serious-discussion

[grim root]

for what?

[obtuse grail]

Hello

[winged galleon]

9 grade maths

[grim root]

yea i can help

[winged galleon]

Its about

Simultaneous Equations

of graph

[obtuse grail]

Mine is the substitution method

[grim root]

what are u struggling on

[winged galleon]

can u teach me

[obtuse grail]

I think I can

[winged galleon]

33x + 44y = 123

44x + 33y = 71

how to do this

[grim root]

rearrange to get one of them by itself

[obtuse grail]

I think I will also learn too

[grim root]

(71-44x)/33=y

[winged galleon]

ok

but

[grim root]

then you can sub into the 33y

[winged galleon]

can u see there's x

[obtuse grail]

Yeah

[grim root]

yea then you can solve the x since now there is only x

not y

[winged galleon]

so x=(71-44)/33

?

[obtuse grail]

U are using the substitution method right

[grim root]

no 44x +33((71-44x)33)=71

[winged galleon]

ok

[grim root]

so just rearrange to get x now

[winged galleon]

pls say it fast

i gtg

bye

[grim root]

gl

[winged galleon]

i understood

thx

[obtuse grail]

Thanks

Are u new on mathcord

[grim root]

yea

im just bored

[obtuse grail]

Same

[obtuse grail]

Me too

U are a good teacher

[grim root]

thanks im currently in year 11 doing IB

so i have done this plenty of times

[obtuse grail]

What is IB ur welcome

[obtuse grail]

Nice

[grim root]

its the international baccalaureate, its like the end of year 12 exams, but its accepted worldwide

[obtuse grail]

Nice

[obtuse grail]

So it u do it u are done with school

[grim root]

yea

[obtuse grail]

That's cool! Congrats

[inland hornet]

dp1 or dp2

[fresh comet]

@grim root welcome to the mathcord

[latent edge]

Many such cases

[winged galleon]

hi

[winged galleon]

thx for solving my question

[subtle vessel]

@wintry wigeon do you still need answers?

[wintry wigeon]

about SJF?

i could not really figure the solution out; i did not want to tag helpers too because, well, this is not exactly a coding server

[subtle vessel]

#help-46 message

[wintry wigeon]

ah

that one, sure

[subtle vessel]

Do you mean in the custom comparison functions?

[wintry wigeon]

int compare_process_arrival_time(const void* a, const void* b)
{
    return ((const struct process*)a).arrival_time - ((const struct process*)b).arrival_time;
}

int compare_process_burst_time(const void* a, const void* b)
{
    return ((const struct process*)a).arrival_time - ((const struct process*)b).arrival_time;
}

qsort(a, n, sizeof(*a), compare_process_arrival_time);

qsort(&a[i], m, sizeof(*a), compare_process_burst_time);```

[wintry wigeon]

yeah

[subtle vessel]

qsort needs a comparison function, and it only accepts a specific signature

[wintry wigeon]

what does it stand for?

[subtle vessel]

They must be of the form int f(const void* a, const void* b)
where f, a, b are just whatever names you want

The signature? It's the set of parameter types and return type of a function

If you're comparing ints, taking a pointer is unnecessary but it wouldn't matter too much for performance anyway

But if you're comparing more complex things, like structures, you need a pointer

In C you can't copy structures just by assignment

[wintry wigeon]

what exactly tweaks the performance?

[wintry wigeon]

ah

[subtle vessel]

The indirection

[wintry wigeon]

did cpp not have a sort function?

[subtle vessel]

Taking a pointer instead of an int means the address is copied into the function and then you need to dereference that (access the pointed-to int)

[wintry wigeon]

also, i was talking about the name "qsort". i was wondering if it implements things using a particular algorithm

[subtle vessel]

If it just took an int directly, it would only copy that int, nothing more

[wintry wigeon]

isn't that too much work?

[subtle vessel]

Oh, yeah that stands for QuickSort

[wintry wigeon]

makes sense

[subtle vessel]

Like I said it's unnecessary but doesn't matter much

The point is that qsort needs to work with anything you throw at it

[wintry wigeon]

what stuff other than structures?

[wintry wigeon]

yes, makes sense

[subtle vessel]

Arrays

In C you have primitive types like int, structures, and arrays

IIRC that's all

[wintry wigeon]

float and all?

[subtle vessel]

That's primitive

Pointers are primitive too

[wintry wigeon]

i see, makes sense

[subtle vessel]

So, qsort takes const void* arguments so that it can accept variables of any type by taking their address, and it guarantees not to modify them (the const part)

Rather the comparison function must take const void* arguments, not qsort directly

But qsort only accepts those kinds of functions

[wintry wigeon]

but when does modification ever happen? do we just not call it once?

[subtle vessel]

qsort modifies the array, not the elements inside

[tawny knoll]

It does?

Which version are you talking about

[subtle vessel]

Yes, it does, it's called std::sort, and it makes it a lot easier than in C

[wintry wigeon]

qsort is in c?

right

[subtle vessel]

Yes

In C++ you'll pretty much never see void* parameters

[wintry wigeon]

i did not know c has pre-defined functions like that haha

[tawny knoll]

Yesss

[wintry wigeon]

for sorting and stuff

[tawny knoll]

Same

[wintry wigeon]

why though? what happens to structures and arrays?

[river moon]

std::unique_ptr<void> ptr;

[subtle vessel]

Most languages have a sort function

[tawny knoll]

Sort(arr.begin(), arr.end()) cpp on top

[subtle vessel]

C++ uses templates

[wintry wigeon]

also, question, why do most people do std::something, and not just use std namespace? (like here)

[subtle vessel]

The general mechanism is called "generics" or "generic programming"; C does it with void* and casting, C++ does it with templates

[river moon]

because it makes it clear that the thing is coming from standard library and not from some other place

[wintry wigeon]

right. i will need to learn more about that

[river moon]

the issue with using namespace std is that if you put that in the header due to how the headers are simply copy-pasted by preprocessor you'll get using namespace in every file that included the header with using namespace std, potentially forcing it on users of your library for example

[wintry wigeon]

eh? does "using namespace std;" not do the same thing (because std is already there)?

[subtle vessel]

using namespace std is terrible practice; unfortunately a lot of online tutorials and whatnot use that because it simplifies small examples

Read some of the answers in there: https://stackoverflow.com/questions/1452721/whats-the-problem-with-using-namespace-std

[river moon]

using namespace std is fine if you do it in local scope or in a cpp file, so that it is not visible outside the scope/cpp file

[tawny knoll]

Then if we import a specific library like algorithms can we do algorithms:: something?

Like a function from algos

[river moon]

no, algorithm doesn't have it's own namespace

[tawny knoll]

Hmm

[wintry wigeon]

okay, thanks for the answers!

[subtle vessel]

(especially the second one)

[river moon]

for instance if you happen to use boost library in your project, it turns out boost has boost::shared_ptr and boost::function much like std::shared_ptr and std::function

if you had using namespace std and said shared_ptr<int> ptr; or function<int(double)> f;, which one are you using?

[subtle vessel]

Everything in the standard library is in the std namespace, and a few things are in sub-namespaces like std::chrono

[tawny knoll]

Ah got it

[tawny knoll]

I see

[wintry wigeon]

question; if using namespace std is so bad, why even create such thing?

[subtle vessel]

@wintry wigeon if you continue with C++ you should learn to manipulate iterators; that's what the standard algorithms (like std::sort) use, and it can simplify your life as well because once you're familiar with them, you can write loops where you manipulate array elements directly instead of indices

[subtle vessel]

using namespace isn't bad, doing this with std is

[tawny knoll]

If u import a non standard library would it have its own namespace? Or what exactly is namespace

[river moon]

it's fine if you do it in a local scope because some namespaces tend to be quite long

[wintry wigeon]

got you

[wintry wigeon]

but still this is bad practice, right?

[subtle vessel]

It all depends on how the library is defined; a lot of libraries you can find online will define their own namespace, like boost

[tawny knoll]

Oh got it

[subtle vessel]

Btw you can also do using std::cout if you want, it allows you to call cout without the std:: prefix, but nothing else

So if you want to use cin as well, you do using std::cin

[wintry wigeon]

what else do we normally use in our basic codes

from std

[subtle vessel]

But really, the main point is this

Standard things should be instantly recognizable, so always prefixing them with std is just good for readability

[river moon]

not really as long as you keep it limited and not just spam it everywhere, for example if you wanted to write a function that does some time measurements using std::chrono it's going to be annoying to write because of std::chrono::high_resolution_clock::now(), std::chrono::duration_cast<std::chrono::milliseconds>, etc

[subtle vessel]

You, not much so far; vector maybe?

[river moon]

you can just locally do using namespace chrono and remove half of the name

[wintry wigeon]

i see

[subtle vessel]

Yeah using is a great tool for keeping long names short (in a limited, local scope)

[river moon]

even better is using clock = std::chrono::high_resolution_clock; clock::now()

you give a short alias to a library name you're interested in instead of including all names from namespace

[wintry wigeon]

question

do we have something like, a library inside a library?

[subtle vessel]

Kinda

[tawny knoll]

More like a library extends other libraries i think

[subtle vessel]

It's just nested namespaces like the std::chrono example

[wintry wigeon]

what exactly is chrono here?

[subtle vessel]

Tools for measuring time

[tawny knoll]

Hmm

[river moon]

it's a namespace, part of a standard library header called <chrono>

[subtle vessel]

There's also std::filesystem

[wintry wigeon]

so whatever stuff is inside chrono, does it automatically not get load when we do std::?

[river moon]

no, you don't want to load entire standard library in every file that used some small class from it

[wintry wigeon]

sure, but does it or does not?

[river moon]

it doesn't

[subtle vessel]

So for example std::chrono::system_clock is a standard type that represents a clock tied to the OS

You can't do std::system_clock

And if you do using namespace std, you still can't do system_clock, but you can do chrono::system_clock

[wintry wigeon]

chrono is a namespace as well, right?

[subtle vessel]

But again, the better way is just to do using clock = std::chrono::system_clock

Yes

[wintry wigeon]

makes sense

[tawny knoll]

I understand that when we include bits/stdc++.h we need to do std:: but std:: isn't there when we import iostream then why do we use it?

[wintry wigeon]

someone told me bits/stdc++.h is bad too

[tawny knoll]

Or is that a part of the std library as well?

[subtle vessel]

It's defined like this:

namespace std {
  namespace chrono {
    /* system_clock definition */
  }
}

[river moon]

namespaces allow for two different types to have the same name as long as they're in a different namespaces, e. g. in standard library you have std::vector in std namespace and std::pmr::vector which is a different implementation of vector in a nested pmr namespace

[subtle vessel]

bits/stdc++.h is non standard, don't use it

[tawny knoll]

Oh

Everyone uses it for competitive prog though

[wintry wigeon]

i get it, i was just wondering if we could call the outer (?) namespace to have stuff of the other namespace as well

[tawny knoll]

Is that okay or not

[subtle vessel]

Don't do competitive prog

[wintry wigeon]

pmr?

[tawny knoll]

Hmm

Fair enough

[river moon]

yes, there's a pmr namespace inside std namespace in standard library (starting with c++17)

[tawny knoll]

But does iostream come under std?

[wintry wigeon]

i see

[tawny knoll]

Namespace

[river moon]

yes

you can't use cout and cin from iostream without doing std::cout and std::cin

[tawny knoll]

Then shouldn't we be doing std::iostream:: method name

[river moon]

you're confusing header name and namespaces it contains

[subtle vessel]

What method name?

[tawny knoll]

Cin or cout

[river moon]

header <vector> for instance doesn't contain the namespace vector, it does contain the class vector

iostream is not a class in standard library

[tawny knoll]

It's defined like this:

namespace std {
  namespace chrono {
    /* system_clock definition */
  }
// iostream stuff
}

is this correct?

[subtle vessel]

iostream isn't a namespace, it's a header file and a type name

Conceptually, yeah

[tawny knoll]

Oh got it

[subtle vessel]

https://en.cppreference.com/w/cpp/header/iostream.html

You can see that cin and cout are just global objects defined in the std namespace

[tawny knoll]

Oh got it and the header iostream gives us direct access to them

[subtle vessel]

It kinda is https://en.cppreference.com/w/cpp/io/basic_iostream.html

[tawny knoll]

I think i got the idea

[sharp mulch]

Don't pollute the namespace!

[river moon]

namespaces can span multiple files, so different headers can contribute different stuff to the same common namespace

[tawny knoll]

Got it, thanks guys

[subtle vessel]

@wintry wigeon any remaining questions? This is probably a lot to take in tbh

[wintry wigeon]

i mean i think i get what you all said but

i will definitely need to read more about all of this and practically implement stuff to see what happens when (through errors)

i do not know if i should do that now though

because this stuff does not really have an ending

[river moon]

if I'm reading this correctly the bits header includes the entire standard library, the issue with that is that when you build a project containing many different files and each of them happens to include <bits/stdc++.h> either directly or indirectly (through other includes) this means that every cpp file will contain a whole copy of the entire standard library and the compiler will have to parse all of it for every single file which can massively slow the compilation

[subtle vessel]

Yeah, there's definitely a lot to learn

[river moon]

only include what you actually use and try to keep includes to a minimum, especially in headers

[wintry wigeon]

doesn't the same hapen when we do using namespace std?

or any other header/namespace, really

like

for instance

when we do #include <iostream>

[river moon]

no because using namespace std isn't a preprocessor directive that pastes contents of headers into your files

it only tells the compiler to try to look for unknown names in a namespace std

it won't go looking into the entire standard library, only in the part that's included

[wintry wigeon]

okay, what about this?

stupid question but what does '#' do?

[river moon]

yes, if you do #include <iostream> in a header and include that header in another header, the same issue happens that it will parsed by compiler multiple times

[wintry wigeon]

but then why does it matter when we do bits/stdc++.h

[river moon]

standard library is massive, iostream not so much (though still big)

[wintry wigeon]

don't they both essentially mean the same thing

eh

[subtle vessel]

# is the start of a preprocessor directive; you've only seen #include but it can do other things

[wintry wigeon]

i mean

[wintry wigeon]

examples, please?

[subtle vessel]

#if , #ifdef, #else to conditionally throw away parts of a file

[golden brook]

Does anyone know a website where all big Primes are listed?

[wintry wigeon]

does '#' not tell the preprocessor to start exactly from there?

[subtle vessel]

The preprocessor is something that comes right become the compilator (technically it's part of the compilator but whatever)

[river moon]

the larger your project is the more there are these parasitic includes that slow down the compilation, it might not seem like a big deal when you only have 5-10 files and it compiles in 10 seconds, but it's a serious problem for larger projects - I've worked on projects that take 5-20 minutes to compile from scratch and these aren't really that big, for instance huge projects like LLVM or Google's can take hours to weeks of compile time which is why people should be concerned about parasitic includes

[wintry wigeon]

i see, that makes sense but i was just wondering if we could code something like

if a header is already included in a file (it checks if it is), it does not really include it again

that probably does not make sense

[subtle vessel]

Not sure what you mean. Example:

#define DEBUG
// some code...
#ifdef DEBUG
printf("%d", var);
#endif
// some more code

The printf call will only happen if the file is compiled with the DEBUG identifier, defined earlier (or via a compiler command line argument)

[river moon]

that's where the cpp comes into play, you have both many headers and many cpp files

yes, you can put include guards that will prevent multiple inclusion, but they will still happen across multiple cpp files because each cpp files needs full contents of it's include headers to compile

[wintry wigeon]

why did we think we had a need to use '#' with 'define'?

[wintry wigeon]

okay, makes sense; thank you

[subtle vessel]

Funny you should say that, it's something that's almost always done everywhere, using a preprocessor directive

It's the include guards @river moon just mentioned

[wintry wigeon]

i see

[river moon]

the hash specifically is more of a legacy system inherited from C, there's really little reason for it existing other than that

[wintry wigeon]

i do not know what include guards are though

[subtle vessel]

https://en.wikipedia.org/wiki/Include_guard small article that explains it

[river moon]

for instance c++20 added modules, which are there to replace headers and their issues, and modules use the "import" keyword to import a module and "export" to export names from this module, import and export are both new keywords and don't use any preprocessor hashtag magic

[velvet wren]

anyone has a video that teaches logical thinking anf how to use the symbols

[subtle vessel]

And yeah, the preprocessor comes from C, and was inherited in C++, but in C++ there are other mechanisms (though it's still used quite a lot by many people)

[wintry wigeon]

does it not mean it always throws an error whenever there's a copy of some header?

[river moon]

that's if you don't use include guards, it definitely happens yes

[subtle vessel]

Next sentence: "#include guards prevent this..."

[wintry wigeon]

right, sorry

[subtle vessel]

Alright I gotta go, see you around

[wintry wigeon]

good day

[boreal wagon]

Any more servers like this ? Informative and stuff, especially related to academics

[sharp mulch]

See #old-network

[lusty atlas]

@subtle vessel r u related to neliel?

[warm umbra]

Welcome to the server @odd cliff

[valid hornet]

How rigorous does one need to make a mathematical proof? Does one need to make it rigorous enough so that it is easily written in a proof assistant language like Lean? I'm having a hard time understanding how small the steps are I need to take.

Like, do I have to put "disjunctive syllogism", or "hypothetical syllogism" or "De Morgan's Law" etc. for each step in the proof?

[fiery stump]

put as much detail as ur textbook does in its proofs is what I've heard

[valid hornet]

Sometimes I get paranoid about my ability to reason about these things so I make the steps very small and obvious.

[fresh comet]

my experience has been that it largely depends on your audience

for instance, if you're writing for an audience of students who're new to math, it's good to prove all the small details like set equalities

but if you're writing say, a topology proof for a more experienced audience who're familiar with basic set theory, then you might be fine ignoring some of the super small stuff

[fathom swallow]

Heavenly Philosophy

[valid hornet]

That was the first one

Here's the second one

[fathom swallow]

Heavenly Philosophy

Heavenly Philosophy

Heavenly Philosophy

Heavenly Philosophy

Heavenly Philosophy

[valid hornet]

The first one makes it feel like I'm conveying how I thought about it, but the second one feels like I'm talking to a robot.

Maybe having both at the same time would be good.

[icy viper]

i agree

[gritty heath]

Write it so that someone in your class can follow the proof

[valid hornet]

The top statement or the bottom one?

Or both?

Should I write a proof like version 1 vs version 2?

[light thorn]

My parents are really trying to encourage me to drop calculus 2 while doing so won't give me a W

Say I'm too stressed out by it

But I don't want to be bad at math. I can't live with being this bad at math

[neat lintel]

Don't worry not everyone is good at everything and if you really wish to improve you definitely will .

Just give your best because there is nothing one can't do .

[icy viper]

first onee

[valid hornet]

Which one is better for writing math?

[icy viper]

the one you find easier

[winged galleon]

Ji

[stiff fossil]

Neat. https://mathstodon.xyz/@divbyzero/115137414728152361

As I was walking home today, I had this idea: Is it possible to turn a QR code into a Truchet tiling that's still a functioning QR code? Yep.

[random void]

Today I met the absolute most beautiful woman in the factory

I hit her with the

🚶‍➡️

'Cause I don't care

[ocean harbor]

ok

[raven plaza]

A senior monk and a junior monk were traveling together. At one point, they came to a river with a strong current. As the monks were preparing to cross the river, they saw a very young and beautiful woman also attempting to cross. The young woman asked if they could help her cross to the other side.

The two monks glanced at one another because they had taken vows not to touch a woman.

Then, without a word, the older monk picked up the woman, carried her across the river, placed her gently on the other side, and carried on his journey.

The younger monk couldn’t believe what had just happened. After rejoining his companion, he was speechless, and an hour passed without a word between them.

Two more hours passed, then three, finally the younger monk could contain himself any longer, and blurted out “As monks, we are not permitted a woman, how could you then carry that woman on your shoulders?”

The older monk looked at him and replied, “Brother, I set her down on the other side of the river, why are you still carrying her?”

[random void]

Because you didn't hit her with teh

🚶‍♂️‍➡️

[old oak]

I tend not to hit women at all

Nor indeed men

[raven plaza]

That is not exhaustive

[old oak]

Nor indeed those nonconforming to the gender binary

[raven plaza]

What about foxes

[old oak]

Fair game

I mean, I only beat up two foxes and it was in Touhou.

Touhou also has a lady who tried to beat me up with a fox.

[reef carbon]

@versed bluff i am a trans woman & i consider "bro", "dude" or other similar masculine terms to be misgendering.

[versed bluff]

i assumed so

[reef carbon]

you can keep entertaining your fantasies of a gender-neutral "bro" but know that it aint gonna fly all the time.

and also it's kind of gauche to say "ok but bro is gender neutral" when called out on it.

[versed bluff]

rare occasion

[reef carbon]

just edit the word out and move the fuck on.

no need to even mention its supposed gender neutrality.

that's it.

[versed bluff]

lit what i did??? u ttagged me here "buddy"

[snow helm]

why so angry?

[reef carbon]

no, you started yapping about "bro is not assuming ur gender".

[snow helm]

its just a common slang

nothin else

[reef carbon]

i can repeat myself personally for you if you want

also "fuck" ≠ angry tone.

[snow helm]

whatever

[versed bluff]

its not... if u arent comfortable with it ok bye sorry

[snow helm]

you people genuinely become angry for no such reason

[old oak]

"Bro" is only "gender neutral" in the sense that "male" tends to be considered the default gender, which is exactly why a lot of people are not happy with it.

[reef carbon]

i am not even angry.

but your insinuation that i am angry, if repeated enough, may become a self-fulfilling prophecy.

ie your continued repetitions of "why are you so angry" might in fact be the thing that makes me angry.

[versed bluff]

👍

[snow helm]

cant help it

[old oak]

I mean, you could have

[junior veldt]

i completely agree

[versed bluff]

was not my intenntion to hurt anyone i apolgized and ill do it again. i see its not the same on discord but all around school we have boys and girls and even lgbtq saying bro to eachother but sorry abt that i will not call someone bro here

[steel mantle]

You can, there's no reason to be obstinate

[reef carbon]

got a big urge to say something very poisonous and sarcastic here, but i won't.

[snow helm]

well

its upto...

[limpid hatch]

yeah i agree with ran1zy i think its dependent on the social dynamic whether its appropriate to call someone bro

the same word can have different meanings depending on how people are used to it being used in their surroundings and how its linguistic profile has evolved in their world so some people might not be meaning offence when they say a certain thing that you may instantly find offensive

[old oak]

Yes, but I think the better response to inadvertently causing offense is to go "Oh, my bad, I won't do this again" rather than "Why you mad, it's no big deal"

[reef carbon]

... which is also what i attempted to say

and also it's kind of gauche to say "ok but bro is gender neutral" when called out on it.
just edit the word out and move the fuck on.
no need to even mention its supposed gender neutrality.
that's it.

[versed bluff]

i lowk did that

[reef carbon]

bro is not assuming ur gender

[versed bluff]

what does mb mean

[reef carbon]

"mb" means "my bad", obviously, but i am unhappy that you even said the "not assuming gender" thing at all.

but i am tired of being a broken record about this

[cloud rover]

You did the latter not the former

[versed bluff]

here let me rephrase. me calling YOU "bro" was not me assuming ur gender. i understand either way u dont like it so sorry

my GOAL was never to assume ur gender

thats all im saying

im sorry

[cloud rover]

And she never claimed that this was an assumption of gender; she just didn't want to be called "bro"

[versed bluff]

and i fixed it

[cloud rover]

It's you who brought gender into it

[versed bluff]

bc i knew that its the reason @reef carbon didntlike it

[neat lintel]

[versed bluff]

bro why are u still on this

leave me alone

like fr

i apoligzed

what do u want

[neat lintel]

[versed bluff]

thank you

[young stirrup]

adtuan

explain our gruend group

er are.

Ohio.

made in ohio only in ihio

sith a pinch of arjadbas,, and among hs

wr are. Fkn chaotic as dih

A barbershop haircuy that costs a quarter

[main elbow]

who from india?

[flat dome]

if x is a number of pupils, and the question states that x>9, must x be 10 because there is no 9.0001 pupils

[main elbow]

. . .

[valid hornet]

Just any number greater than nine. It probably is unspecified. It could be 11 or 12 or ...

Probably a natural number, though

[old oak]

Unless you've got a sharp cleaver

[flat dome]

forgot to mention it must be the minimum value of x

[valid hornet]

So, x is a natural number greater than 9, and every other natural number greater than 9 is greater than or equal to x.

There also would be no minimum if we were talking about the rational numbers or real numbers because of their density property. There is no smallest rational or smallest real greater than 9.

[flat dome]

so then x=10 is not correct?

even if it’s a word problem?

[valid lance]

Hii

[flat dome]

also

how is every natural number greater than or equal to x in this

[valid lance]

Broo

Can u explain me a question

[flat dome]

never mind i understand it now

[flat dome]

what question

[random void]

Yeah it's 10 @flat dome

[random void]

No

[fresh comet]

https://tenor.com/view/motivational-gif-chibird-motivational-cartoon-greetings-good-fortune-cat-gif-16891294

[icy ferry]

hii

[icy ferry]

thanks! needed this

[fresh comet]

hello, and welcome to the mathcord

[icy ferry]

thanks 🥰

@vivid echo if u wanna join in here

[vivid echo]

Hiii

Oh red

Ur new to mathcord

[icy ferry]

hii

[vivid echo]

I didn't welcome u

[icy ferry]

which yr u in

yeah newly born

[vivid echo]

Welcome to mathcord @icy ferry

[icy ferry]

thanx

[fresh comet]

year of what?

[vivid echo]

[icy ferry]

few emojis

[icy ferry]

college

or whatever u folks call it, freshman, sophomore thing

[fresh comet]

I’ve recently started my third year

[icy ferry]

nicee

brb

[vivid echo]

[north topaz]

congrats higher!

[pure hollow]

Old

[valid hornet]

I was learning about integrals with powers of sines and cosines in my class yesterday and my professor was like "by the way there's something with complex numbers you'll learn later on that allows you to solve all of this in one line" and I want to know what that is.

[inland hornet]

de moivre's theorem i presume? not sure

[daring fog]

not quite

you don't want to expand sin(x)^n or sin(nx) before evaluating the integral

you would still use exp(inx) thought

[valid hornet]

Maybe he was exaggerating, but he definitely thought it was simpler if you used something from complex numbers.

[twin flicker]

is it something w euler

euler formula

[snow helm]

hi again mate

@daring fog

[daring fog]

hi again

[snow helm]

you asked my qualification aint it?

im just a 17-18 old kid

[jade owl]

https://cdn.discordapp.com/attachments/1208181901492486175/1354080542189944938/togif.gif

[daring fog]

it can be done in a line

[daring fog]

i'm 17 too

you know taylor series?

[snow helm]

ik basics of calculus, trig, bino, stats, vector and 3d algebra, functions, sequences,complex nos, and maybe a bit of integrals too

[valid hornet]

I've heard of taylor series as polynomials that approximate functions.

[snow helm]

dont interrupt when we are in a serous discussion here

[jade owl]

True

[jade owl]

My bad sir

[snow helm]

yes

kind of

like f', f'',...

[daring fog]

it's ok

[valid hornet]

Analytic functions are perfectly represented by an infinite taylor series in their domain.

[snow helm]

...

[jade owl]

Indeed

That's how we define analyticity

[snow helm]

what's it indeed?

idk anything about it at all

[jade owl]

Let's not focus on that first

[snow helm]

ik only the things which i mentioned above

[jade owl]

You'll have to begin with power series

[valid hornet]

$\exp(x) = \sum^{\infty}_{n=0} \frac{x^{n}}{n!}$

[fathom swallow]

Heavenly Philosophy

[valid hornet]

Like this.

[snow helm]

ik this

[jade owl]

Yuh that's a common example of an analytic function getting represented via a power series

[daring fog]

yes but a little bit circular, an analytic real function must be infinitly differentiable at every point

[snow helm]

[jade owl]

Yeah that's true

[daring fog]

and then you can say that its taylor series converges to the function everywhere

[jade owl]

For complex variables it's easy we just have it to be holomorphic on it's domain

[jade owl]

Indeed

[snow helm]

outta my game and head

cant

[cunning horizon]

.

[jade owl]

It's okay you'll learn about it slowly

Take it easy

[snow helm]

yes

ik that but still

[valid hornet]

Does being everywhere differentiable on the complex plane entail being holomorphic on the complex plane?

[daring fog]

if you take for granted the taylor series and the weierstrass product of the sine function, then you can "prove" that zeta(2) is pi^2 /6

[snow helm]

i learnt that by heart

it was proved by a mathematician

maybe euler?

[daring fog]

yes but it must be complex differentiable everywhere

which is sufficient for it to be analytic on the complex plane

[daring fog]

yes

did you see the "proof"

the one with sine

[valid hornet]

Well, you would substitute $x$ with $i\theta$ and then seperate the two series (although I'm not quite sure when it's valid to take a series apart like that)

[fathom swallow]

Heavenly Philosophy

[daring fog]

and also necessary

[snow helm]

never

i never dared to see it

[daring fog]

https://youtu.be/terkglX1wWM?feature=shared

only weierstrass is needed

[valid hornet]

Can't you relate it to a trigonometric function and then do something like that?

Like tangent?

[daring fog]

it's not always valid, and most of the time is not convenient

[daring fog]

the classical formal proof uses tangent, but for a deeper understanding of it calc 2 is required

[snow helm]

😔

[daring fog]

did you understand the video?

[fathom swallow]

Heavenly Philosophy

[zealous garden]

Worth

[ocean harbor]

teto

[solar hawk]

holy peakl debian teto

[zealous garden]

I'm not a Debian fan

Debian and Gentoo are the only distros that ever gave me grief

Including FreeBSD

Quite the charmer that BSD

[ocean harbor]

yes

[ocean harbor]

i use arch btw

[zealous garden]

I use Artix btw

[warm umbra]

Welcome to the server @orchid frigate

[orchid frigate]

Thank you

[ripe jolt]

what about fedora

[zealous garden]

Artix>FreeBSD>Fedora>>> others

[ripe jolt]

i heard fedora is the best and most like windows/mac

[zealous garden]

There is no such thing

You can rice and config pretty much any distro to work pretty much however you want

[rotund estuary]

me being just an ordinary guy with ubuntu

[hollow ginkgo]

Giygas

[tranquil bronze]

Does anyone else here use Math Academy?

[tropic pivot]

Heard first time

[tranquil bronze]

?

[tropic pivot]

Math academy. Famous app or any institute?

[tranquil bronze]

Yeah the program

It’s 50/month 500/year. if you want to learn at a vastly accelerated pace, that’s the way.

https://www.mathacademy.com

I’m just a student using it, not being payed or anything - I just think it’s really great

[whole mountain]

50 dollars a month for ai based learning seems like they just want lots of cash

[tranquil bronze]

Ai isn’t teaching you really

[whole mountain]

I understand

im looking at the how it works plage rn

page, sorry

[tranquil bronze]

Sweet

Yeah just check it out

It’s so great

[whole mountain]

it seems cool I just wish I could do 50 a month lmao

[tranquil bronze]

Yeah…

[whole mountain]

😫

[tranquil bronze]

I mean technically you could do a month and get a refund

[barren anchor]

what math are you trying to learn?

[whole mountain]

is there like a diagnostic for where to start

does mathacademy make you take a test

[barren anchor]

if it's anything high school / early college, there are gonna be a lot of free resources for it, the foremost of which I think are khan academy and open courseware

[whole mountain]

im using khan academy rn for my courses

I love khan academy

[barren anchor]

it's solid

[whole mountain]

I do prefer tangible things though so I do splurge on some textbooks

[barren anchor]

I don't even undersatnd that. How exactly does any textbook provide spaced retrieval?

[whole mountain]

wdym spaced retreivel practice? Similar to bringing back up a topic to ensure it's still in your memory?

[barren anchor]

I think you are confusing a learning resource with the internal mechanics of learning

they can't make you like, think about what you read thirty minutes ago

[twin ermine]

KA can get slow

[barren anchor]

I'm saying there's no difference. That's not a feature to look for externally.

you just need to know how to study, whether that be video lectures or online homework or textbook problems

[tranquil bronze]

“Spaced repetition, also known as spaced retrieval or distributed practice, means that reviews should be spaced out or distributed over multiple sessions (as opposed to being crammed or massed into a single session) so that memory is not only restored, but also further consolidated into long-term storage, which slows its decay. The most effective means of constructing long-term memories is to re-engage with concepts at progressively greater intervals (the spacing effect). In contrast, doing a large number of a specific type of problem within a short-period, known as massed practice, has little to no long-term benefit but numerous negative side effects, most notably—boredom, burnout, and the inefficient use of time. Math Academy’s highly sophisticated algorithms track every single question a student completes and continually updates the student’s personal learning curve for optimal efficiency.”

[barren anchor]

are you an idiot?

I mean I hear you, it's nice to outsource learning how to learn to an app

much like nudges, etc

[tranquil bronze]

Yeah I’m not saying textbooks don’t do this. I’m saying khan academy doesn’t. That’s all. If you know how to study, then I’m not doubting your ability to practice spaced retrieval

[barren anchor]

but that may well compromise the quality of your education, because you'll get something that is engagement-hacking rather than providing a suitable standard of quality

this is like those people who use duolingo forever but never read a book

I agree, khan academy does not encode the optimal intervals into it

[tranquil bronze]

Im not doubting your ability to learn or do math. But math academy isn’t engagement hacking. I think you should check it out. That’s all I’m saying.

[barren anchor]

sorry to be a jerk here

[tranquil bronze]

Your good

We’re just talking

I’m being a little scattered in my writing

[barren anchor]

well my first inquiry was not exactly polite

I understand you now and appreciate it. If you do want to lean on an app to support some optimal studying behaviors besides the actual content provided, it may be a good idea. I'm just suss of that

because there's a huge market for stuff that is somehow different, but one of the ways to avoid paying actual educators is to have one software engineer be like "look, it reminds you 30 minutes later than your last engagement the prior day!"

[tranquil bronze]

Here I’ll send you this link that’s more specific. I may be explaining it wrong. I totally understand what you’re saying here so I’m definitely misrepresenting what the program is doing.

https://www.mathacademy.com/how-our-ai-works#knowledge-graph

This whole page is really great, even if you’re not planning on using the program. lots of info on how the brain works

[barren anchor]

website actually looks like it's from 1995, and the quality of the explanation of why the programming works is abysmal

we're talking like, I could take a dump and it'd be a blog post looking better than that site

I studied neuroscience and hugely appreciate spaced retrieval as well as targeted (in terms of difficulty) programming

so that stuff all sounds fine, but that's like not even baseline now

[tranquil bronze]

That’s very interesting that you think that.

[barren anchor]

seems like a site to farm data

kick it off with a 45 minute exam

[surreal bison]

spaced repitition!

[tranquil bronze]

This site is very highly rated and tons of parents sign their kids up for it and have proof that their kid is learning math at 4x the time of their peers.

Trust, bro

[surreal bison]

me when selection effects

[barren anchor]

I'm confused, they're accredited?

[tranquil bronze]

Correct

[barren anchor]

what exactly is it?

[tranquil bronze]

It’s very popular for home school students

[barren anchor]

do I pay them?

do I buy their online class?

[tranquil bronze]

Dude it’s a way to learn math

[barren anchor]

that's not what I mean, I mean like as a business

[tranquil bronze]

I sent you their faq page

[barren anchor]

yeah it's such a shit website it's unclear yet

not one of those faq questions is "what is our business"?

this whips ass XP, or eXperience Points,

[tranquil bronze]

You’re welcome to look up the site on x.

There’s tons of people who rave about it

[barren anchor]

they give eXperience Points

oh, you're pointing me to testimonials on social media?

[tranquil bronze]

No

Independent people who pay to use the site

[barren anchor]

it's no issue, I don't disagree with their emphasis in technique

I'm just saying like, testimonials are silly as hell man

and independent how?

and who are these independent people? independent fools?

it's not a reasonable thing to indicate as support

you're being a testimonial yourself

you're confused about what quality of evidence is meaningful

this is what I'm thinking of https://www.tandfonline.com/doi/full/10.1080/09588221.2021.1933540 https://pubmed.ncbi.nlm.nih.gov/36859717/

yeah trust me bro I do my own research

don't be concerned you need to substantiate or not anything to me

it won't affect me

[tranquil bronze]

https://x.com/justinskycak?s=21

[barren anchor]

word of mouth is straight up insanity to act on in any way other than perhaps take a peak at the most empowered inquiries into the relevant question

+many hats he eXperienced

[tranquil bronze]

lol

[barren anchor]

seems like a nerd who spent 10000 hours inventing their use of a dumb way to make a word different

just link me the peer-reviewed studies. I'm just basically a skeptical person.

why? I dunno, maybe because literally everyone thinks they have it figured out, and if that were true, we'd all be geniuses

not only that but like, I've dated a ph. D in cog sci, and I'll tel lyou

the number of those people who have an ed-tech or ed programming angle is just what you'd expect (all of them.)

like, no doubt they believe in themselves, but they also have some motives that might interfere with their objectivity, e.g. their research history and their desire to benefit themselves

100% of them

(that I've met. so 20/20)

[tranquil bronze]

Let the discord logs show that I believed that Math Academy is the best way to learn math at an accelerated pace.

In a few years, I’ll see ya @barren anchor

And we’ll figure out whose right

[barren anchor]

now you seem like a shill

were u paid to come here and talk about this?

but yeah sure later. See you in a few years

and not before then

[tranquil bronze]

No bruh I pay 500/year for tho site 😭

[barren anchor]

alr enjoy it

[grand birch]

Just use ixl fr fr

[tropic pivot]

Dollars?

[tropic pivot]

It sounds like a movie plot.

[tropic pivot]

What course?

[cloud pewter]

Hi

[tropic pivot]

Hello

[cloud pewter]

I want to ask you a question

One of the most difficult complex numbers or differentiation applications

[tropic pivot]

Maybe I can solve it or maybe not because I'm noob. But you can share the question.

[calm ice]

pls

[unique snow]

Ok I missed the discussion but I'm a Math Academy subscriber and here's my personal take/what I like about it:

• space repetition that is managed for me, I am not a very good self-learner for making and giving myself a structured syllabus/curriculum so I'm very glad someone/thing is doing it for me; without online resources like Khan/Math Academy/etc I'd never be at the sparse mathematical mind I have right now
• this is more of an abstract thought but the content is really . . . connecting the dots on fundamental things in math that I just wasn't formally taught. Like, the content is amazing about how it dips your toes over and over into the next thoughts/paradigms or what have you in math that a lot of ((American)) middle/high schools lack in teaching
• in the top left corner there is an "Estimated completion is month, year" and in some ways this is both demoralizing and empowering. SOOO many times I fell off the cliff of my own personal math studying journey and would log back into Math Academy to see "September 2030"" psycological damage, but if I just did a few practicing/studying everyday I could get that back to "December, 2026" by far the biggest motivator that affirms my own ability to achieve if I continue to make the active choice

What I do not like:

• the price is crazy. $50/month is nuts and honestly if I was not financially well off I would not be trying Math Academy at all. I think it's incredibly prohibitive to something that is really amazing. Like, when I'm tutoring I wish I could give my tutorees Math Academy but can't on good conscious. They are middle/high schoolers in the foster system - and the price makes me upset that this incredible resource/supplement has this high financial barrier
• you cannot “click” or revisit specific modules of your own choice. It does it for you, because of spaced repetition, and is also a business choice likely because . . . if I could click on specific subjects/topics I would be using them for my tutoring

[snow helm]

@short bloom wo sawaal hogya?

was nice tbh

i was going to start it

[short bloom]

No

@snow helm

[snow helm]

then why did u close it?

[short bloom]

No one helped 😭

[snow helm]

Mai hu na

Will try and report in an hour

Rn I'm outside home

Hence an hour is needed

[jaunty bison]

Hi , anyone have solutions of erwin kreyszig Advanced engineering mathematics, 10th edition?

[short bloom]

U were about to start solving a math problem outside home? 😭

[snow helm]

i just saw it

and thought why not give a try

@short bloom dm the qn

[fresh comet]

@short bloom welcome to the mathcord!

[reef carbon]

@junior rampart jsyk im not a man and i rly dont like getting called "man" esp twice in a row.

i'm a girl.

[barren anchor]

The revisiting issue I suspect, from glancing at their website, is just because whoever wrote the web application doesn't know what a router is and didn't develop a cohesive navigation scheme before starting to write it. Cool that you like it, nice to have another firsthand account.

ime the best apps (duolingo being standout) set you up with both options, and they nudge you along a path but they always let you get back to something you are particularly interested in reviewing / locking down.

[junior rampart]

Mb.

but dont have to publicise as though its a crime (considering you felt hurt cuz u put this in general as well as that help channel)

[reef carbon]

im not trying to insinuate it's a crime. i just wanted to discuss it in a space that's not a help channel, is all.

that's why i forwarded it here

it's not a crime it is the verbal equivalent of you stepping on my toes.

[junior rampart]

You pinged here once and there too once.

[reef carbon]

i pinged you at the initial "bro". then, when you did it again (misgendered me), i pinged you here instead.

[junior rampart]

Whatever sense you wanna take it in its your wish, I didnt mean any harm.

[reef carbon]

or well ok

i did ping you there too but when the channel already closed. split second diff there

[junior rampart]

misgend-
yea I see many girls calling eachother bro but cool, ill chill with this. Mb and i apologize

[reef carbon]

yeah, the "gender-neutral bro" thing is not universal, sorry.

[north lynx]

What to include in short notes for JEE in maths and chemistry
Short notes is a summary which i usually remember but the detailed thing uffff

[vernal oasis]

You made me think for a second and then I realized that I would feel a bit weird if a random girl called me sister

My girl friends though, they can call me sister lol

[reef carbon]

honestly, as an informal and somewhat familiar term, "girl" is not that bad

"girl went out of her way to color-code the example"

[livid night]

Can someone give me a million dollars

[mellow wedge]

Maths I can tell and chem mai mere kabhi 45 se upar ni gae 🥀

[north lynx]

pls

sure

[reef carbon]

what do you want to talk about and why does it need to be in DMs

[north lynx]

understand

[reef carbon]

.... ok but no guarantees

[north lynx]

ok

ty

[snow helm]

🥀

[severe ether]

szia bazsa

[left surge]

fasz

https://cdn.discordapp.com/attachments/1348055564537696265/1369031518189650001/caption-10.gif

[icy ferry]

😭 jee...

[flint oriole]

arcsin =1/sin

there

you can scratch that one

[zealous garden]

$\ftgc$

[fathom swallow]

wraithlord_kojima

[ocean harbor]

this hurts my head

[idle copper]

Hlw

[idle copper]

What the hell is this 😭🙏

The signs

[vivid halo]

Stokes theorem moment

[icy ferry]

reminds me of Aleph Nulls video

[umbral forge]

French interval notation is better though

[vivid halo]

@dull salmon

[umbral forge]

https://ncatlab.org/nlab/show/ultracommutative+ring+spectrum The first result is an empty nlab page

Wth is ultracommutative

[vivid halo]

lmao

[vivid halo]

hey it's not empty, it includes a citation to the one paper that defines this

[umbral forge]

836 pages

[vivid halo]

cope, seethe

[umbral forge]

I’ll be back in 5 years when I understand the definition

[umbral forge]

Yeah I saw but I’ve unfortunately not done homotopy yet

[zealous garden]

nG should I watch Borcherds' videos on commutative algebra

[foggy meadow]

What is this called?

[zealous garden]

This is the fundamental theorem of geometric calculus, (using notation I made up and can't recite for you off the top of my head lmfao)

[vivid halo]

on 2x speed sure

[zealous garden]

I could figure out what exactly I meant when I added that to my preamble by checking the textbook on my desk

[vivid halo]

if having video content to listen to helps you then sure these are not bad lectures

though it's no replacement for sitting down and working through Atiyah-MacDonald or something similar

[zealous garden]

But it's supposed to be a concatenation of the two sided fundamental theorem of geometric calculus, which has 3 terms total I think

[zealous garden]

True but it's certainly not my focus at the moment. I want to learn more definitions and get an outline of concepts utilizing them so that I can better decide my direction and understand conversations happening around me

I want to know a bit about schemes, spectra of rings, nullstellensatz, and varieties

[vivid halo]

yeah that's reasonable

[latent edge]

Local cohomology was mentioned in seminar

[vivid halo]

definitely worth getting a sense of the big picture before committing to spending a bunch of time on exercises

[vivid halo]

nice

isn't it great that excision makes sense for QCoh

[hazy viper]

Pick a number from 1-10 that you believe the least other people would choose for this question
https://forms.gle/dhMsUqTP16c1cfcK7

[ornate bridge]

You mean in the sense of not a replacement for exercises?

[zealous garden]

Screw exercises, build the theory with me

[vivid halo]

yes

[zealous garden]

nG you weren't kidding about the 2x speed

[vivid halo]

theory stalls due to lack of exercises

[ornate bridge]

Right, exercises are the most important

[zealous garden]

I have replaced "the proof is trivial" with "\begin{exercise}"

[ornate bridge]

have you ever had it happen that you were using some book that didn't have any problems?

what did you do in that case

I guess if you weren't self-studying it didn't matter because your prof provided them

[vivid halo]

yes this is most of the time for me lol

[zealous garden]

Talk unending amounts of shit about the book

[vivid halo]

make up your own exercises

it's not hard to come up with good exercises

[ornate bridge]

Really? I thought most graduate texts have exercises, I assume you're talking about papers

[zealous garden]

I'm not sure about that

[vivid halo]

loads of graduate texts don't

and yes most papers don't either

[zealous garden]

Maybe once you get to a certain point or have enough context it's easy enough

Like graduate texts and papers would assume you do

[ornate bridge]

Oh true, there are always questions that come naturally, I guess you can view them as exercises

[zealous garden]

The issue is scoping

[vivid halo]

I mean most good exercises are like, take general thing that paper proves and specialize it to the simplest interesting special case you can think of, make things very explicit and do some computations, unwind definitions, etc

[zealous garden]

Collatz is a great exercise huh

Someone should interject before you accidentally suggest it to yourself

[zealous garden]

Ah yes try to actually apply it, I suppose that is an exercise after all

Who knew that doing something counted as an exercise

[ornate bridge]

Well you probably wouldn't run into something like that with most of the questions you ask yourself, I meant more stuff in the flavor of 'oh what's a nice example of a Banach space? Is there something else that we could identify it as? ...'

[zealous garden]

More likely than you think, I think.

Sylvesters law of inertia classifies real symmetric bilinear forms neatly, you only need 3 parameters

Care to guess what it looks like for rationals?

[ornate bridge]

owh, is that problem open?

[zealous garden]

No not open

Just complicated

Far more complicated than the real case

[ornate bridge]

Fair

[vivid halo]

wow I can't believe global objects are more complicated than local objects

[kindred glacier]

looking for calc TUTOR

[zealous garden]

It's fair when you don't know, which is the person who is asking the question

Like if you knew the answer and its complexity, you wouldn't be asking

[ornate bridge]

Probably if you aren't self-studying this won't ever be a problem though

Your prof will always give you problem sheets to do

[zealous garden]

If you knew what global and local meant in this context you might not ask the question

[vivid halo]

you can't rely on this forever

[foggy meadow]

Just make sure you know it works well over the p-adics.

[ornate bridge]

fair enough, beginning from a a PhD student you won't have this anymore

[vivid halo]

yeah maybe first year of PhD it's more common to be asking professors for exercises like this blindly

pretty quickly you learn to think of your own problems and then instead of asking professors to give you problems, you ask them whether the problems you're thinking of are good or bad examples

[foggy meadow]

Can you give me a problem involving lattices?

[vivid halo]

idk what's your background

[foggy meadow]

Idk maybe R^{3} or R^{4}.

Maybe Z^{4} I really work with Lattices in Z^{4}

[vivid halo]

sure here's a fun problem to consider which is reasonable in low rank: classify the positive definite quadratic forms on R^d which are perfect, up to GL_d(Z)-equivalence

(feel free to look things up and do some reading on this, it's a very lovely topic)

for context the perfect quadratic forms correspond to local minima for the Hermite invariant: they correspond to extremally dense lattice sphere packings

[foggy meadow]

Quadratic forms are the most new thing here for me

[vivid halo]

they are the same as lattices if you like

[ornate bridge]

Btw how important is it to make friends during undergrad if we just look at it from a research opportunity POV for later on; does it happen often that one of your friends specialize in something you do and then you collaborate? Or is this more something that becomes important starting from grad school

[umbral forge]

Lattices are so cool, I know a friend who worked with them for a project and I wish I could learn about them too

[vivid halo]

their number grows quite quickly but up through like dimension 4 or 5 things are manageable

[foggy meadow]

Oh 2!

[umbral forge]

I keep hearing about the E_8 lattice and I want to know why it’s so special eventually

[vivid halo]

yeah dimension 4 is the first really interesting case

[foggy meadow]

Roots.

[umbral forge]

I know it comes from a root system yeah

But also it gives optimal sphere packing and other cool things

[vivid halo]

there is a beautiful story about how perfect quadratic forms are related to the geometry of the Voronoi polyhedral decomposition of GL_d(Z) symmetric spaces and this is related to some very deep objects in number theory like algebraic K-theory for example

there's a similar story for other kinds of lattices, a favorite of mine involves perfect Hermitian forms over imaginary quadratic fields and this gives you these nice Bianchi polyhedral decompositions of hyperbolic 3-manifolds

[gleaming panther]

Could anyone let me know how useful or publishable this is, specifically if I was to build on it further slightly and publish a paper with comparisons with other methods possibly?

https://www.desmos.com/calculator/gwjxljwlw1

[warm gull]

OH MY GODDD

[flint venture]

The Infinite Sum of Reciprocal Squares (Basel Problem)
https://youtu.be/psAKUx9XGzY

[dense hare]

hiii

[vivid halo]

now do odd reciprocals

[elder patio]

Wsg

[dense hare]

Wsp

[velvet dagger]

Wait huh

Sum_{n odd} 1/n^2 or smth else?

[vivid halo]

odd powers

I wonder if Euler believed \zeta(3) should be a rational multiple of \pi^3 and if he was forever salty about it

[velvet dagger]

Yeah I remember having an exercise to prove it was transcendental

[vivid halo]

lmao

[uncut marlin]

hey guys

is anyone gonna participate in NASA apps challenge?

[snow helm]

@lone chasm wkt minus into minus gives us +, hence the equation transforms into:
x+40=-80

now diy

[foggy meadow]

function approximation!

[foggy meadow]

Why the cone?

[vivid halo]

the interior of this cone is the symmetric space for GL_n(R)

[foggy meadow]

For 2d?

[vivid halo]

in this picture yes

[foggy meadow]

Okay, that makes sense, I can see that.

[vivid halo]

in particular you have an action by positive reals by scaling, if you quotient by this scaling action then you get the symmetric space for SL_n(R)

for n=2 this is the hyperbolic plane in its usual disk model

[vivid quest]

A measure $\mu$ is sigma-male if for all $(A_i)i$, $I$ countable, such that for all $i \neq j$, $(A_i^cmaleA_j^c)^c = {}$: [ \mu ({male}{i \in I} A_i)={male}_{i \in I} \mu (A_i) ]

[fathom swallow]

almond 🐦

[vivid halo]

the way you form this infinite polyhedral decomposition of these symmetric spaces is you form convex hulls of vectors on the boundary

[vivid quest]

Don't let this flop

[foggy meadow]

polyhedral decomposition & on the boundary mean here specifically?

[vivid quest]

I made it even flopier

[vivid halo]

yes

[foggy meadow]

Idk how to take that.

[foggy meadow]

I feel like the stuff you know is a lot of stuff I like.
But, I have like only a some of the knowledge to understand it.

[zealous garden]

Many such cases

[foggy meadow]

True, I mean some of it like makes some sense.
But a lot of it I'm like "what?"

There's a lot of terms thrown around that I'm like "why?"

[brisk harbor]

hi guys

im new

[sharp swan]

Hello, i am a human.

[vivid quest]

Hi new

I'm guy

[brisk harbor]

to the server

[lunar ruin]

Hi guy
I'm not new

[sharp swan]

Human?

[lunar ruin]

I think, therefore I am

[sharp swan]

Prove it

Rigorously

.

[brisk harbor]

$:\tan \left(a\right)+\frac{\sin \left(\frac{1}{6x^2}\right)}{\sin \left(\theta \right)}-\frac{\sin :\left(\theta :\right)}{\cos :\left(\pi :\right)}=\sin \left(\theta \right)$

[fathom swallow]

theonlygardener

[sharp swan]

Hey I suck at math but isn't cospi = 0;

Dividing by 0 no?

[rocky shuttle]

,w cos(pi)

[fathom swallow]

Results provided by WolframAlpha

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

Requested by zanarcane

[sharp swan]

Cos180 = -1 ; yes I'm dumb

I forgot the unit ccle again

[brisk harbor]

gusy we have tomsolve fo x

@sharp swan u there

:\tan \left(a\right)+\frac{\sin \left(\frac{1}{6x^2}\right)}{\sin \left(\theta \right)}-\frac{\sin \left(\theta \right)}{\cos \left(\pi \right)}=\sin \left(\theta \right)

$:\tan \left(a\right)+\frac{\sin \left(\frac{1}{6x^2}\right)}{\sin \left(\theta \right)}-\frac{\sin \left(\theta \right)}{\cos \left(\pi \right)}=\sin \left(\theta \right)$

[fathom swallow]

theonlygardener

[sharp swan]

Pi * m where m is some integer

[brisk harbor]

solve for x

[sharp swan]

It's pi * m

Where m is some integer

Wait no

[brisk harbor]

it is

[sharp swan]

Look I got to some expression like a + sin(1/6x^2) = 0 ; so 1st term and 2nd must be 0

But

For 1 /6x^2 to be negative

[brisk harbor]

$x=\sqrt{\frac{1}{6\left(\arcsin \left(-\sin \left(θ\right)\tan \left(a\right)\right)+2\pi n\right)}}$

[fathom swallow]

theonlygardener
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sharp swan]

Huh?

[brisk harbor]

yes

this is what i got

[sharp swan]

Well I'm getting 1 = 0;

:d super cool stuff that I can't understand

[brisk harbor]

$x=\sqrt{\frac{1}{6\left(\arcsin \left(-\sin \left(θ\right)\tan \left(a\right)\right)+2\pi n\right)}},:x=-\sqrt{\frac{1}{6\left(\arcsin \left(-\sin \left(θ\right)\tan \left(a\right)\right)+2\pi n\right)}},:x=\sqrt{\frac{1}{6\left(\pi +\arcsin \left(\sin \left(θ\right)\tan \left(a\right)\right)+2\pi n\right)}},:x=-\sqrt{\frac{1}{6\left(\pi +\arcsin \left(\sin \left(θ\right)\tan \left(a\right)\right)+2\pi n\right)}}$

[fathom swallow]

theonlygardener
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[brisk harbor]

t

o

be precise

$factor:\lim _{x\to :4}\left(\frac{x^2-6x+8}{x-4}\right)-sin\left(\theta \right)$

[fathom swallow]

theonlygardener

[brisk harbor]

new enemy found

[brisk harbor]

new enemy found

[sharp swan]

A

[brisk harbor]

what the

[sharp swan]

x-2 - sin0

[brisk harbor]

$-\sin \left(θ\right)+2$

[fathom swallow]

theonlygardener
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sharp swan]

Where did the x go?

Oh right

Applied limit

Oopsie

[brisk harbor]

its fine

[sharp swan]

Really bad at math :_:

[brisk harbor]

no

u good

[sharp swan]

No I trash this is just 1 problem I got lucky at

[brisk harbor]

frequency:\sin \left(x\right)

[hollow quartz]

whoever needs any kind of assignment help, I'm willing to help. Just reach out via my dm

[lunar ruin]

Easy. But it'd require drawing a picture, so ask me in chill if you want undeniable proof.

[ocean harbor]

help ppl on help channels

[sterile glacier]

Anybody know any good free online courses to learn geometry/trig

[gleaming panther]

@foggy meadow Hello, thanks for responding, I was wondering how I could implement that, since the most direct way I could thing of how that works would be how this method gets closer to linear approximation add the “a” variable increases, but I don’t see any other similarities with other curves that this could approximate

[dry ember]

how well known of a concept is rubber ducking?

at least around here

[lunar ruin]

I'm a programmer, so my answer might skew results

[velvet dagger]

Probably moderately?

[zealous garden]

Many of us are

I'd assume rubber ducking is well known here

[velvet dagger]

Math folk will likely be more acquainted with programming than is typical + there are gonna be a bunch of programmers here

But also I think the principle of it is known vaguely even among those that don't have a label for it

[lunar ruin]

True true to the messages above. So... Yo answer the q, it's pretty well known

[north lynx]

How shall I make short notes for JEE chemistry and maths
Don't tell me to summarise I can memorise that well but those small things deep stuff

[dry vector]

NOOOOO

i saw the sierspenski triangle in 11D

[fresh comet]

@dry vector welcome to the mathcord

[zealous garden]

God have mercy on your soul, how much DMT did it take?

[true zinc]

quite well known

[flint venture]

That sum diverges to infinity 😅

[warm umbra]

Welcome to the server @heavy kite @neat lintel

[hybrid burrow]

anyone who read hartshone here?

[fresh comet]

there're definitely a few, but what are you curious about?

[hybrid burrow]

i have some questions to ask

[fresh comet]

if it's a review of the book, you might be better off asking in #book-recommendations

if it's questions about the material, then #algebraic-geometry is the channel for you

[valid hornet]

I feel like there's a part of the diagonalization argument that I don't get. It says that if the way you write the two decimals are different in a single place, then the two numbers are different. But, 0.9999... and 1.0000... are the same number but are written differently in every place, so that's not necessarily the case.

[icy heron]

Yeah, for a proper proof you want to modify the digits so you don't end up with repeating nines. For example map every digit to 1 except 1, which you map to 2

[valid hornet]

Is there a proof that the new number doesn't equal any number on the list that doesn't rely on that general false principle?

[icy heron]

What false principle? You just generate the new number so that you don't need to think about 1 = 0.999...

I think you need to avoid both repeating 9s and repeating 0s, but mapping to 1 or 2 solves this

[valid hornet]

I'm talking about the general false principle stated here. So, the principle that for any string of infinite 1's and 2's, if that string differs from any other infinite decimal in one place when written, then those two numbers are different is true. I don't really know what "when written" means either because no one can write out an infinite decimal.

[neat lintel]

Every number with a last digit in the "regular" representation has exactly two decimal representations

Say, 0.5 and 0.4999...

If it doesn't end in trailing 9's, or trailing 0's, there shouldn't be a problem

[tawdry stratus]

you will never be him

[warm umbra]

Who are we referring to here.

[valid hornet]

https://proofwiki.org/wiki/Definition:Basis_Expansion/Positive_Real_Numbers I think this is helpful.

For me to understand what exactly is going on here.

[valid hornet]

Is there a proof that the well-ordering principle is equivalent to the principle of mathematical induction?

[neat lintel]

do you mean transfinite induction? because wop is equivalent to the axiom of choice, and induction is true even in ZF.

[valid hornet]

I found this. https://proofwiki.org/wiki/Equivalence_of_Well-Ordering_Principle_and_Induction

Also, this says they're equivalent. https://en.wikipedia.org/wiki/Well-ordering_principle#Equivalent_to_induction

[neat lintel]

oh nvm I'm just stupid lmao.

Well-ordering principle is about N

[valid hornet]

It feels like I'm going down a deeper and deeper rabbit hole with mathematics by asking "why?" Is there a book that deals with the absolute foundations and basics?

Like, the only thing you can assume is the axioms, and every single other result is proven from the axioms.

The axioms of ZFC.

[neat lintel]

Let P be such that P(0) and P(n) implies P(n+1).

Then, suppose, for contradiction, there is an m such that not P(m). Since N is well-ordered, there is a least such m, so we can assume m is the least element satisfying this.

Then, since P(0), m~=0, therefore m-1 is a natural number too, but then P(m-1), which implies P(m), a contradiction.

This should work for well-ordering principle->induction

For induction->well ordering principle

Let P be some subset of the natural numbers, and assume there is no smallest element. Then, let Q(n) denote the statement "there is no natural number smaller than n that belongs to P". Q(0) is true since 0 is the smallest natural number, and, supposing Q(n) for some n, Q(n+1) must be true, because otherwise n is the smallest element of P.

Hence, P is empty.

(So every non-empty subset has a least element)\

[light patrol]

So I (fortunately or unfortunately) got sucked back into Collatz Land for the 2nd time this month. Just trying to find patterns nothing formal so take it all with a grain of salt

My friend and I were trying to look at it from the perspective of binary to see if we noticed anything

He figured out that one of the most interesting patterns came from having a number of the form 1010...101(2), which after applying odd rule becomes 1000...000(2). There was something that was claimed about ...11...(2) Being in other numbers for something to have a chance of happening but it sounds wrong when I think about it now

I tried messing around with sequences of digits within each binary representation of a number to see what would happen I think that went nowhere

Stepped away from the binary work for a hot second and went into some modular stuff with it. Recognized that for odd numbers in the 3 mod 6 class, they could only be the start of a sequence. Didn't show that until later but we'll get there

That left me with 1 mod 6 and 5 mod 6 for odd classes. Was primarily focused on odds because in binary even numbers seemed simple enough it was just removing 0s from the end of a number string.

Then I found a video online today from SoME 3 where this guy explored Collatz in his own way and he primarily looked from the perspective of even numbers (because that was the baseline for how his tesselation representation was made)

Figured I could see if there's synergy between the 2 parity classes and by golly there is.

The way he organized his even classes was also in 3 classes:
One Division ending in odd
Two division ending in odd
Two division ending in even

Primarily because the claim he had was from top down start at a "node" or a fork in the tree he made where a number can be represented by odd and even rule can reach another node in either 1 or 2 moves.

Take it with a grain of salt again but his One Division Odd class would always map to a number in 5 mod 6 and his Two Division Odd class would always map to a number in 1 mod 6 from what I saw on my own

[lunar ruin]

Collatz mentioned. Great start to my day

[light patrol]

Sorry ^^'

[lunar ruin]

Lol. Nah. I've been obsessed with collatz. But I know what you're talking about because I have that in my notes too.

[light patrol]

Great

Likewise 1 and 5 mod 6 mapped back onto these even classes.

They both mapped to One Division Odd when for 6k+1 and 6k+5 respectively k was odd (I felt like calling this Meta Collatz)

And they alternated Two Division Odd and Even on k = 0 mod 4 and k = 2 mod 4 for that same 6k+1 6k+5 thing (1 mod 6 started with Two Odd and 5 mod 6 started with Two Even)

Then I looked at Two Even by itself and I got brick walled.

I see the pieces to it
The seed of a ...101(2) ending to each number within the odd numbers that initiate Two Even, the alternating additions based on which odd modular class Two Even was chaining off of.... I just can't for the life of me trace a pattern for how Two Even maps to the other even number classes including itself

[lunar ruin]

Not exactly sure where you're stuck, but from what you seem to want to do, is grouping those nodes such that every number is an odd number or even that divides into that odd number.

[light patrol]

It was a 1:1 translation of a system where node grouping was where a number can be both represented by odd rule and even rule.

I see what you mean by grouping nodes to end on odds but I'm not sure how that 3rd category plays out beyond reductions

Like if it's an odd number of even rule applications would in be the same as One Division Odd in the old structure and similar for Two Division Odd. (Would answer that by looking myself but I'm trying to fall asleep while I think this through XD)