serious-discussion

[static loom]

just think of it like gravity

magic invisible hands pulling you down but you just don't question it with the same critcality cause you're used to it

[leaden torrent]

🐗

[long beacon]

hi how can i ask for help for meta questions (about the functioning of this server)? something like Math Stack Exchange Meta?

[pale orchid]

you can ask here, i guess

[static loom]

thinking of it in those terms is already thinking too seriously lol

[cyan goblet]

i see…

man i gotta go major in humanities or something instead

[long matrix]

ryc is a pigeon

[deep mango]

[lilac snow]

i think it's like that part of physics that you can learn but not understand because our minds are finite in their understanding

like trying to imagine higher dimensions

breaks your brain

and you still can't wrap your head around it

no?

that's the classical interpretation

yeah

lol

plus i don't think it's one upon

the quantum definition of spin

or if you go look up the quantum model of the atom then you'll find a discription of all four numbers

which might help in

understanding

i think spin is the only one of the four that is difficult, if not impossible, to entuit

the other ones are easy to grasp

what are you learning

out of curiosity, of course

right right

then it shouldn't be way beyond

i learnt the quantum model of the atom before i learnt all of that^

yeah

we cover all of that in high school

i'm only a senior

you'll get it no problem haha

easy peasy for you

(:

[delicate knoll]

hello mathy people

how do you do ?

[long beacon]

hi a math room was closed before the question asker received a reply: #help-15 message

from #❓how-to-get-help it seems that it's not good to DM/ping him/her so I'll write here

write $i^i$ in polar form

[fathom swallow]

vin100

[long beacon]

$$i^i=(e^{i\pi/2})^i=e^{-\pi/2}$$

[fathom swallow]

vin100

[long matrix]

well ping them with the reply otherwise they'll never see it

[modern geyser]

Not imaginary so does it have polar form?

I guess it would just be e^ln(that number) * 2pi * i

[weary steeple]

simply beautiful

[lime sorrel]

I just did a video on this on my YT channel

https://www.youtube.com/watch?v=ATPkYQN9ahA

it's not the best but it's correct

I hope it helps tho

[neat lintel]

howd u get 3k subs but no vid has 100+ views

[lime sorrel]

Deleted them.

Don't ask questions.

I accidentally published Riemann Conjecture's proof and got some followers but then had to delete it

[median hill]

Lol I need to see that proof video that gained you 3k subs

[hot cipher]

1+1=?w

[surreal sapphire]

take your bad memes elsewhere, this is not the place

[bright hill]

$\varnothing$ should be the canonical empty set

[fair mural]

varnothing

[fathom swallow]

DarQ

[bright hill]

thx

[fair mural]

{} superiority

[bright hill]

everything is better than $\emptyset$

[fathom swallow]

DarQ

[neat frost]

Yesh

$\o \O$

[fair mural]

well it’s not actually that bad

[neat frost]

[neat frost]

[bright hill]

[fair mural]

shut up you can’t sully me

[neat frost]

[bright hill]

[neat frost]

[fair mural]

https://tenor.com/view/dont-care-stay-mad-eating-gif-23514287

[rocky shuttle]

$\not o$

[neat lintel]

anybody wanna fight

or have serious beef

[sleek wing]

Odd request

[rocky shuttle]

I want some beef steak

[dire mulch]

Sure place and time.

[frigid lark]

is it ok to write on the seminar handout, that the prof is my supervisor?

or do we usually write this stuff only on thesis...

[tender tulip]

[neat lintel]

friday 1.50pm

Im waiting

[fair mural]

that’s oddly specific

also why is there a phone number in there lol

[astral iris]

He wants you to call him

[median zinc]

Can you meet me instead

1600 Pennsylvania Avenue

[rocky shuttle]

Or me

P. Sherman 42 Wallaby Way, Sydney

[fair mural]

are there any abstract algebra prerequisites to reading loring tu’s “introduction to manifolds”, other than just knowing the definitions of a few algebraic structures?

[tender tulip]

I’m bored what if I just decide to define some algebraic objects I know purely through set theory and subsets of Cartesian products with axioms

Aka rules on the existence of its elements I guess

[odd narwhal]

Then you'd be.... Formally defining Algebraic objects

That's how they're defined

Sets with n-ary operations satisfying some Axioms

[dire mulch]

Bet.

Damn bro, your in a different state, guess I can’t slide through. 🙂

You got lucky.

[deep mango]

I don't know if this is a real address or not but I'm deleting this post, please for fucks sake do not post your real address on a public discord server which literally anyone can see

If it was a meme address, I got got.

[sturdy finch]

hmm, gotta love being a 2nd year bachelor student and apparently failing at 6th grade maths https://media.discordapp.net/attachments/827949459001704501/963537955664850964/unknown.png

[neat lintel]

the only time a mod deletes something reasonably

it was a random address but its ok

[neat lintel]

damn

[neat lintel]

no

[bright hill]

the mods here are pretty reasonable

[neat lintel]

Allahuakbar

[neat lintel]

not all

my friend got banned here for saying there are 2 genders

mods said he will get unbanned in 1 year

[bright hill]

[neat lintel]

he said joke in brackets

idk who banned him

[neat lintel]

1 year is not bad

[neat lintel]

mf in 2023 we will have an apocalypse

this earth been going downhill since 2019 lmao

we wont

[old fox]

hope it's not an inclusive we

[bright hill]

weird how people expect to say the most racist, sexist mysoginistic shit and end it with "(joke)" and expect to get away with it

worse yet

they expect it to be funny

[neat lintel]

I'm not gonna die till I get tired of math

[bright hill]

[inner finch]

why say this

[neat lintel]

idk i think he wanted to piss off the mods

[bright hill]

well, good job

[neat lintel]

this is me

[neat lintel]

literally

[bright hill]

he got what he was looking for

[inner finch]

tries pissing off mods
mods get pissed off
noooooooooo why'd they get mad it was just a joke

[neat lintel]

so I'm immortal

[neat lintel]

this dude was weird lmao

we are just discord friends idk how he is

[old fox]

I don't see any problem with anyone saying allahuakbar (assuming it isn't sarcasm)

[inner finch]

lole

[old fox]

that's just another way of saying omg

[neat lintel]

my friend is muslim and we went outside and like

somebody called the police

[inner finch]

sure but why say this in chat

[neat lintel]

just because he looks like that

I got banned permanently from a server in 2019,
and the server went downhill since then...
it's probably like a desert now

[old fox]

honestly what's the problem with that?

[inner finch]

It comes off as like a joke

[neat lintel]

nah letst not discuss it

[inner finch]

and can be seen as insensitive

[neat lintel]

we know what the issue is and talking wont solve it

[old fox]

it's subjective

[inner finch]

?

[bright hill]

I don't see how it can be used non sarcastically tbh

[neat lintel]

that is reasonable

but lets end the topic its just a word

[old fox]

them being muslim?

[neat lintel]

nah ppl say allahuakbar as joke

i just randomly said it

but its a word lmao

can we not talk about it anymore

[inner finch]

are they? And if they are, what purpose does sending allahu akbar in chat serve. At best it's a complete nonsequitor

[neat lintel]

im leaving

[inner finch]

[old fox]

well, this is discord. People don't say allahuakbar as a joke here where I live, so you might be right

[neat lintel]

I think the religion itself just made a bad image because somebody like bin laden exists

and saying a word of it always starts a convo like now

[bright hill]

dude

please stop

[neat lintel]

but its not important

[neat lintel]

alr mister

[neat lintel]

its two words

[neat lintel]

technically

yes

not technically?

it always has been

in every context

i thought technically means "to be exact"

but yeah actually its 2 words

yes but it implies there are not exact contexts where its one word

ah alr

also if you want same sentiments just say mashallah

are you a muslim or do you just know much about islam

im neither and speak arabic

alr

[inner finch]

oh cool

been wanting to learn arabic for a while

[bright hill]

what?

mashallah is an exclamation similar to something like "wow" or "that's so cool" except it's more religious

you say it when you see something impressive or favorable

I'm not really sure what you mean by "wanting same sentiments"

[hushed turret]

mashallah can be used when anything happens that you are thankful for really

i don't think it's restricted to "cool" things lol.

[neat lintel]

no?

mashallah means thank god

or praise god

thats best english translation

cool sentiments are not there

[hushed turret]

yeah

[inner finch]

oh isn't the translation something like the plan of allah is great

[neat lintel]

idk if its that long

[hushed turret]

ive only heard praise be to allah

[neat lintel]

yeah

[inner finch]

makes sense with how we say inshallah

[neat lintel]

i dont even say mashallah

idk a translation for omg though

nah?

inshallah is def not a translation for omg

[odd narwhal]

Ya allah maybe

[neat lintel]

oh thats why you talked it down so much

i thought ur a liberal guy just critizing it

arabic is ok, reading it without the little things on the words is like impossible for me

[neat lintel]

for sure

[tender tulip]

Gonna ask this question again

Can all abstract algebraic objects be considered as subsets of (nested) Cartesian products of sets of which have certain axioms over its elements

Which is rather interesting

Gonna try to define topologies through set theory

Purely basic set theory, Cartesian products, power sets, existential quantifiers, some logic

[neat lintel]

yes

its not as interesting in my opinion though

[tender tulip]

t is a subset of P(S) such that
null set element of t, S element of t
AND
For two elements X and Y in t
3. {x : x element of X AND x element of Y} is an element of t
4. {x : x element of X OR x element of Y} is an element of t

[neat lintel]

There are easier ways to word things less confusingly

[tender tulip]

symbolically I guess

[neat lintel]

Nah

[tender tulip]

basically Union and Intersection

[neat lintel]

i mean using words

t is a collection of subsets of S where the empty set and S are within t.
t is closed under union and intersection.

[tender tulip]

That defeats the purpose of what I’m doing

[neat lintel]

what are you doing then?

people define topologies through set theory already

[tender tulip]

Topologies as an example

[neat lintel]

you can always expand out to symbols but that just makes reading more convoluted sometimes

[tender tulip]

In a way topologies sorta are a combination of two monoids over a power set I guess

(t,Union) is a monoid cuz it’s associative and it’s identity is the null set

(t,intersection) is a monoid cuz it’s associative and it’s identity is the set the topology is over

That whole infinite Union, finite intersection thing might fuck with it

infinite union is what screws me over

[neat lintel]

you can still be wrong?

[bright hill]

no

[neat lintel]

thats so cool is just off

[bright hill]

yes

but not like how it's used in english

[neat lintel]

yeah

ive heard it in exclamation

like they believe something ive said to be interesting

but not thats so cool

you gotta localize in your translations

you cant just have same semantics without context

[bright hill]

but

[neat lintel]

bruh

[long matrix]

kakuii desu

[neat lintel]

the purpose of translating is to make meaning and context apparent

literal translations suck most of the time if they dont convey these

[bright hill]

as I was saying

[neat lintel]

there is probably a good translation for thats so cool

[bright hill]

if you think something is cool you'd probably say "mashallah"

[neat lintel]

but id need to think

[neat lintel]

i agree

[bright hill]

that's what I meant

[neat lintel]

we agree

[bright hill]

you mean kakkoii?

[long matrix]

shh

[tender tulip]

Is there a way to describe finite-intersection/infinite-Union closure through set theory in the way I described

[honest veldt]

i have a huge dilemma

i need to ask a pretty small question in a channel, but the last question posted there looks significantly more important and id be pushing it away from view

can we duplicate all channels for a minute

[long matrix]

be rude and crude

could open a thread

[fervent pebble]

ask here

[honest veldt]

Love that grindset, good idea

New thread: important question, ignore that other one

here valley

[tender tulip]

NOOO

Bernoulli inequality

[honest veldt]

why does the fella bother putting 1 + nx_n <= (1+x_n)^n, doesn't nx_n alone serve the same purpose?

[honest veldt]

I don't know what that is, I'm afraid to look it up

[rocky shuttle]

This is Bernoulli's inequality

[honest veldt]

Oh actually? I thought the inequality just held because all terms of the binomial expansion were nonnegative

[tender tulip]

Classical case of induction proofing

[honest veldt]

and this Bernoulli fella holds if 1 + x_n > 0?

for all n

[bright hill]

wait what

if that was true, why did rudin mention the binomial theorem?

[tender tulip]

0 < x
Base case: n = 2
1 + 2x__<__ 1 + 2x + x^2 = (1 + x)^2
thus 1 + 2x < (1 + x)^2

assume the inequality is true

[honest veldt]

I think the reasoning you and I used wasn't wrong either, darq, since he uses it in the very next proof

[tender tulip]

1 + nx < 1 + nx + (n-1)x^2 = (1+x)(1 + (n-1)x) ** < (1 + x)(1 + x)^(n-1)** [assuming the hypothesis is true for n - 1] = (1 + x)^n

Thus it is proved

[bright hill]

but if that's true, then why the added 1?

I hate that about rudin

[honest veldt]

thank you once again rudin.... . . . . . . . . . . . .

Clean stuff Miz, I just can't tell why he doesn't mention it at all

you'd think he'd acknowledge its existence, but whatever

should get used to this

[bright hill]

btw, congrats on reaching chapter 3!

being stuck on point set for a month must've been a drag lol

[astral iris]

How is analysis

[bright hill]

eh

still not that interesting yet

[astral iris]

Lol

Nice

[honest veldt]

My man, thank you

[honest veldt]

The chapter itself didn't actually take that long, I spent like 2 months doing the exercises lmao

[bright hill]

based

[honest veldt]

but i enjoyed, it was worth

cant wait to see how long this one will take.... i took a look at the exercises section, and some of them take up like half a page individually

i fear for my life

[bright hill]

[bright hill]

bruh

[sick burrow]

how to do math:
step 1: find a nice intuitive concept you want to formalize (distance, space, continuity, shape, etc)
step 2: find a nice formalism and set of axioms that describe the thing you want it to, and can prove the properties you want to prove
step 3: generalize generalize generalize
step 4:

this post was made by Stone Spaces

[rocky shuttle]

Who is Stone Spaces...

[sick burrow]

me

my full name is actually Stone Spaces

[fervent pebble]

^ can confirm

[ancient flame]

my physics teacher made this problem for us LOL

[waxen lily]

amgus

[primal seal]

Phys 1(01)?

[ancient flame]

AP physics 1

[strong hull]

Hey guys, Im not entirely sure if this is the correct place to ask but im self studying real analysis in high school and if anyone could help me get through the books and tutor me a little please drop me a DM... It would really be helpful bc im struggling with some of the exercises and proofs, and i couldnt find solutions for quite a few of the exercises. Thanks.

[ancient flame]

you can ask specific questions in #real-complex-analysis when you have them

[sleek wing]

#fake-complex-analysis 😂😂😂

[strong hull]

thanks for pointing me there, but i was also looking for a study buddy

so

[ancient flame]

oh okay, then maybe it'll be a bit difficult to find one here (but it is possible)

[strong hull]

yes i really really need a study buddy i think

self studying is hard for me bc i lose motivation sometimes, and its so frustrating to just figure out an entire textbook myself

[hushed turret]

what point are you at in your text

[strong hull]

well i am at dedekind cuts in Pugh's real analysis

[strong hull]

i did an exercise, i think it shld be correct and i put it in Stack Exchange for verification but no one replied yet so im waiting a bit

i think the motivation is a big factor for getting a study buddy or study grp

bc like school can be stressful and sometimes im just so frustrated i kinda give up

so im kinda desperate for a study buddy lol

[hushed turret]

i guess you can ask in #real-complex-analysis if anyone is at a similar point and would like to study alongside you

but generally you should be fine asking there for help on specific problems/explaining things if you don't understand them

[strong hull]

alr

[calm frost]

btw I ditched rudin a few days ago after chapter 2

don't know whether it is due to skill issues or lack of studying or whatever but it was way too dense and uncomprehensible for me

[neat lintel]

baby or papa rudin ?

[calm frost]

baby rudin

[bright hill]

I tried doing that actually

and then I realized, this server is just a huge ass study group lmao

[calm frost]

i know some books that have solutiosn

I recommend using some of those books just for problems

[bright hill]

that's point set topology right?

yeah, rudin require some mathematical maturity

[calm frost]

yep it is called basic topology

[neat lintel]

darq are you using rudin

[calm frost]

but I wasn't able to understand anythign after compactness

[bright hill]

you can check out hatcher's notes on pointset topology

they're more accessible

[bright hill]

kinda?

I'm not yet committed but I have finished chapter 1

[calm frost]

tbh I kinda trusted myself too much and tried rudin as a first rigorous math textbook

bad idea tho

[neat lintel]

why not spivak

spivak iirc is a good transition from handwavey hs math to serious math

[calm frost]

isn't spivak sort of like difficult calculus book?

[bright hill]

bad idea

[calm frost]

maybe I should use abbott or ross first

my professor recommended me zorich but doesn't seem taht easy

[bright hill]

it's watered down analysis

[neat lintel]

spivak's calculus is more like an intro to analysis

[calm frost]

oh okay

maybe I should check it out

[bright hill]

you can check it out but if you've already done calculus I think if you ask in #book-recommendations they'll give you better recommendations for doing analysis

[calm frost]

okay

[neat lintel]

https://tenor.com/view/heino-rat-woestijnrat-gerbil-rodent-gif-14660931

[swift sinew]

The kind architects of Minneapolis put a straight line homotopy in my neighborhood park

[fast thistle]

wth thats trippy bro

[primal seal]

Tell me you deserve a raise without telling me you deserve a raise

[analog salmon]

my cryptography class is gonna make me lose my mind

for the simple fact that the permutation $$\sigma=\begin{pmatrix}1&2&3&4\2&4&1&3\end{pmatrix}$$ has the convention that $\sigma(1)=3$

[devout nacelle]

How is this representation even working lmao

[long matrix]

"sigma" = sigma^-1

[torn willow]

Are you sure that's not
$\sigma(1)=2 \ \sigma(2)=4\ \sigma(3)=1\ \sigma(4)=3$?

[fathom swallow]

BYE BYE!

[torn willow]

AKA (1,2,4,3)?

[analog salmon]

I've asked multiple times, he's confirmed that $\sigma(1)=3$, $\sigma(2)=1$, $\sigma(3)=4$ and $\sigma(4)=2$

[fathom swallow]

cgodfrey

[analog salmon]

for no apparent reason

[neat lintel]

is this a subjective question on a math test? sign me the heck up lol

[devout nacelle]

Maybe ask them to specify an algorithm for reading this notation?

[surreal sapphire]

just flip the rows manan

[devout nacelle]

Oh

This is so silly

😵‍💫

[surreal sapphire]

it's bad notation either way

[devout nacelle]

Yeah

Cycle notation good 😌

[surreal sapphire]

its ok

i never know whether to compose from left or from right

[devout nacelle]

Kind of seems to be the best of the lot but gets a bit icky because of left-to-right or right-to-left conventions that different authors use

[devout nacelle]

Yes, that

[surreal sapphire]

also in tex its kinda

how much spacing should there be

nobody knows

[devout nacelle]

Oh hmm, that's true

[surreal sapphire]

but yes, its the best available

mainly because it doesnt take 2 lines for no reason

[devout nacelle]

No spacing, all the sets I permute have less than 10 elements, marked 1-9

[devout nacelle]

Right

Plus it checks out with how function composition works if it's read right to left

[ancient flame]

just got my free tuition confirmed :)

[fervent pebble]

AYYYY

let's go

where?

[ancient flame]

well that's for any florida public university

state scholarship

but im going to UF

[toxic schooner]

wait g mod is a florida man?

everything makes so much more sense

[ancient flame]

LOL

[toxic schooner]

anyways nice gmod

make metal teach u

😌

[devout nacelle]

Congratulations gmod!

[cold needle]

nice bright futures clutch

[toxic schooner]

someone wish me luck for getting into a good uni as well 😭

[neat frost]

Good luck for getting into a good uni as well!

[toxic schooner]

[hushed turret]

good luck shyshu

[bright hill]

Shyshu, I believe in you!

[neat lintel]

How’s you get it?

[ancient flame]

good luck!

[ancient flame]

good gpa + test scores + 100 community service hours

[toxic schooner]

whats a community service hour

[ancient flame]

oh right you're in india

100 hours of volunteering

[neat lintel]

Did u apply for bright futures in junior or senior year?

[ancient flame]

this year

even though I was eligible last year

I got the aice diploma at the end of 10th grade if you're aware of what that is

[neat lintel]

Never heard of it

What is it?

[toxic schooner]

for what?

like helping at places and stuff?

[bright hill]

I wonder if mit would notice me if I get a top 0.1% score in my country

senpai mit

probably not

[charred mortar]

You can always apply

[bright hill]

applying isn't free iirc

[toxic schooner]

i mean, they probably have single one of those 0.1% score people applying there, so its not going to help much

i think

[toxic schooner]

isnt it like a 100 bucks or something?

[bright hill]

[toxic schooner]

[mint patio]

Discrete math is actually kind of cool

Or maybe it's just because the problems are more puzzly and less proofy LOL

I was helping my friend out with some of her problems and had to read her textbook to understand, and it was so much cooler than I thought it would be. They're on relations right now. I love the stuff about representing relations using matrices and thinking about what compositions of relations look like and whatnot

Being able to study relations by representing them as digraphs is cool

I love that stuff in general, when you phrase the same problem from a different point of view and it becomes more accessible to study that way

[bronze pelican]

Discrete math is hella cool

More math depts should have discrete math courses

[hidden violet]

What is a non-empty set?

[abstract mulch]

The empty set is a set with no elements; its cardinality is zero. So a non empty set is just a set which does have elements

[hidden violet]

K

[wind abyss]

@deep mango @vivid halo @neat frost here’s my school pizza

[deep mango]

I see

That seems like the typical school pizza

[bright hill]

the empty set is unique i.e. there is only one such set i.e. any other set is non-empty

[alpine kindle]

there's no red on that

[bright hill]

wait wtf

I didn't notice that

[dire mulch]

prove it.

[alpine kindle]

that doesn't look nice

[bright hill]

it's an axiom I believe

[alpine kindle]

axiom of extensionality

[bright hill]

[dire mulch]

Are you serious? Wait axiom of extensionality says what again? sets are determined by their elements?

[alpine kindle]

a set is uniquely determined by its elements

[dire mulch]

ah yeah I see.

[alpine kindle]

therefore the empty set is unique

[neat frost]

That doesn’t look too bad?

[vivid halo]

It looks pretty lame

But not horrible

[neat frost]

Looks like typical pizza

[deep mango]

slurp is in need of help

[neat frost]

Yes

Which begs the question, ryc

Where are the pictures?

[deep mango]

let's draw a line here between "pretty bad pizza" and "typical pizza"

oh do you want to see 3 pizzas

from the student probability seminar last week

[neat frost]

Is it pretty bad? Looks a wee bit too cheesy, that’s about it tho

[neat frost]

Obv it probably tastes bad because it’s school pizza, but it doesn’t look bad

[deep mango]

idk wtf these are

but they were good

[neat frost]

Uhmmm

Not my type of pizza

[deep mango]

left one was the best

[neat frost]

[deep mango]

yeah idk who has the task of getting pizzas for an event and goes "lemme get 3 weird ass pizzas" instead of at least getting one cheese

[neat frost]

Yeahh

[deep mango]

the left one was just margherita though

[neat frost]

Oh?

[deep mango]

and it was pretty good

[neat frost]

Then why does it look weird

[hushed turret]

what are the toppings on the middle one lmao

[neat frost]

[deep mango]

sausage and fucking spinach and onions or something idk

it was good but like

why

[hushed turret]

wack

[deep mango]

right is eggplant, red peppers and olives

i appreciate the free pizza but next time get 1 cheese, 1 pepperoni, and 1 veggie please

[neat frost]

Lol

Yesh

I’ve had sabich “pizza” a few times

Pretty good

That’s the wackiest pizza I’ve had

Anyway ryc, any other pics you’re hiding

[deep mango]

idk

i would have to scroll through the archives

there are no more recent pics

[neat frost]

I see

[deep mango]

i really really want to put together a nice photo website soon

the problem is that when i feel motivated to do things i try to spend that doing math

i need more energy

[hushed turret]

that is understandable

[neat frost]

Yeah

[neat lintel]

put more pizza pics pls

[deep mango]

i'll scroll way back

let's see what's in the archives

This was fucked up

biscuits and sausage gravy

way way too much food

[neat lintel]

it looks like one big egg

that popped

[deep mango]

western middle of the US is crazy

[neat lintel]

western middle you say

[deep mango]

Yes

This was in western Colorado

[neat lintel]

i wonder how the us is partitioned and what the true "center" of it is

very weird

[deep mango]

Ah, we almost went to visit the geographic center of the contiguous states

https://en.wikipedia.org/wiki/Geographic_center_of_the_United_States#Contiguous_United_States

on the border of kansas and nebraska

but it would have been a 2 hour detour for us so we didn't bother

[neat lintel]

And how do people from there consider themselves ?

Middle middle

[deep mango]

this is considered to be part of the midwest

How about this nice croissant and coffee in Barcelona

[hushed turret]

yum

[neat lintel]

[deep mango]

It's a chocolate croissant

[neat lintel]

sorry

it's called pain au chocolat

or chocolatine

[deep mango]

Yes I heard plenty about the chocolatine debates

[neat lintel]

pain of chocolate ? /s

[brave hollow]

being associated with anything french could be painful

[deep mango]

I don't think people in Barcelona cared much though

[honest veldt]

finally... . . . .. i got to the series part

i stand proud today

[hushed turret]

[clever knot]

YES

I hate this so much

my google search bar has been my basic calculator because of thi

s

[earnest briar]

If mathematics is difficult for me ( I am in the university, studying computer science), should I try building a solid knowledge foundation, or should I quit, because math is not for me?

[sick burrow]

You should quit. Stick to cs topics like computer graphics and machine learning

[deep mango]

If I'd been out then... 😩

So true gamma

[sick burrow]

makes obvious shitpost
gets sullied

[deep mango]

No. Shut up dont make me think about this

I will go back eventually

[earnest briar]

are you talking about me? Shitposting?

[sick burrow]

Stick with math

[astral iris]

What kind of math are you doing

[sick burrow]

cs people who don't know math are awful

[earnest briar]

@astral iris just analysis, discrete math, linear algebra. The last two are fine, but analysis fries my brain a lot

[astral iris]

Ah yeah analysis is typically harder than those 2

So it makes sense you're struggling

I'd say to continue trying

[earnest briar]

I like math symbols

[sick burrow]

They'll unironically post shit like this

[astral iris]

That is a bruh moment

[sick burrow]

Me when I gatekeep math by using notation

[earnest briar]

I mean, for a non-mathematician pseudocode is much easier to understand than mathematical notation

[leaden torrent]

for a programmer it's easier to understand

[earnest briar]

not true, my dad understood ~80% of things that I wrote in pseudocode

[leaden torrent]

he'd probably also understand "sum 3n from n=0 up to 4"

also, what non-programmer would understand for(n=0, n<=4, n++)?

[earnest briar]

it is so clean

it is so good

[leaden torrent]

???

[earnest briar]

never mind

[leaden torrent]

i've TAed intro CS classes and a lot of students get absolutely mystified at for-loop notation for the first couple weeks

[earnest briar]

btw in what language do you put commas instead of semicolon in a loop?

[leaden torrent]

they figure it out eventually of course

well, you said pseudocode

¯_(ツ)_/¯

[earnest briar]

okay

[swift sinew]

This is also a pretty bad argument in general. With this logic, any terminology specific to a field shouldn’t be used

[leaden torrent]

like this is just anecdotal but

ive TAed intro CS and intro calc classes

students get \sum notation immediately

like within a couple examples

well, basic $\sum$ notation at least, something like $\sum_{\rho\text{ a 2-permutation of }\mathfrak{S}} f(\rho)$ would still throw them

[fathom swallow]

Namington

[leaden torrent]

but that would also have much more involved pseudocode so

not counting that

meanwhile, a decent chunk (maybe 1/4?) of the class struggles with basic for-loops on the first assignment

common causes of confusion are using < when <= should be used or vice-versa, thinking they need to increment the index in the loop while also using n++ in the for statement, or not realizing that you can loop backwards (or do anything else when you loop, even)

among other things

also more language-specific stuff like failing to say int n=0 or auto n=0 in C++

also god forbid you need to teach them to loop through a standard template data structure in C++ lmao

[astral iris]

That's a gnarly looking s lol

[leaden torrent]

holy shit students struggle with that

understandably, to be fair

but still

[swift sinew]

This is also even bypassing the obvious argument that pseudocode is not rigorous

[leaden torrent]

(auto is god's gift to mankind)

with mathematical notation you just declare an index and use words

im not saying programming notation is worse, to be clear

it does its job: be machine-interpretable

it's just pretty ass for communicating anything except algorithms.

(obviously it's very useful for algorithms, though, which is why algorithms in mathematics are usually presented in a very loose pseudocode)

oh and if you think these confusions about for loops go away later on in the course

i have graded finals for a second semester programming course

where the problem had a loop of the form for (int n = k; n >= 2; n = n//2) or something

and there was nothing else difficult in the problem, it was just parsing what the loop did

and so many students got it wrong

like way more than youd expect

30%-40% of the class

again this was a second semester course

the question wasnt confusingly written, the actual behaviour of the loop was just "increment a variable and print something" or something like that

all of the wrong answers were students not understanding what the loop did

at this point im going on an unrelated side-ramble but

man

this isnt as intuitive as youd think lmao

[sick burrow]

Namington have you considered the alternative hypothesis that cs students are just dumb

[astral iris]

Lol

Some of them are, but you'd have to be intelligent enough to finish a cs degree

[sick burrow]

Do you?

Cs get degrees

And with grade inflation Cs aren't exactly hard to get

[clever knot]

what does n = n//2 mean?

[leaden torrent]

each time through the loop, divide n by 2 and round down

wait im using other language notation lmao

[clever knot]

well i mean if it is an int isn't it just trucation?

[leaden torrent]

in C++ itd just be n = n/2

[clever knot]

n /=2

?

[leaden torrent]

yeah

sorry its been forever since i wrote C++

thank god

// is comment lmao

[clever knot]

do people use auto in c++

I seen it introduced as a "here is this thing" and that was about it

[leaden torrent]

you wouldnt use it in simple for loops but you do use it if you have to loop through a standard template library structure like a map where the best way to do it is by defining a map<type1, type2>::iterator it and then (it = map.begin(); it != map.end(); it++)

[clever knot]

from what I recall auto just tries to match some declared value and set that as the type of the variable

[leaden torrent]

far cleaner to just go for (auto it : map)

god help you if your data structure doesnt have an interator object that permits it++ tho

since auto relies on that (or at least it did in C++11)

[clever knot]

sounds like for each loop

[leaden torrent]

like just work with the standard template library and youll understand the power of auto

[clever knot]

what benefits does it have over just coding in the right type from the start?

[leaden torrent]

none

[clever knot]

does it just make it more broader in use

[leaden torrent]

its just cleaner and easier

and requires less brain power working out wtf your types are if you dont care what they are

[clever knot]

hmm

[leaden torrent]

//without auto. Not that good, looks cumbersome
SomeType<OtherType>::SomeOtherType * obj1 = new SomeType<OtherType>::SomeOtherType();
std::shared_ptr<XyzType> obj2 = std::make_shared<XyzType>(args...);
std::unique_ptr<XyzType> obj2 = std::make_unique<XyzType>(args...);

//With auto. good : auto increases readability here
auto obj1 = new SomeType<OtherType>::SomeOtherType();
auto obj2 = std::make_shared<XyzType>(args...);
auto obj3 = std::make_unique<XyzType>(args...);

compare

[clever knot]

I see but ideally the programmer fully knows what obj they are working with when they do this?

like obj1, obj2, obj3 are

[leaden torrent]

sure

the point is that, if the type is either:

• obvious
• irrelevant
  then using auto produces easier and cleaner code

[clever knot]

Guess it isn't exactly hard to parse that the obj1 would have to be whatever type the thing on the right is

[leaden torrent]

in the examples i gave above, the type is obvious

in loops with iterators, the type is typically irrelevant

(as long as you can increment it, you dont care what "it" actually is)

in both cases, theres very little downside to using auto

abusing auto can hurt readibility, of course

auto output = foo(input) is terrible C++

dont do that

do int output or double output or char output or whatever

[clever knot]

for (int x : arr) cout << x << endl;

[leaden torrent]

thats another case where auto would be silly, yes.

like, here's an example: how do you loop through an STL unordered_map<int, vector<char*>> in C++ without auto?

yes, it can be done, and any C++ programmer knows how to do it

but do you know the type without looking it up? and do you really want to type out a 40-character-long type name every time, rather than the 4 character long auto?

[clever knot]

shame I don't know enough c++

my instinct would have said some "Object" type

but looking it up it doesn't seem to be a thing in c++

[leaden torrent]

you'd use the iterator type for unordered_map<int, vector<char*>>

and there are some cases where it makes sense to use this type

well, you're using the type no matter what

auto just automatically finds it for you

but there are cases where you want to spell it out to make it clear that's what you're using

in 99.9% of for loops though, you dont really care exactly what the iterator looks like — all you care is that you can increment it (and therefore use it to loop)

and if you want it to be clear, just add a comment

// loop through stringMap or whatever

[clever knot]

i need to really looking the whole c/c++ paradigm

this intro class hasn't taught us anything how it is structured overall

and I see lots of use of std:: but our exercise/book don't to that because they use the namespace

using namespace std;

[leaden torrent]

yeah thats considered dangerous practice in a lot of cases

but its fine for simple stuff

(i think C++ programmers tend to be too anal about using namespace std;, it's almost always fine)

[clever knot]

what is the difference between . and -> I was trying to help someone in there data structures course and I kept seeing ->

[jolly thicket]

using namespace std; pollutes the global scope

[jolly thicket]

-> references members on a pointer to a struct/class

i.e methods of a class use this pointer, so you can do this->member,

obj-> is equivalent to (*obj).

[clever knot]

oh

hmm

so you can just do

obj.

obj.method(); ?

[jolly thicket]

yah

[jolly thicket]

btw this is not always the case when you overload an operator iirc

ie overloading *, . and -> operators to do different things

[clever knot]

I have an example that shows this

[jolly thicket]

yes, the dot operator can access a member of a class object

TimeHrMin is not a pointer, it's the raw class, so it's perfectly fine

now if it was TimeHrMin*, then you would need to dereference it to then apply the dot operator, just to access a member of it

which -> does

[clever knot]

well why would people want to have an extra variable that points to that variable to do that

[jolly thicket]

because pointers can point to various objects

[clever knot]

Guess just depends on use case

[jolly thicket]

i.e:

int PlaySound(Sound* mysound) {
 // do sound stuff
}
//...
Sound test;
PlaySound(&test);

[clever knot]

SongNode::SongNode(string songTitleInit, string songLengthInit, string songArtistInit) { this->songTitle = songTitleInit; this->songLength = songLengthInit; this->songArtist = songArtistInit; this->nextNodeRef = NULL; }

this was someones code from assignment and it just seemed weird that it was done like that.

like provided by the book i think

anyways I guess if you are passing a pointer into a function you would have to do that

[jolly thicket]

yeah

[clever knot]

this was one of the provided constructors

[jolly thicket]

it allows you to reuse the function for various objects that are derived from, or are a SongNode

[clever knot]

can variables store functions in c++?

[jolly thicket]

yes

std::function<return_type(arguments)> my_fn

there is also the C-way, but std::function is more useful, esp. since it supports lambdas

[jolly thicket]

you can't store them per se, but you can point to them

[clever knot]

hmm I just recall some languages you could store them and even pass functions as a paraamter

[jolly thicket]

thats self modification

[clever knot]

maybe that was javascript

[jolly thicket]

and i think only people from 1970 did that

[clever knot]

but not sure if c++ supports things like that.

[jolly thicket]

c++ supports that

std::function<int(void)> lol(std::function<void(int)> my_lol_fnc)
{ /* do ur stuff */ }

[clever knot]

do you know some resource I can get a run down on best practices and understanding the layout of c++?

[jolly thicket]

nope :/

[frozen venture]

Does lcm(a,b) = lcm(a,c) imply that b*c divides a?

Where b and c are relatively prime

[earnest briar]

@swift sinew I wasn't arguing for or against anything. That was merely a conclusion made on a basis of first and second-hand experience

[dire mulch]

“this->” doesn’t that bother u when u use it?

It gets very messy.

[dire mulch]

Yes u can do this in c++ though it gets technically.

[clever knot]

it isn't me

it was an example that was predefined in someones online code assigment

like given to them to use

[dire mulch]

Oh ok.

My main reason for disliking it is that it’s way too long.

[jolly thicket]

i like them because they provide more context

esp. when you have to read old codebases

[fair mural]

do any of you have anything you did that really helped you when you started doing proof based math?

[torn willow]

Olympiads

[cloud glen]

Hi I was wondering if there is a formal proof about Taylor series coefficeints being equal to the 'limit' of orthonormal projections of polynomials of a certain degree to that function

[rose dock]

The limit as the interval around the point where you're taking the Taylor series of shrinks?

[tender tulip]

What’s the inner product then

[ancient flame]

I try something for like 5 minutes then give up and look at the actual proof

then to put the cherry on top I always say "ohhhh that makes sense"

[fair mural]

that doesn’t help at all

[ancient flame]

exactly!

[swift sinew]

Gathering and really understanding definitions and theorems and understanding why they are the way they are (why this rather than a slight variation to the definition or theorem) and understanding why a proof technique makes sense for a given problem, are all extremely helpful in developing skill in proving things. I’d honestly argue that they’re some of the most important things to stress on when first getting into proof-based math

[primal seal]

Agreed

Messing with hypotheses and investigating the outcomes and coming up with counter examples should be added tol

[near fox]

Here's an alternative suggestion that I haven't seen mentioned here at all: studying with a friend enabled me to study 10x more effectively, better than finding a better book, online notes or lectures, or even a teacher. My friend helped motivate me every day and made the learning more interactive. I know a lot of people are just self-studying here, but if you can find a friend (in real life, not online) to study with that would be very beneficial in many cases.

[primal seal]

Yeah that trumps all

Difficult to do when your friends have families or No interest whatsoever in mathematics. But it’s the best possible advice for younger folk here and, especially, enrolled students

[vapid kernel]

Hey. About that: how do you keep yourself studying different things as you get older and work piles up? I'm a math teacher and I keep struggling to study math at all, let alone things beyond whatever I teach at high school.

[primal seal]

It can be difficult to sit and read through chapters of dense (esp.math) books without large chunks of time- or consistent time at that (since you know it won’t amount to much if it’s not consistent to some degree).

One thing I did when I had less free time was to read what I could in whatever time I had, but I’d take exercises corresponding to that material everywhere with me

@vapid kernel

[vapid kernel]

Consistency always gets me. Teaching is a time sink like no other, partially because it sinks your time outside of class as well (and energy)

[primal seal]

I completely understand man, you have my respect; not sure I could do it either if I were in the same boat

[vapid kernel]

Are you also entering your thirties?

Really miss having some free time like I had a few years back. Not even looking back to when I was in university

[near fox]

I am in my thirties. I'm a mathematician but even then I find it tricky to find time to read or learn new things unless they're directly related to my work.

I sometimes look back at my old notes from school and am surprised how much I forgot

[primal seal]

I am in my early thirties

[velvet dagger]

Damn

[primal seal]

Old folks home in here

[toxic schooner]

[velvet dagger]

Still closer to 20 years old than 30 but not for much longer

I miss being in college 😢

[plucky dawn]

Is anyone here a trader for a prop trading firm

[velvet dagger]

I'm considering that as one of my top non-academic choices for a job

Basically my top 3 atm are academia, trading/quant research, and research in tech

[plucky dawn]

that's fair man

I've got an offer for BBIB & an offer for a top prop shop and I'm weighing my options right now so I wanted to ask some people haha

[rancid meadow]

chase the bag

[neat lintel]

best practices ? maybe check out books by Scott Meyers, Herb Sutter's GoTW blogs etc

[plucky dawn]

but what is the bag? Who really makes more, bankers or prop traders in the long run?

[velvet dagger]

@plucky dawn it's probably fairly firm-dependent. Another relevant factor is time

[plucky dawn]

I guess one of the big concerns i have is that I've heard that traders' compensations are capped after a while (unless you make head of trading/partner) & there's zero exit opportunities

[velvet dagger]

Hmm, so what I've heard of is that you get performance bonuses. How good those are, again depends a lot on the place

[plucky dawn]

Where I'm from, I think it goes from 150k USD first year -> around 600k in 5th year

all in comp

I guess I'm concerned that the comp will eventually be capped at high 6 figs

[velvet dagger]

So, my take is that 600k/year is... enough to set yourself up perfectly imo no matter where you live

So that's where I'd say the other factors kick in

Like I'd rather work closer to 40-50 hours a week and stay at high 6 figure forever than cross to 7 figure but have to sleep in my office

[plucky dawn]

that's perfectly fair

For me though, my goal has always been to get to a billion bucks

[velvet dagger]

Is that realistic even in banking?

[plucky dawn]

It's theoretically possible if you invest the vast majority of your returns in the hyperleveraged Australian housing market

[velvet dagger]

I feel like the number of people who work in banking is... quite a lot higher than the number of people who are billionaires

And given that they probably prioritize money over most other things I would think a lot of them have fairly good ideas how to invest their income

But yeah I don't have enough detailed info to be of particular help here. If you're optimizing for money and think that banking does win there long term then that's probably the strat? Unless there are other factors I'm yet unaware of

[plucky dawn]

yeah

tbh I've been trying to get in contact with senior people in industry

to see what the progression really is

[velvet dagger]

That's a good strat

[plucky dawn]

all I have so far is wall street oasis hearsay, which as you would be aware, is highly unreliable

[velvet dagger]

But yeah I've mostly not looked much at banking because my impression about the hours makes it feel... not very worth it to me relative to my financial goals

[plucky dawn]

that's a very crucial consideration tbh

are the 80-90 hours a week worth it

even if you earn more than trading in the long run, it's only like 40% higher, not a different magnitude entirely

[velvet dagger]

Perhaps said goals are modest, but pretty much I'm gunning for, first owning my place, then having enough passive income to, let's say double my lifestyle if I'm not going out of my way to be conservative

[plucky dawn]

tbh that's probs all you really need. Apparently satisfaction from money depreciates exponentially fast after you earn >$300k a year

[velvet dagger]

But I'm on a grad student stipend right now and I'm surprisingly not wanting for much lmao. I'm not a sports car person or anything. So I feel like once I own a place, even if I live in a place like NY or Bay Area, no way I'd be spending more than... 200k/year? Even if I just throw money wherever I'd like it

So okay let's go ballsy and say 500k passive income after tax is my big financial goal. And I think I can hit that somewhat quickly in trading

[plucky dawn]

unless you're buying a tesla every year haha

[plucky dawn]

definitely. Within 10 years max

[velvet dagger]

That was my mental timeline lmfao

[plucky dawn]

oh wait passive income

that would be difficult

maybe 14 years?

[velvet dagger]

Or I guess I meant 10 hours after working. So that clock isn't starting for a while and I kinda have some ideas on investments

[plucky dawn]

wdym 10 hours after working

like income from 10 hours worth of work?

[velvet dagger]

*years not hours

rip

[plucky dawn]

ahaha

I was gonna say

don't think ur gonna make $500k in 10 hours in trading

[velvet dagger]

My investment ideas are fuckin cracked lmfao

😛

Nah but yeah

[plucky dawn]

unless you yolo gamestop

[plucky dawn]

my investment strategies are less risky haha

[velvet dagger]

Actually I'll move to DMs this is getting a bit specialized

[sacred elk]

2/6 babyyy sheeeeesh
🟩🟩🟩⬛🟩
🟩🟩🟩🟩🟩

https://wordlegame.org?challenge=Y3JhdGU

[bright hill]

in real life, not online
I'm doomed

[hasty silo]

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

can anyone tell me if this is wrong

randomly found this youtube video

and im assuming some random guy didnt solve this but his video has 0 dislikes also

[crystal stream]

if it's not wrong i will record myself eating a hat with a fork

[fair mural]

i will hold you to that

[odd narwhal]

I will eat a fork with a hat

[fair mural]

even better

[swift sinew]

Has 0 dislikes

[bright hill]

if RH is proven wrong I'll literally give whoever did it another million

just to spite everyone even more

[neat lintel]

The hat

[deep mango]

That's too much guac for me to eat in one sitting

[neat lintel]

Never a thing as too much guacamole

[rocky shuttle]

But can you approximate the hat from below using simple functions?

[neat lintel]

Something something pi

[delicate knoll]

Divide with some who need it a bit.

[ancient flame]

I NEED THIS

[hasty silo]

lmao this is exactly why i hate that youtube removed dislikes lol. (I downloaded an extension that adds them and nobody who has it happened to also dislike the video)

[fair mural]

isn’t this an analysis question?

[rocky shuttle]

It is

[fair mural]

that’s a question in axlers ladr lol

not even calculus, just straight up analysis

[empty stratus]

Calculus is analysis, though.

[fair mural]

you know what i mean

[rocky shuttle]

Calculus is fake analysis

[empty stratus]

No, Schneider's book on "non-archimedean functional analysis" is fake analysis.

It's actually a book about algebraic geometry.

Doesn't even mention integration.

😭

[zenith forge]

gabe

[steep mountain]

this wasn't uncommon
its sorta teasing into some functional analysis lol

at least thats what i felt during my course

[toxic schooner]

[tribal talon]

can someone explain to me why 0! = 1?

[bright hill]

sure

you see

[sleek wing]

PauseChamp

[bright hill]

I think we can agree 1!=1, 2!=2*1, 3!=3*2*1... etc

[rocky shuttle]

How many bijections are there from the empty set to the empty set?

[tribal talon]

like why isn't this wrong?

[torn willow]

this is wrong because it's gibberish

[tribal talon]

I just used the gamma function to evaluate -1!

[sleek wing]

Factorial isn’t defined for negative numbers for a start

And why can’t 0 times infinity be 1

[tribal talon]

it's undefined but I think it should be ZEROOOO

[sleek wing]

Take the limit of 1/x times x as x goes to infinity, this clearly approaches 1

[sleek wing]

0! = 1!/1 = 1

[tribal talon]

what?

[sleek wing]

The empty product is 1, the number of bijections from the empty set to itself is 1

There are so many arguments I could use here

[torn willow]

(-1)! doesn't even exist

[tribal talon]

I used the gamma function

[torn willow]

You are using what your calculator thinks is the gamma function

[tribal talon]

I just don't understand why plugging it into the formula contradicts 0! = 1

[torn willow]

Your calculator can output whatever it wants when function at a point is not defined

[sleek wing]

The gamma function at -1 is undefined isn’t it

[torn willow]

(-1)! Is "teddy"

[tribal talon]

= infinity

[torn willow]

Is equally valid as saying (-1)! Is infinity

[bright hill]

the same reason multiplication works for non integers

even tho repeated addition doesn't make sense there

it's called domain expansion (or some shit idk)

[torn willow]

Ah domain expansion

[bright hill]

[tribal talon]

bruh, okay, I'll just accept it as it is, but it still breaks when I plug it into the equation

[sleek wing]

,w plot the gamma function

[fathom swallow]

Results provided by WolframAlpha

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

Requested by Wew Lads Tbh#0864

[sleek wing]

Thanks wolfram very cool

[bright hill]

[torn willow]

,w gamma

[fathom swallow]

Results provided by WolframAlpha

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

Requested by DrunkenDrake#1521

[bright hill]

[torn willow]

,w gamma function

[sleek wing]

(n-1)! = n!/n
(1-1)! = 0! = 1!/1 = 1

[fathom swallow]

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Requested by DrunkenDrake#1521

[sleek wing]

I don’t see why you’re confused by this

[torn willow]

Genius

[tribal talon]

okay I get that, but how come when I sub zero straight into the formula it doesn't work

[bright hill]

what can we do without wolfram

[torn willow]

Life

[bright hill]

coz the formula only works for n>0

[tribal talon]

but... but... you solved for 0! and N = ZEROOO

[bright hill]

yes

it made sense to define 0!=1

coz that's how mathematicians do stuff

[neat lintel]

$$n! = n(n-1)!$$
$$! = (n-1)!$$
$$1 = n-1$$
$$n = 2$$

[fathom swallow]

Blitz

[neat lintel]

You're welcome

[bright hill]

[neat lintel]

[bright hill]

yeah, exactly

[tribal talon]

1! = underfined

[bright hill]

no it isn't

1!=1

[neat lintel]

0! = 1, (-1)! is undefined

[bright hill]

@tribal talon just think of it like this

[tribal talon]

But I just demonstrated that 0! Equals undefined, and subbing that into 0! For 1! Gives 1 times underfined

[neat lintel]

n! = n(n-1)! holds for n>0

So your argument is wrong

[bright hill]

4!/4= 3!, 3!/3=2!, 2!/2=1!

[tribal talon]

I'm really sorry for stupid quetsions, it's just this idk how math

[bright hill]

then surely you must agree that 1!/1=0!

right?

[neat lintel]

It's ok to ask questions to understand things, even if they're stupid

No need to be sorry

[tribal talon]

by that arguement, you'd agree, 4/4 = 1, 3/3 = 1, .... 0/0 = ONEEEEEEEEEEEEEEEEEEEEEEEEE!

[bright hill]

sure

[sleek wing]

No because dividing by 0 isn’t well defined, dividing by 1 is

[neat lintel]

Wheels?

[tribal talon]

I love maths, it's just some of this stuff is so axiomatic with logic but it's just wrong apparently and it's annoying me

[neat lintel]

For this argument to work we need wheel theory

[sleek wing]

Alison has ruined this fuckin server I stg

[sleek wing]

You’re the one breaking the axiomatic logic

You’ve been told that n! = n(n-1)! Only holds for n > 0 and yet you keep trying to apply it to n= 0

[bright hill]

what is that supposed to mean

[tribal talon]

Yeah but I'm using your arguments that you used to prove something wrong and I break it but apparently i'm in the wrong

[sleek wing]

So we try and extend the definition by rearranging that definition to a form that does work

[bright hill]

domain expansion

that's what I'm talking about

[sleek wing]

so the form n!/n = (n-1)! Actually still does not work for n = 0 because it is identical to n! = n(n-1)!, but we can define 0! using it

[neat lintel]

0/0 = ⊥

[deep mango]

[tribal talon]

= 1

[neat lintel]

No

[tribal talon]

think of it like this

[deep mango]

8/4 = 2
6/3 = 2
4/2 = 2
2/1 = 2
0/0 = 2

[tribal talon]

you can't have nothing if you have nothing to compare it to so it must be something