#serious-discussion
1 messages · Page 173 of 1
I see what you're saying and I agree because I've just realised I'm in the same trap as those people because I've been juggling multiple things I've spent 1.5 weeks on one chapter of Stewart's precalculus
Basically I think what I'm saying is know when to move on to the next chapter of whatever it is you're studying.
Also I was the same, I think it's the typical experience in a structured course.
And indeed when you come back to it later, it suddenly turns out to have been much easier than you originally thought
I think I should probably also just manage time more effectively, if I expect to get somewhere then I should definitely make sure to make my Math sessions more dense
Since if I do want to self study effectively I can't do so at the leisurely pace I'm on at the moment.
Thanks for mentioning this because it's somewhat of a wake up call 😅
But also it depends on why you're self-studying, because if you just want to learn some math for fun, it might not hugely matter where you go with it.
And how "efficient" you are
It's basically for fun but the long term goal is to supplement myself as a programmer in a way, I know getting all the way up to Real Analysis is probably overkill but again, primarily, it's just for fun.
learning for fun is how i started my self study journey like a year ago
i kind of ask my self how'd i stay motivated for a whole year
But with the pace that I'm going at it could take me a year to finish Stewart's precalculus which is a bit too slow, but I didnt realise until you mentioned what you said before. Then again, self-learning is a skill I will get better at, so maybe it shouldn't be as much of a worry because I will naturally be more efficient.
Oh man, I wish I could ask myself the same going to gym
"its fun" is just so powerful
I think its just become habit now because I do hate it but I enjoy it at the same time
do you study for x amount of time everyday?
pacing is an issue i'm facing as well
it wasn't a problem at all when i first started
Varies, I try to do at least 5 days a week, at the very least 4. Usually 1-2 hours
do you have a pomodoro (timer) going on?
It's difficult because I do have to balance it with programming as well, because I'm a software developer that loves his personal projects.
i used to do that but imo it wasn't that effective for me
I find that it breaks up my flow
yeaa me too
At work, I'd put music on, and then switch off until 5pm, lots of work gets done.
what kind of projects do you do?
i surely do want to go back into programming, but math is needed in my case (i want to go into ml)
I'm not too far ahead in my career, Full-stack dev by day, and then by night I just do whatever I find fun, working on a Gif parser in Rust, with the part 2 that's currently pending implementation is a gpu renderer for it
recreational programming rocks
In my case I actually lack a degree which is partly my drive to learn at least Calculus 1, 2, 3
i see, you're in EU right
Question, dont take this the wrong way. But dont you hate doing the same thing all day?
Yes, UK.
gif parser sounds fun, especially in rust
i quit rust when i found out you can't write camelcase 🤣
It's why I try to do someone new on weekends, Math is something new that I picked up to make my weekdays less dull. But you do grow numb to it.
I like snakecase more for some reason haha, to each to their own
do you guys have national entrance exams in the UK?
interesting
As well though, even if the routine is the same, the contents of the days aren't necessarily the same. Cliché to say but enjoy the little things
For university?
yea
Yeah, otherwise life passes you by
As I've recently found out 🤣 you start aging a lot quicker when you get past 18, for me at least, since I went straight into work
are you going for the entrance exam ones?
its "fun" trying to pass one
(one of my reasons of motivation 🤣 )
aging as in time passes by faster or as in you develop wrinkles and pains
I'm not aiming to go to university at all, I've kind of cheated at life where I've broken into the tech space of jobs without needing to go into debt
the first one, I'm not that old 🤣
fair fair
reverse aging technology when?
Its all perception, when you tend to focus on longer term goals, like getting a mortgage, your relative scale of time seems to change
you wouldn't use it?
Oh ok seems like I will have to wait for a true doglover
I wouldn't, it just seems like something that's not for me
it's funnier to be a doglover not owning one
sorry to let you down like that ...
It's ok
@robust brook Whereabouts are you from?
because I learnt geography in the UK I have no idea where that is unfortunately...
it's alright people barely know that 🤣
also what chapter are you studying in that precalc book?
I made plans to get onto it 5 months ago but only just made the commitment to do it, I've finished the first chapter yesterday. However, when I was in education I covered about 70% of the material there when learning Calculus in UK. The education system's structure of learning Math is a lot more different than America's
It's been really easy so far don't get me wrong, but I'm going to stick with it.
ironically self studying has been faster and more fun for me
i always found the school math pacing always so slow (even though i never paid attention lol)
if you pour 1-2 hours everyday you'll definitely go so far
(i did not know such thing as "algebra" existed like 2 years ago)
Exactly, but for me I find it comes from the reason that I actually want to do it now. And because I actually want to do it, I'm finding that I'm going out of my way to learn stuff in more depth
that's crazy, good on you man
well, maybe not everyday, but every almost day I will
yea about 5 days a week is good enough
Out of interest, what's your way of note taking and managing notes
oh man
my teacher's always saying to "take notes" but i never do that 🤣
it's a thing i never did in my self study journey
i always use a online whiteboard to do my math problems, then i transfer them to the paper
Haha I do it in reverse, I note down things which are worth noting as to not copy the whole text book, do the problems, and then later in the week, I archive my notes in a pretty latex format into Obsidian as a way of easily revising my perspective on something I learnt. I feel like it might help with retention. Of course, the best retention comes from doing the actual problems in the book.
Awesome to be honest, but no notes only got me so far, but you are most definitely different
A lot of overhead though so I wouldn't recommend if you don't want any extra chores haah
it's definitely a bad thing to get used to, you're doing a better job taking notes 🤣
when i forget something i have to read thru the entire book and whatnot
Yeah, I think of it as a way of materializing the effort and time I put into learning a concept
you're actually memorizing more from writing it down and whatnot
so that's a huge benefit
Well anecdotally I might remember more, but if I actually do or not, we'll see haha. But anyways thanks for the conversation man, I'll probably see you around at some point when I've crunched through more of precalculus 😅
Thanks for the help btw
alright, see you later, good luck on your precalc journey
@old oak @surreal sapphire Again, thanks for the insight
i'll add you on discord if you don't mind
Already sent a request lad!
Btw, I suck at online, you will probably hear from me in a year or after I've gotten through the book, unless if you message first, so yeah
it's alright lol, i'll message you later on
@errant ridge 
±0 these two numbers are so cool
how long has Neam spent? 
It seems that abbott has been the area of research from 20/11/2022 till the present 😂
is that why I've seen it joked that Neam never got past Abbott level analysis? 
yes, I'm aware of his physics journey too
lotta things to learn, not enough time 
agreed
Cool
do you think eminem would look good with curly hair
for the people who live in europe: how common are unleashed friendly dogs
cause i was in this rural area like a week back with my sister and there was a big dog that walked around sometimes and when we walked near its house it got excited and started jumping up and down, licking my hands, etc
and like yesterday maybe i watch a video of someone basically saying keep your dogs on a leash unless you are very confident you can recall them
i live in qatar, dog owners are scarce, so i don't know how common is this situation or what the responsible dog practices are
what kind of question is that
It is probability question
what would be the pre reqs for topology btw?
uhhhh
is abstract algebra required?
according to Arti, almost nothing
no
Artichoke recommends PST as an introduction to proofs, in fact
comfort with proofs is all that is required in e.g. Munkres
but like
idk i see people also say that some analysis is nice to see first
for whatever reason
im not really sure i agree with this sentiment
i recommend against this having had bad experiences explaining stuff 
arti probably considers basic set theory utterly trivial
like i feel like any sentiment along the lines of "oh you might wanna know xyz before learning <insert sort of standard topic>" is sort of tautological
i think it's convenient to know about metric spaces beforehand, but the book i used (Lee's ITM) includes an appendix on it if you don't
The more math you know as an undergrad the easier it is to learn these topics
Yeah convenience is true
i do agree with that
pst = point set topo i guess
yeah
I was thinking of the acronym for like 10 min
anyway i had one experience where someone kept confusing the topology (set of open sets) with open sets themselves, and couldn't get this straight when attempting to prove stuff about cts functions and taking preimages etc.
it was pretty painful
so i don't agree that there are no prerequisites, you should have your elementary set theory straight before attempting topo
you should know facts like "x in A u B iff x in A or x in B" by heart, stuff like that
and de morgan's law
no ZFC?
uhh
as far as i know most people do not need to learn zfc except for people working in foundations stuff
I feel like Munkres is painfully abstract if you don't have any motivation
including some category theory folks
I feel like every math major should learn that it exists and see the list of axioms once
I was very shocked when talking to math majors from other schools when I had to explain what ZFC is
that is insane
Because I said I liked logic, and they asked me what it was, and I was like oh you know, there's a couple different subfields like set theory, proof theory, model theory, etc., and I thought set theory would be the most accessible to explain
So I was like "oh you know the continuum hypothesis, about there being a set of size between the integers and reals?"
And I got the blankest look
So I was like, huh, I guess I can't make assumptions about math majors
And then I mentioned ZFC and they were like, I've never heard of that in my life, Z what?
Bit of a culture shock, it was the very first thing our math classes started with when I took linear algebra haha
Yeah I think it's also useful to do a couple basic proofs, like oh construct a Cartesian pair (a, b) and prove that (a, b) = (c, d) if and only if a=c and b=d
Just to see like oh yeah, you can really get any sort of structure you want just by using sets
true, everyone should experience the joy of reinventing math from the ground up 
Then again, lambda calculus is bread and butter to me, but no math or CS major I talk to knows about it, I swear 
like constructing N from the empty set
It's weird thinking about what's trivial to you and not to the other person, and vice versa
I feel like every working mathematician should practice explaining things to little children
I've heard some mathematicians talk that... oh god...
Maybe they were just ready to retire and didn't care anymore
i was told that i should "try to get nsf grfp or to find an advisor with money" as soon as possible, and i feel like this kind of mentality sucks
the reasoning is that i need to be working more on my thesis
what's grfp?
grfp is a grant for grad students basically
essentially i just need to replace my TA stipend with one of these
or advisor funding
the reasoning is that it buys me more time to work on my thesis => thesis is better => job prospects are better
i just graduated indeed
i start grad school in august ish
ohh I see
yeah that's sucky
i dont really like that this is the new rat race
TAing is a nice experience
Because teaching is so important
i love teaching
thats all i ever wanted
and i also fully believe in my research abilities but idk
It just sucks to see grad students be told something like this
Though presently it does seem like the majority of grad students do have to do some teaching experience anyways
whether for stipend or by requirement to graduate or something
Same vibe as "you're too smart to be a teacher"
Can someone explain to me how B=2XB, X is 1/2 not 2 ?
like in the next two or three years if i dont manage to pull through and escape being a TA there will be this mild sinking feeling
I hope i can avoid that feeling
I think you just need to know what you personally want in life
what you'd personally feel successful about looking back on your life
and write it down somewhere
yeah
right now the answer to that question is I have no idea

maybe I should make a list of things to do before I'm 30
The one light i have so far is that my thesis advisor told me something very important when i was in the dumps about the grad school process
He told me that these struggles that i was going through and will face are just sort of details in the big picture
and that in the long run things will work out
i need to remember this more often
(at the time i had heard back from 8/14 grad schools in the negative, and it was late february of this year lol)
Kind of the scariest time of my life lol
it was so funny because i was so confident i wouldnt get comically depressed about grad school
and then it happened anyways
I feel that
Honestly
I feel like if I don't get accepted into any grad school, I won't even be that mad, I'll be happy to get a job doing something fulfilling
that's good
Well okay I'd be mad about the like $1k in application fees 
I was talking to a middle school teacher I had the other day who told me she did a postdoc and convinced the uni to let her take teaching classes for free to improve her scientific communication, then after the postdoc she dipped out of academia and interviewed for teaching jobs
Because she didn't want to like start her own lab, and she didn't think she was the right kind of person suited for that, plus she always liked teaching
Icon tbh
damn
that's real guts i think
To know what you want and like push to follow through with it
I asked her if she had any regrets about spending all that time in academia, and she says she loved it and she thought doing her own research made her a better teacher anyhow
anyways, recently I've come to the conclusion there's only two kinds of math
math that I know and math that I like
they form a partition of all math
(half joking)
There is ±0% error in these statements
you don't like math that you know? 
Lol
a lot of them are like
really obvious things
like "the union of a set of sets is a set" or "given sets x and y, {x,y} is a set"
axioms of union and pairing respectively
that's so comically wise lol
metals advisor:
low, they all are tied to the owners if you are walking down the street
if you are in a park or on the beach, it's higher
higher…
Higher....
kid named higher
Hire her? Who’s her?
higher? i barely know her
Let A={0,-0}
Hello guys
never on the street
often in parks and such
https://discord.com/channels/268882317391429632/1257723267544776837 can someone explain this?
!noadvert
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
new to discord i didn't knew the rules
This conversation is dead lol
I don't think not knowing the rules means you can break the rules.
what do you mean "never" i saw one with my own eyes
Did you hear this from math grad students?
Because I've mostly hard this kind of thing from non math people
Ignorance of the law is not an excuse or something
i mean infrequent
I've never seen one
someone has probably done it at some point
yeah, I can't just isolate myself from knowing the law to kill a person without consequence
Find advisor with money is usually the suggestion. But I heard more on the line of you should not pay for your studies rather than to only find professor with money
yeah a few math grads a few profs
and also non math grads
Mostly non math people though
Thing is this usually makes no sense for US math phds. You're dept funded, not on a professors grant
People who have that opinion just hate teaching
Or they can't multitask
Fr
In the US, it is more on the line of if they don't have funding for you, they just reject you. At least that is from my experience
hi, aside from the abstraction of going to university and studying , or getting a phd
how is to become a mathematician ? (like in concrete terms)
It's very bad, happiness becomes imaginary and you become irrational
seems like a pretty "complex" emotion
No joke it's Real
but it is continuous?
Yes it is continuous without any limit
so I can drive faster than light. great!
But you will never reach infinity
if anyone can help me out, send me pm thanks
read #❓how-to-get-help for how to make a question channel here
@static loom send me a pm please. thanks
nope
Enzi time 2, hi there.
hai
hai
hai
join obsidian
💀
i lost 2-3 last time right
😂
yeah
Minecraft?
Bleh.
what does this mean
not this
glhf?
good luck have fun
Exactly.
LMAOOO
wtf
nice use
NOOO

chat in the vc chat💀
wait i thought enzi² was just a server nickname its even in ur display name
noooo i was typing
ez
this is the worst gif ive ever seen
whos that
a keyboard
for phone users
lol
lol
android
I mean it could be anything
i dont have gboard
you need to install it
nuh uh
i added latex symbols on gboard as well
oh
its good :3
meh
yuh uh
wonder what they prompted the ai to generate this
I think this was here before ai was released
nah
a
ETERNAL DAMNATION ‼️
how do i close a post and mark it as solved in the help forum??
Just type .close
is it a tablet or like a laptop with touch screen
idk if this counts then, but android is linux and I'd imagine you can find something on there
Is the cursor the only thing that bothers you in the app?
.
You could try creating an issue in their github
Can someone explain to me how vector AB=B-A
I'd say draw a picture and calculate it to compare
like pick some specific example, like A=(0,1) and B=(1,0) if that's not too boring
<@&268886789983436800> this kinda freaks me out seeing this in discussion
i wasn’t sure whether i should
You didn't prove Collatz
The collatz thing?
So knock it off
no the call to action
Oh I see.
i wouldn’t have done it if it were just “i solved collatz”
Weird soliciting ppl to hop in dms is sketchy
we can do that ?
crazy
how did u do it ?
me need that 
∫ ∂∅∩τ κ∩∅ω
nuh uh
=τκ∩^2ω∅^2/2 + c
Wow first Terrence tao and now Einstein, legends are joining
what about the cat? is cat one of the legends?
The vector B brings you from the origin to B. so -B gets you from point B back to the origin. Going from B to A is the same as going from B to the origin, and from the Origin to A, or -B +A. Going from A to B is the same as doing -A + B
So, BA = a-b, AB = b-a
No, Cat is meowstermind villain
Does anyone have any experience with the Casio Classpad II?
I currently have a Casio FX CG 50, but I am looking into a CAS model
particularly to solve linear systems of equations with symbolic/variable coefficients
bro so i got something about conlaltzo conejutre
Finally!
I wanted to ask the opinion of some people about what I should do.
I am going into 9th grade in September. Because I am entering high school, that opens up multiple science olympiads that I can take part in (USABO, USNCO, USAPhO, F=ma, etc). I wanted to ask about which olympiad I should start with this year.
For more context about me, I got a 5 on AIME in 7th grade, made MATHCOUNTS NJ states in both 7th and 8th grade, and have won a couple of local math competitions. I also take part in USACO, where I am silver right now, and have won a couple of local coding competitions. I am decent at science, me and a few of my friends won a local science bowl tournament this year. I know all of the math necessary to do physics (up to calculus and matrices).
I have the textbooks to study the respective science subjects as well (Campbell Biology, Zumdahl & Zumdahl for chemistry, and University Physics (Young and Freedman)).
Feel free to ask for more information about me, and let me know what you guys think!
Do none of the olympiads. Read analytic number theory instead
Are they required anyway for getting into something you want?
just for fun
i mean I can, and I want to do all three by some point in high school, but its all just for my personal gain and fun
I guess go for it then
my question was, which one should I go for first
There might be logistical factors around which of these you can do when
And which youd be most likely to do well in earlier vs later years
Though idk any of these, in a math server youll be less likely to find people who did these
yep exactly
Anyone use one of those habit tracking apps? Any recs? I'd like an app that reminds me to do shit rather than relying on my feeble brain.
Not an app, but you could write it on a piece of paper or calendar and stick it in your room in a place you can't ignore
I don't wanna stuck stuff on my walls or anything + I move between two households alot right now
I find that if I right what I want to do in a day down anywhere, like a google doc, or a random page of a notebook, and if I allot time to each thing, I usually get everything done by the end of the day
I already have a todo list
This is more I want something that tracks for me how many days in a row I've done something
And having it in an app is a nicer user experience in theory than plaintext
I was like who tf is enzi^2
Hi akira
does anyone now what software used by maths tutor
My teacher use zoom


#nocats
Thank you
#cats domination


pew pew pew
How do people avoid becoming complacent and mediocre?
By being proactive and extraordinary.
so true
I guess it depends on what you want
reject the premise of mediocrity and live your life the way you see fit :)
based response
Oh, that's too easy. I don't know why more people don't try it.
People use 80-20 rule, 20% hard work 80% rest
amiright? Why sleep when you can just do math instead?
Sleep is very important
to function
And functions are important in maths
So sleep is important for maths
Yeah, i was being ironic. Your proposition seem absurd, so i think irony is a good choice here

Can't argue with that logic
I should really sleep more so I can become good at math
Yes you smart
why is it absurd
it is extremely reasonable
40 hours a week is about 23% of the time in a week
Because it seems to assume people should practice a difference balance of work and rest, which i believe to be absurd.
Sorry if i was an asshole
It's okay friend 😊
if ur love's gone away just like mine, you feel like cryinggg
sing along maybe once maybe twice, lets try here togetherrrr
some sweet day no one knows he'll return, and you'll be happyyyyy
shout it sweet in a song listen to your heart it is singinnnn
Guys do you think you can become the best mathematician in the world by studying the subject in and out or is it mostly genetics
there are a lot of factors out of your control that don't just boil down to "genetics"
Yeah being a genius itself won't get you anywhere
I don't even think it's possible for a person to become the best mathematician in the world at this point
too much math
u can become the best mathematician if just memorize all of mathematics, somehow create a time machine, go back in time and then just say u are the best mathematician from the future and prove it by laying them the so-called forbidden knowledge of mathematics
Delusional
chatGPT is the best mathmetician because it knows every theorem and through it's many wierd math mistakes has created many which dont exist
the only real delusional ones are those who don't accept chatGPT's solution as a real answer
its existence but we are too poor in mind to understand it
but GPT is much more efficient
no it is not lol
your brain uses like 5 W of power
an nvidia gpu uses like
300 W
power effieciency is nothing when it comes to chatGPT's gross incorrect theorem output
I think you are getting very delusional the more you rely on ChatGPT. Get some help.
nah man, i believe in my guy. i passed my essays and stuff because chatGPT give legit pointers. even if sometimes the math solution given by chatGPT is not satisfiying to my teachers, i still believe there is some hidden values that we cant still comprehend with our current understanding of logic
whack
I've never heard of someone referring to chatGPT as "my guy"
soon chatGPT will be "Bestie"
I honestly can’t tell whether this is satire or not
people have already been dating AIs
I look forward to the first report of a murder suicide because irl friends were dating the same AI
Do you think most of maths is already been proven or is there still loads to go ?
ooo u interested? ofcourse there are conjectures and such that are still unproven, and as long as there's still possibilities for improvement, it's worth a try to improve mathematics as to create opportunities for engineers and scientist to discover new things as well. i want my grandchild to live in an advanced and possibly resourceful world, so no reason to stop here yet
the rule thingys say those are for specific math problems
mine is just concept thing
Idk friend just ask
i can help
I think its belived that genetics does effect the max intelligence an individual can achive
Yes if you are talking about "the best in the world" then there are genetic factors, your surroundings and other things also matter
What even is max intelligence
How can one even measure that
as in someone cant surpass a certain inttelgence measuremnt I dont think
idk its just something Ive heard
The thing is we don't even know what is intelligence
im mainly talkin about I q
Intelligence here as in competence how good you are in your field as compared to others
Globally
Don’t bypass the filter
LMAO
ya I know
but thats what they say
that you may not be able to achive a higher one
and your max cna be determined on genetics
obsiviously not all intellgence is just genetics but I think there can be a signifciant advantage from genetinics
Peak higher reference?
Yeah, genetics always play a role in almost anything. But to me, a genius is just a person who has studied their whole life
The fact that you had to bypass the filter should have made you pause and reflect.
i love jacob collier
We have a lot of genius today. It is just that modern science research is often being done as a collaboration of many people not just one.
💵💵💵 is the real genius
Only briefly, need to go back to work so I'm not going to see this trainwreck scintillating debate pan out in real time 😦
yeah, i need to sleep as well. Hope you get what you need done. Unfortunately, i am addicted to watching trainwrecks play out :P
but I hope you're doing well.
Mostly fine; thanks and likewise!
sounds like buffons needle
i need 100 frozen hotdogs
my pronouns are
bro
real af
Math is Make All Teachers Happy but they didn't include anything about students
Meth Amphetamine Taken Habitually
Methamphetamine Always Transforms Health
Meth Amphe Tamine Heals
Meth Amphe Tamine is Healthy
Methamphetamine All day every day Thats right Hooray
Methamphetamine Always makes Trying times Happier
i think u have a problem
yes i am out of meth
wont be long now
My Amphetamines are in the mail and should arrive The day after tomorrow Hell yes
racetams are keeping me alive atp
how would you show that (1+1/n)^n is e
,, (1+\frac{1}{n})^{n} = e
,, \bigl(1+\frac{1}{n}\bigr)^{n} = e
,, \biggl(1+\frac{1}{n}\biggr)^{n} = e
רי-ית
why did your latex not show
You don't see it?
only last line
I deleted the first two
let me fix it
Because parentheses too small
Ok
,, \lim_{n \to \infty} \left(1+\frac{1}{n}\right)^n = e
limit?
Oh i see
938c2cc0dcc05f2b68c4287040cfcf71
i thought u were enzi but u kenzi
with great difficulty because it's not true
Is set theory just SQL?
Simply take n = 100
You can try: $\lim_{n \to \infty} e^{ln((1+\frac{1}{n})^n)} = \lim_{n \to \infty} e^{nln((1+\frac{1}{n}))}$
relational algebra u mean
Wdym
then what doee
i forgot to say its the limit
Closer
sure
L'Hopital rule?
okay
,align &= \lim_{n \to \infty} e^{ln((1+\frac{1}{n})^n)} \&= \lim_{n \to \infty} e^{nln((1+\frac{1}{n}))} \&= \lim_{n \to \infty} e^n \cdot \left(1 + \frac{1}{n}\right)
938c2cc0dcc05f2b68c4287040cfcf71
,, \lim_{n \to \infty} \sum_{i=0}^n \binom{n}{i} \left(\frac{1}{n}\right)^i
רי-ית
Lol
You can simply it to this: $\lim{n \to \infty} e^{nln(1+\frac{1}{n})} = e^{\lim{n \to \infty} nln(1+\frac{1}{n})}$
Not sure
rightt
Closer
latex fail
but I still have the n inside the limit
You can simply it to this: $\\\lim_{n \to \infty} e^{n \cdot \ln(1+\frac{1}{n})} = e^{\lim_{n \to \infty} n \cdot \ln(1+\frac{1}{n})}$
Yeah
938c2cc0dcc05f2b68c4287040cfcf71
$\lim{n \to \infty} nln(1+\frac{1}{n}) = \lim{n \to \infty} \frac{ln(1+\frac{1}{n})}{\frac{1}{n}}$
wait what
It is an indeterminate form of 0/0
Closer
Damn my latex is being sh*t
Yeah
Yeah. I don't know if it works, though
,w differentiate 1/x
,w differentiate 1 + 1/x
If everything works out, the limit should be 1
,w e^(((-x^(-2))/(-x^(-2))))
Well, that limit is like an "elementary" limit now so it should be true
sure
My major is not related to math and I like math and I had some research on pre calculus my last subject was taylor series and I don't know what should learn after it I will be thankful you guys answer me
You should learn not to ask the same question in six channels
There's a discussion here
Lets you argue that the difference between (1+1/n)^n and e is of the order of 1/n, asymptotically
Which would make the series divergent
Ah, because we find a divergent lower bound with that, right?
Or just straight limit comparison test with 1/n
if comparison test with harmonic series, 1/n diverges due to p-test with p = 1, right?
Well, it doesn't diverge due to the p-test, but if you know the p-test, then that's how you can conclude the divergence.
horizontal vertical and oblique asymptotes, inflection points, absolute maxima and minima, concavity convexity, taylor polynomials, maclaurin polynomials, p-series test, integral test for series, ratio test, root test, fundamental theorem of calculus part1, fundamental theorem of calculus part2, integrals, integration by p, integration by u-sub, partial fraction decomposition, overall convergence and divergence of sequences and series, for sequences there is a d'alemberts criterion that is similar to ratio test, theres is also cauchy criterion for sequences, you can learn about solids of revolution, volumes, areas with integrals, there is so many stuff to learn
☠️
You really list all of that?
I don't know what should learn after it I will be thankful you guys answer me
I was just trying to help a bit
there is a upper bound of error you can also calculate for the taylor polynomial
intermediate value theorem, mean value theorem, rolles theorem, cauchy mean value theorem, bolzano-weierstrass theorem, taylors theorem, fermats theorem of finding minima maxima
Sure, but what are you going to do on the second day?
@pulsar finch thanks
so true
doesnt this converage to zero when n approches infinity?
oh right my bad I misinterepreted the quesiton
hi
Hello laylap
Guys was learning about complex numbers what I found out is that they add additional dimension to our real number line. My question is the vectors in 2D they also do the same rotation and other stuff can anyone explain this. Yeah i heard about e^thetai thing and using sin cos but a 2 or 3D vector is also doing the same.
The complex numbers are a 2-dimensional real vector space. I think this answers your question.
Specifically, consider the map $\varphi:\mathbb{C}\to\mathbb{R}^{2}$ given by $$\varphi(x+iy)=\begin{bmatrix}x\y\end{bmatrix}.$$
Fruitbini's Theorem
You can show that this is linear, injective and surjective, and thus an isomorphism of vector spaces.
Alternatively, you can show that ${1,i}$ is a basis for $\mathbb{C}$ over $\mathbb{R}$ directly.
Fruitbini's Theorem
Wait I misread your question. You want to look at the matrix $\begin{bmatrix}\cos\theta&-\sin\theta\\sin\theta&\cos\theta\end{bmatrix}$.
Fruitbini's Theorem
@vast surge yes you kinda answered my question but the thing I cant understand is Iam adding a new imiginary dimension when introducing complex numbers. Using this dimension I can rotate and do other stuff right
@vast surge why cant I use a vector 2D it can also rotate and do similar things
You can! Look at the matrix that I provided.
The vector space structure isn't what's interesting about C; it's the multiplication structure that sets it apart from R^2.
Specifically, it sounds like a lot of your questions are on linear algebra, not really anything to do with the complex numbers themselves. Have you studied LA? If not, I recommend this book: https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf
sorry out of curiosity, is this a jacobian matrix?
No.
can jacobian matrices have any use in rotation
i distinctly remember some theory about that
when considering frenet bases in differential geometry I think there's one point where jacobian matrix comes up in the taylor expansion of something, it represents by how much the basis would rotate if you were to travel for some time
this map pretty cool
well, some things on here are downright depressing, but very much important elements in the history of science and its many intersecting fields, such as politics
also rather frustrating that in many places they mention some idea or technology at some specific time in history but without any reference
Calculating Empires takes Donna Haraway's provocation literally that we need to map the “informatics of domination.” The technologies of today are the latest manifestations of a long line of entangled systems of knowledge and control. This is the purpose of our visual genealogy: to show the complex interplay of systems of power, information, and circumstance across terrain and time, in order to imagine how things could be otherwise.
We suggest taking your time and reading slowly - a radical act in an era of speed and simplification
😭
Hi guys does anyone know where I can follow a youtube course on group theory ?
I would suggest reading a book instead, maybe Fraleigh for example
I dont know if this sould go in some help channel , but how you really measure mathematicians performance?
I mean, there are tests , but there is something else?
(and also which are the most important tests?)
how you measure for example, is someone knows enough algebraic geometry?
(I am not talking about research papers and so on , since it could be papers with almost no impact or something like that, and finally time is what tell us if something was important or not)
you talk about it
yeah, i think, the real question if there is a objective measure
I don't think you need one to answer whether someone knows enough of <math topic>
well you seem to answer your own question with the last statement, if you want to evaluate the quality of a mathematician (“objectively”), you want to measure the impact of their work, perhaps picking some metric about citations
but i don’t think it’s so useful or easy to do that, and i don’t think citations are the right metric
i just wanted to throw something out
yeah, I was confused, I finished answering the question to myself , sorry
what about quals exams , are them a good measure?
(for general math problem solivng skill and knowledge, not research skill)
also
which is harder IMO vs quals phd math? (in problem solving level skill)
I don't think there is any standard test for mathematicians the real test is whether you can help in development of maths but my knowledge has a limit and my domain is restricted so I could be wrong
yeah , I am just talking about formalities like tests , etc.
if someone is good or bad , that's opinion
Neither. The question is are you willing to publish good research or not
Math is very sad subject
at least is happier than the others
You can do perfectly fine as a mathematician without publishing any good research, it served me well for over 15 years.
I want the same confidence you have sometimes
i will take this to heart in case of need 🦆 🙏
bad 

Very bad, going in negative direction with exponential increase in speed
erm you can't have negative speed 🤓
(i don't know that, just a joke)
but do you guys need anything?
Yes money and time
oh
fight with my English teacher to give me 4.0 gpa

a
b
geometry gd
also nice shaders usage
thank
whats your hardest
killbot
noob
username?
fishyfox84
personally I hate people flexing their cp only with one level
so what? I don't care
i mean
its insanely hard to do
not even making the level
that took me 2 weeks tops
getting it rated was the hard part
I mean I can tell that you're a hacker no?
what
you got banned on lb lol
uh
lmfao this is funny
did you use megahack?
i sometimes noclip demons ive already beaten as daylies
weeklies*
but i do that for daylies aswell
lmfao
not like ill ever stargrind pft
I can understand why you're banned on lb
I believe you cheated and then they reported you to get banned on lb
theyre pretty tight about that
but i haven't yet because i got skills more than you
they think you should rebeat demons and shit
go check mine
whats your ign
kensukeken
sometimes weekly are shit
like most of them are buggy as fuck
@ocean harbor why have i played ur level
s
it shows i have progress on them
specifically ultra paracosm copy
ah this
it was just a practice level
when beating this demon
I got a video for this and i tried to publish it ig
wtf
so that means i found your level either in the recent tab
or like
something else
you havent commented on any of my levels
let me check rq
used to but not much
those are not really my levels
just a copy
it doesn't show you're here lol
its weird since you uploaded the level 3 months ago but i remember playing it like 3 weeks ago max
odd
again im lb banned lol
so it probably wont show there
ill just forget about this and assume it never happened because the odds of this naturally happening are genuinely in the millions
we must have met somewhere else by accident or something
its your fault for cheating on gd
but normally none of my friends on gd are cheaters
they're all on lb
i beat killbot like i said, crowd control and marathon
show me a video
those are my only extremes
without hacking
for marathon i dont have one so youre gonna have to trust me
thankfully i have one for cc
and ill use my record on the demon list as proof because the actual video is super mega cringey
i was 13
how old are you now lol
I mean ive been playing this game for 10 years and I cannot beat any extreme demons yet
some people get 200 demons within one year
this is crazy you know
reddit user 
i feel like I need to start skibidi sleepmaxxing fr
its on the official pointercrate page
if u wanna check
i do have the video
if you really care
i know..
clicks per second
there we go
the number on the right is the total amount of clicks
gg
Thank god I am 13 years and 1 minute old
im 16
btw
i just remembered i forgot to reply to this
I started gd in 2015 and now im 19 in a month
still can't beat any extreme demons lol
i started in early 2020
nice
start of pandemic pretty much
i mean just practice one for long enough
if you can beat an insane demon then you can beat an extreme
an easy extreme that is
im not saying you should be beating acheron or something
acu is a good place to start
it says invalid
i went on a rage fit last year trying to get my level rated and deleted everything
thats why my reddit account is gone
same for youtube
i still have the video tho
i feel like the only days i have that are really meaningful are those where i do something im normally averse to or where i go out with friends for most of it. does anyone else feel like they have a limited class of "days that are meaningful"?
wait i remember you lmfao
I just checked the level
wait how
this lol
personally I don't talk with people flexing their cp only for one
because they're toxic
its just a hard achievement
if you ran a marathon and were talking about running to someone youd probably mention it
i wasnt trying to flex a singular creator point
im an advocate of abolishing cp entirely but thats a debate for another day
I was happy doing my level but its gone sob
huh?
lmao
i said that as a joke..
its ok i forgive you
i do talk to people who dont have cp
ohh okay yeah i remember
I see
i mean
look
stuff happens

if i see someone has something like then they probably got banned
I have seen this a lot
try mine lol
it shows your lb position
HI.
save your progress sillyhead..
lol
I did
sometimes when I load
things disappear
thats how loading works
it puts you back to your latest save
cat
I always play daily levels but then I keep forgetting to continue for my level
https://youtu.be/WlwGoLSMf0M i made this semi-recently
lets say when i have to upload and then I do that
without knowing that my level has removed
ill check rn
noclip again?
you didn't die
yes..
im a hacker
muhahah
its for showcasing purposes
you see
i dont wanna learn my levels just to be able to play them without noclip
fucking hacker
thats probably not even hacked lol
I wanted to join with you
join what
so we can create levels together
you mean collab
i changed my mind
oh
I don't join with hackers
okay
go away

for i have been a careless hacker
how about creating a new account and don't hack next time
lets create a level together
:3
i shall then repent my sins and move on to greener pastures
does this mean robtop is god
nah everything lol
a whole ass level?
yep!
why dont we try making a layout first
😭
i dont even know how to merge stuff
i guess itll be good practice
im gonna start with like easy or nomral level
nah



