dire mulch
I see.
deep mango
We do things a little different up here.
dire mulch
Do you live in New York ryc?
deep mango
I live in new york city
dire mulch
You always mention it.
forest jackal
I have had many an inextensible pizza, and I agree NYC has some good pizza.
deep mango
You always mention it.
I feel like I'm being owned.
deep mango
Cool
forest jackal
some pizzas from mediocre places feel more like symplectic manifolds than riemannian ones though, very floppy locally.
forest jackal
now I am feeling hungry for pizza, thanks a lot RYC
deep mango
not really, I was just curious.
Yeah I'm a graduate student at NYU.
forest jackal
I do have an exciting lunch dessert ahead, as I am making Thursday lunchtime pancakes, it's a Nordic tradition that I have decided to steal.
dire mulch
I had milkshakes and chicken sandwich for dinner. Was tired of eating Chinese food.
ancient flame
HI RYC
dire mulch
I have to start eating healthier.
deep mango
I had milkshakes and chicken sandwich for dinner. Was tired of eating Chinese fo...
Wow that sounds good
deep mango
I do have an exciting lunch dessert ahead, as I am making Thursday lunchtime pan...
Oooh nice
Are these pancakes filled / topped
forest jackal
they are baked, and amazing. this is the finnish version, which is what I am going to do:
dire mulch
Looks good, looks like corn bread.
forest jackal
I feel like weekly pancakes on thursdays is a tradition worth stealing
deep mango
I would love some cornbread
forest jackal
well its much more sweet than savoury, but I guess cornbread can be on the sweeter side too
deep mango
I had milkshakes and chicken sandwich for dinner. Was tired of eating Chinese fo...
What sorts of milkshakes
forest jackal
I love cornbread
dire mulch
What sorts of milkshakes
Cookies and creams.
deep mango
forest jackal
yum
deep mango
Best milkshake flavor
dire mulch
Yah tasty. The place I got it from only had medium size which made me sad.
dire mulch
I have a fast metabolism, I will always look fit but sometimes I am not.
forest jackal
and I am fairly active atm with tennis and some running.
dire mulch
Plegasus's summer bod arc is off to a good start
Yep. At least I run a lot.
forest jackal
although my back is a little fucked from last nights tennis sesh
deep mango
My summer bod arc needs to really kick into gear this week
forest jackal
I used to play competitively in highschool and early UG, but its been ages
deep mango
Sigh
forest jackal
and I had some bad habits technically, so am getting some coaching as well
one of the things was the way I was holding my back on groundstrokes, so I made a conscious effort last session to work on that, and I suspect I overcompensated lol.
such a fun sport though
dire mulch
That reminds me I was in gym class and we were playing tennis. I decide to jump over the net but my leg got caught and landed face down. Most embarrassing thing and I did track(high jump) during that time.
forest jackal
ouch
my tennis coach was telling me about a high jump knee hyperextension injury he had a couple of years back and it sounded pretty horrific
dire mulch
That sounds painful. So glad I never had any major injuries for sport.
forest jackal
same
wooden flax
unfortunately some pizzas are quite thin and of questionable structural integrit...
🙁
I hope to go to NYC someday
the theorem will definitely hold for those!
fair estuary
Guys, is Algebraic structure something that can be seen as a visual model or is it more like some written rules type of situation?
celest vault
Guys, is Algebraic structure something that can be seen as a visual model or is ...
Highly depends on algebraic structure , sometimes u can make visual models but sometimes just visualization which is not rly a model because for example it presents the structure very inaccurate
slender ember
Can u help in something it's gonna be quick
celest vault
Guys, is Algebraic structure something that can be seen as a visual model or is ...
But its mostly just a mathematical construction so , i guess it isn "rules type of situation" whatever that mean lol
tender tulip
For any (possibly infinite) set S in ZFC
S can be partitioned into a family of subsets, F, such that for every element of P(S) there exists a unique subset in F that it is an element of.
Can this be proven exclusively with the Axioms of Choice, Power Sets, and Unions?
hushed turret
i don't understand what you're trying to say here
bright hill
I'm back
bright hill
Hello twice
bright hill
how were exams
The math exam was
I was basically drained for the rest of the week after that lmao
I technically still have a philosophy exam in a bit but fuck that shit lel
hushed turret
ah rip
bright hill
How were your exams?
hushed turret
ive still got quite a few to go but this week has gone well 
bright hill
Nice 
I can't believe I'm saying this
But after getting forced to do HS shit, I so miss rudin
Lol
sleek wing
exam gang @bright hill
bright hill
Les gooo
sleek wing
wtf does that MEAN
sleek wing
i just did algebra exam
I've got an algebra exam tomorrow
bright hill
wtf does that MEAN
Check your dms
bright hill
Wtf are you waiting for then?
bright hill
i wrote "j'ais laisser la feuille vide"
Imma do that for the philosophy exam 
sleek wing
I'm not going to watch it
brittle socket
The math exam was <:monkey:651816857153699840>
I actually got back 2 of my math papers today, and in one of them I lost 8 marks because of 1 careless mistake: I forgot to apply lg(x) to the data before I plotted it bruh.
bright hill
I actually got back 2 of my math papers today, and in one of them I lost 8 marks...
That's literally the worst
I hate those mistakes so much
brittle socket
Same
sleek wing
what's the point in giving you 8 marks for a question if a slight mistake means you lose all the marks
just make them all 1 mark questions
tender tulip
For any (possibly infinite) set S in ZFC
S can be partitioned into a family of ...
Axiom of choice implies there is a set for every partition of a set (union of the family) that's intersection with any of the partition's elements is a singlet. I'm wondering if it can go in reverse
brittle socket
what's the point in giving you 8 marks for a question if a slight mistake means ...
Don't ask me
bright hill
Careless mistakes are the worst
our physics course is literally just "enter the right digits in the calculator"
brittle socket
bright hill
and I swear, the exams are intentionally designed to maximize careless mistakes
it's so damn annoying
arctic grove
exam gang <@345954969628704779>
am i in this gang as well?
bright hill
hell yaa
arctic grove
our physics course is literally just "enter the right digits in the calculator"
yall get a calculator?
bright hill
yall get a calculator?
ye but I don't use them much
bright hill
I once forgot my calculator so I instead of asking someone to lend me theirs I computed the 5th degree taylor polynomial of cos
arctic grove
god knows who tf thought this was a good idea
arctic grove
please do my calculations for me
bright hill
arctic grove
one of the smaller practice problems for school physics final is
given that the mass of the proton is 1.07825u, mass of neutron is 1.089439u, find the mass defect and energy of fe, given that mass of fe is 55.91211212 yadayadaya
arctic grove
one of the _smaller_ practice problems for school physics final is
given that th...
this is absolute pain
neat lintel
one of the _smaller_ practice problems for school physics final is
given that th...
yes
pain
bright hill
taylor series of cos is not bad
ye, but have you tried to do it by hand?
neat lintel
yes
neat lintel
not in an exam though
neat lintel
i dont like seeing so many numbers all at once
arctic grove
this is so annoying
arctic grove
torture, thats what it is
surreal sapphire
just replace everything by variables and plug it into your calculator at the end?
neat lintel
you mostly require the answers till like 3 or 2 decimal places
bright hill
just replace everything by variables and plug it into your calculator at the end...
calculator
neat lintel
ye obviously but calculator is not allowed in shyshu's exam
arctic grove
yeah
surreal sapphire
neat lintel
if i remember its JEE, right ?
arctic grove
most entrance exams dont allow them either
surreal sapphire
well then
arctic grove
yeah jee but also school exams
neat lintel
i read about it
surreal sapphire
just replace everything by variables
arctic grove
just replace everything by variables
no i mean the answer is also a number, so idk how replacing it with variables will help
neat lintel
like all entrance exams maybe
arctic grove
looks like a shithole
indeed
neat lintel
ITS ALWAYS JEE THAT JEE THIS
torn willow
99% of JEE's difficulty is "yo you can't use a calculator"
torn willow
If calculators were allowed,JEE will be baby shit
arctic grove
india needs education reform
oh yes please
arctic grove
If calculators were allowed,JEE will be baby shit
unironically this
even advanced which people wont stop circle jerking about
neat lintel
isnt india like super good in math
torn willow
Like most chem questions are "yo calculate nRT/V upto 2 digits of precision"
bright hill
india needs education reform
you don't think it's intentionally bad?
neat lintel
intentionally bad ? 
torn willow
I think here it's artificial difficulty
arctic grove
at least kvpy allows an on screen to be used
its annoying since u have to use ur mouse to input
but still
not half bad
bright hill
torn willow
You have breaks?
bright hill
rookie shit
neat lintel
if one is done with JEE in less than 3 hours, are they allowed to leave ?
surreal sapphire
my guess would be the indian education system tries to create as many engineers as possible
bright hill
my math exam was 5 hours
surreal sapphire
which is a good goal i think for such a country
arctic grove
my guess would be the indian education system tries to create as many engineers ...
yeah
surreal sapphire
you just have to wonder if what they are doing is the best way
arctic grove
the education is very engineering focused
arctic grove
you just have to wonder if what they are doing is the best way
very much no
torn willow
You have to stay for the entirety of 3 hours if you choose to attend
charred mortar
Damn
neat lintel
why
neat lintel
isn't it computer based exam
charred mortar
What if you need to use the bathroom
charred mortar
Welp
arctic grove
idk actually i havent given jee yet
charred mortar
Ah ok, just no early leaving
torn willow
Just there won't be any water in the restrooms
neat lintel
Just there won't be any water in the restrooms
huh ??
bright hill
holy shit
charred mortar
Wut
surreal sapphire
tbh it makes sense to not allow people to leave
we do the same
you cant leave x mins before end
bcs it will just disturb everyone else
charred mortar
Yeah no early leaving makes sense
neat lintel
fair enough
torn willow
I wrote jee in like 2 different colleges
surreal sapphire
you can leave in the beginning
torn willow
Both of them didn't have functioning bathrooms
surreal sapphire
so there is always people asking if they can take the exam questions
torn willow
It's like a trend
surreal sapphire
and then they just leave
charred mortar
Damn, do people finish those tests ultra fast or what
neat lintel
no functioning washroom in...colleges ?
torn willow
I wrote the Indian equivalent of USAMO in a school once
arctic grove
Damn, do people finish those tests ultra fast or what
lmfao no
torn willow
Literally there was no boys' restroom
charred mortar
Or do they just give up
torn willow
Literally didn't exist
neat lintel
no restroom or no boys restroom ?
torn willow
No boys' restroom in like 2 floors
I have to go to ground floor to take a piss(And I still had to search for where the restroom was)
Well That also didn't have water as you would have expected
charred mortar
guess your building engineers failed jee
neat lintel
i wonder if its all part of the elimination based exam system
bright hill
you can leave in the beginning
our schools rebel do that then start to make a racket outside
it's...
torn willow
Well I did write pre jee(called JEE Mains) in a uni
bright hill
childish at best
torn willow
And that uni had washrooms with water
neat lintel
And that uni had washrooms with water
can't take that for granted 👍
surreal sapphire
so we throw them out the building after exams
fast ivy
HS
arctic grove
HS <:sully:651816820122189834>
bright hill
HS 
neat lintel
i used to do the same in school
arctic grove
god i want to be in uni 
neat lintel
sometimes..
surreal sapphire
once you are in uni you want to be done with it
bright hill
childish at best
and when I say this I'm being very VERY polite
surreal sapphire
most people do anyway
bright hill
since it's very distracting
sleek wing
once you are in uni you want to be done with it
I cannot wait to leave this fraudulent institution
surreal sapphire
tbh the only annoying thing is
sleek wing
I hex on their houses I say! I hex!
surreal sapphire
i want money
bright hill
once you are in uni you want to be done with it
uni is objectively better than HS tho
arctic grove
once you are in uni you want to be done with it
i am very sure it will be a million times better than hs
surreal sapphire
dunno uni is a lot more work
fast ivy
sleek wing
nah uni is wayyy easier than high school
neat lintel
uni is a lot more independent work as well
bright hill
dunno uni is a lot more work
is that bad?
arctic grove
dunno uni is a lot more work
but its more work that i kinda want to do
surreal sapphire
free time is nice
sleek wing
you so true me but I'm right - guess what you don't have to deal with in uni life?
highschoolers
neat lintel
but not many people manage it well because for one no strict supervision unlike school
sleek wing
but not many people manage it well because for one no strict supervision unlike ...
which is why first year (usually) doesn't count