serious-discussion

[raven haven]

groups too?

[modest rune]

I think you are conflating different usages of the word closed

[pulsar bane]

When you say "closed" you have to say what is closed (i.e. operation)

Yes, vector addition, multiplication, and scalar multiplication are closed but that's not the same as closed algebraically.

[raven haven]

both of them, vector addition and scalar multiplication

[raven haven]

aaaah

[modest rune]

Yes, vector spaces are closed under these properties

[raven haven]

how come

[modest rune]

Definition

[pulsar bane]

For an operation + to be closed it means ∀a,b∈S, a+b∈S.

[modest rune]

In fact, I would argue that if you define these things properly the word closed is simply redundant

[raven haven]

no i mean how come they're not algebraically closed

[modest rune]

why would you write this symbolically lol

[modest rune]

the closure under the operations does not guarantee algebraic closure

[pulsar bane]

derp

[modest rune]

most fields are not algebraically closed

[raven haven]

i see ok thanks

[sick burrow]

bruh

in class rn my prof is trying to parse a homework problem that he literally wrote for this week

someone asked him "wait how do I do this" and now he's rereading the problem to remind himself how it works

[cinder flume]

Of course they are not alg closed

You can define a vs such that the element satisfying root not be there

Sorry if the conv Changed

[sick burrow]

it has been 20 minutes and he's still working out the problem

[limber thunder]

[errant furnace]

you guys are probably stressing him out

[steep mountain]

is that weird ?

my professor once forgot a certain solution to a problem and we went on to prove it together in the next ~25 mins lol

it was very productive and idk if he did it on purpose

[fair mural]

james new pfp

[steep mountain]

oh ye im just messing with my friend who dislikes anime for a bit lol

ile go to old one later

[fair mural]

[sick burrow]

[modest rune]

Sometimes profs pretend to know less than they do but most of the time they just haven’t thought abt it in awhile

[steep mountain]

ye that's fair enough , you can't keep up with every single problem all the time.

[potent aurora]

hey, I was in help room 12 and it just disappeared, can't find it among occupied, available or hidden, what do I do?

[tall badge]

@potent aurora #help-12

[potent aurora]

thank you very much

[fathom tendon]

why is the discord server picture a coffee mug

[pulsar bane]

Cuz' donuts, y'know.

[sick burrow]

coffis

[terse flax]

It's not a coffee mug, it's a n-dimensional hypermanifoldian Laplace pi-surface solenoid.

[fathom tendon]

da frik

[compact tartan]

[wispy dune]

does anyone have a link to the stackexchange thread that was pinned to one of the analysis channels long ago

i remember it was a really difficult problem on polynomials and compactness(?) where some dude said it was a problem from a first year course in calculus

even though it very clearly wasnt

[limber thunder]

I think the solution involved Baire's theorem or smth

and the guy had misread the quantifiers and it became trivial if they were like, the other way around

[hybrid rune]

Sorry to intrude but my brain is a bit off today. Do you guys what is meant by evaluating this integral? The context is a grad real analysis course and no helpers seem to be available.

$lim_{n \to +\infty} \int_{0}^{\infty} [(nsin(x/n)/((x^2+1)x))]$

[fathom swallow]

chernberries

[limber thunder]

I guess you're supposed to calculate that limit

[hybrid rune]

I’m in help room 22 if you want to see my attempt

[limber thunder]

using e.g. dominated convergence thm

[hybrid rune]

Yeah I’m not sure of a canonical way to find the right function that bounds f_n

I’m pretty sure I got it; just let F(n) = that integral, take the derivative then use DCT

Have to use MVT somewhere I think

[limber thunder]

https://mathoverflow.net/q/34059

[real canopy]

i need people to study with. but all my friends dont care abt their grade cuz its senior hs. is there anything i can do

[rotund steppe]

hire a tutor

[neat lintel]

are you a graded module

[neat lintel]

Because better acceptance rate?

Yeah??

If you choose a big major with limited classes then theyll always pick the guus with 95% average over someone with 70% average

In uni?

College?

??

For better acceptence rate in the later schools?

I just said it

[deep mango]

not every country runs on the same application timeline as the US...

[cyan goblet]

if you're bold

go to a local library when you study

and sooner or later if you see someone who you think would be fun to sit next to

walk up to them and ask politely if you can sit next to them

and just study

and once they leave be like "hey id like to get to know you" or something

be like "im looking for a study friend" or something

[compact tartan]

lol imagine caring about your next school before you finish the current one

[carmine geyser]

guys simple doubt :

{0,1}^4

is it true that above notation means lot of sets with 4 elements in it ?

like :

{1,0,1,0},{1,0,0,0},{1,1,1,0},{1,0,1,1} etc

[empty stratus]

Yes

[carmine geyser]

thanks bro

[empty stratus]

It's the set of al length-4 sequences of 0s and 1s.

Good.

[rotund steppe]

you want us to design your experiment for you ?lol

[cobalt star]

make better friends

[frail sail]

bru ur on discord

use DISCORD!

literally so many study grps

[carmine geyser]

A = {ω ∈ Ω|(ω1, ω2, ..., ωn) ∈ A(n)}.
i am confused on what this set looks like

anyone please help

[alpine kindle]

not sets
tuples

you could also describe it as the set of all functions from {0,1,2,3} (the set notation for 4) to {0,1}

[alpine kindle]

could you put it into latex

[carmine geyser]

A = (ω1, ω2, ..., ωn) like this ?

[alpine kindle]

that was in response to your previous question

[carmine geyser]

i cant, i am not familiar with latex

[alpine kindle]

people will be able to help you much more easily if you learn it

it's not very difficult

[carmine geyser]

so this one wrong ?

[proper patio]

In case you have heard before of the Steiner symmetrization, I made a simulation that lets you play around with it https://jsfiddle.net/25zbc8ao/

[stray kite]

does there exist multivariable complex analysis

f : C^n -> C^m

[toxic schooner]

[ripe wasp]

hm

is there an n- dimensional calculus

like calculus i-ii covers 2 dimensional mostly

calc 3 covers mostly 3 dimensional right? or is this where n- dimensional is covered

[stray kite]

lol what

[toxic schooner]

calc 3 covers multivariate

and yes there is n dimensional calc

probably even infinite dimension

idk

[stray kite]

how do you only learn 2d but not generalise that lol

how do american calc courses work

[neat lintel]

Shyshu calc 3 done ?

[toxic schooner]

nope

[neat lintel]

Upto Calc 2 then?

[stray kite]

is it like only for R2->R2
why would you do that lol

[toxic schooner]

kinda

[pulsar bane]

Differential Geometry is pretty much the "n-dimensional" version of calc 3.

[deep mango]

in one of my classes we just started using all the calc 3 theorems in R^n instead of R^2 and R^3

and it was just like

ok, i guess all that shit was the same in any dimension? but no one ever mentioned it

[mellow moon]

Curl operatorS in n-dimensional setting

[deep mango]

😌

[neat lintel]

i want a cool partially ordered field that isnt R or C with usual orders

?

thatd imply 1<=0

i asked for a ordered field not for a field with a order in its underlying set

kid are you kidding

[bronze pelican]

Check out real closed fields

[fair mural]

superreal numbers

[tender grotto]

what does it mean if something is closed

[neat frost]

its not open

[tender grotto]

whats the difference

[neat frost]

tbh thats not even true

its when its complement is open iirc

idk havent taken topology yet

[modest rune]

what context

Oh the above image

[tender grotto]

well in general ig

[modest rune]

it means many unrelated things

But in this context I also have never seen this usage of closed

@bronze pelican

Do you know?

My guess is that the closed here refers to "closed under the first order properties of the reals"

but thats not very good

[modest rune]

I read this

[devout nacelle]

Sounds right

[modest rune]

but this does not explain the usage of the word closed

[tender grotto]

well what does that mean

[modest rune]

in particular the only other usage of closed on that page

is to say that the real closed fields are not algebraicly closed lol

[modest rune]

It means that very simple statements about the real numbers are also true in these other fields

[devout nacelle]

True

[bronze pelican]

I think model theorists just wanted the abbreviation RCF to rhyme with ACF which stands for algebraically closed fields

[modest rune]

cursed

[tiny marten]

this is why i do analysis

[stray kite]

are all global extrema which arent at endpoints of a continuous function definition also local extrema?

[surreal sapphire]

why the endpoint condition

[stray kite]

cant have local extrema at endpoints can you

[surreal sapphire]

why not?

[stray kite]

arent they defined on open interval subsets of the domain

[surreal sapphire]

yes

but e.g. [0, 1/2) is open in [0, 1]

anyways, i think if you use sane definitions global extrema are also local extrema

[stray kite]

ok youre right idk why i thought that then lol
anyway ty

[median zinc]

[rotund steppe]

I actually understood lecture today

[long matrix]

$(\exists l\in{lecture})(l\in{things understood})$

[fathom swallow]

Shuri2060

[long matrix]

👀

${thingsunderstood}\neq\varnothing$

[fathom swallow]

Shuri2060

[long matrix]

👀 👀 👀

[crystal raft]

What is the criteria to be a helper?

[mint patio]

Literally none

Just ping a mod and ask for the role

[crystal raft]

Ah cool

@compact tartan could I have helper?

[neat lintel]

imagine wanting to be an helper

[median zinc]

Wow just directly pinging mnoop

[neat lintel]

i have cancer ok

be careful with what you say

i can explode

[mint patio]

Bahahah that’s what I was thinking too

[compact tartan]

I don't mind

if it's not annoying

[midnight iron]

how could we use Bayes' Theorem to analyze situations when the sample space is partitioned more than once?

phrasing this question to make it look right took a lot of time btw

[neat lintel]

[tender musk]

Inside of #help-1

[wanton tartan]

Is there any standard variable when working with quaternions

Like x for reals or z for complex

[sleek wing]

I've seen q used

[wanton tartan]

Makes sense

[solar hound]

What facts should I add to the site?

My goal is to make every number have interesting facts about it.

[frail sail]

if u do that...then maybe the facts would no longer remain intteresting

[charred mortar]

How many numbers are you adding in any case

Like are you stopping at 500? 1000?

Wikipedia has some properties of the lower numbers which could be useful as a starting point

Although later on it peters out (see 502 = 2 x 251)

[midnight iron]

I think that's the best I can do. anyways, it was just a curiosity. maybe as I learn more and more of it, I will get the answer by myself.

thanks Todd

[inner finch]

https://www.probabilitycourse.com/chapter1/1_4_2_total_probability.php @midnight iron is this what ur looking for

[edgy tartan]

what are kinds of functions that f that after dividing by x i can find inverse function explicitly
i mean inverse(f(x)/x ) exists in symbolic form

?

(ping if answered)

[midnight iron]

thank you mirza!

[dawn sluice]

I enjoyed answering the homework question so much. Is there any platform where you got paid for tutoring?

[mint patio]

I dread data analysis

I hate doing things

I love learning things

Hate doing

[charred mortar]

Learning is doing though

[toxic schooner]

but u gotta do stuff to leanr as wlell

also wait, is that u in ur dp?
u look cute

[neat lintel]

learn how to automate as much as possible

so you can do less and learn more

[mint patio]

Yes it is me, thank you 🥺🥺

[mint patio]

ahah don’t I wish

[solar hound]

It automatically generates facts

[charred mortar]

ah auto-generated

[solar hound]

But some parts of it are customized for specific numbers

Like divisibility tests for specific numbers are customized

[charred mortar]

I'm assuming stuff like factors or whatever can be automated without too much trouble

[solar hound]

Yep

It even looks in the OEIS for sequences containing the number

[charred mortar]

that part's pretty cool

[solar hound]

@charred mortar I'm trying to find more facts about numbers to add to it though

Like more tests I can apply to see if the number has any other interesting properties

[charred mortar]

I still think you could search wikipedia's list of properties for low numbers, like say 6 or 12, to get some ideas

and probably have those properties apply to most of the integers in some fashion

[solar hound]

I actually have been doing that

[charred mortar]

Ah well I guess a number theorist would be able to provide better answers

[solar hound]

One of the things I want is more tricks

[charred mortar]

I’m not one unfortunately

[solar hound]

Like the sum of three palindromes one

[median zinc]

Is it JS driven?

If the facts are generated I hope they are done once then stored in database, then perhaps verified once and then called as wanted

You might want to RNG at either the server side or client side to vary facts shown

Could be more interesting to not mention 1729 as a taxicab number to some visitors

[solar hound]

Yes

[solar hound]

I could cache them in a database

but if you mean manually verified that would be very tricky

since there's so many numbers that would get random visits

[median zinc]

Would be good to at least verify some of them, or you get 57 being a prime

[solar hound]

It does a full prime factorization before identifying if a number is prime, so it's thorough

[solar hound]

Hm

That's true, I should add taxicab numbers lol

[cyan goblet]

does the equation below 5.14 denote

$\Re(Ce^{i\omega t})$ or $\Re(C)e^{i \omega t}$

[fathom swallow]

anamono

[cyan goblet]

i assume the latter because C is defined as a complex number?

[sly vale]

since C is complex I'd assume Re(entire complex number)

[compact tartan]

same

[analog salmon]

who tf decided to have reduced and irreducible not mean the same thing in algebraic geometry

[mellow moon]

PROPAGANDA²

[toxic schooner]

[neat lintel]

small thing

[neat lintel]

Hui and Grigor are going to play a game with the following rules.
(a) Hui begins by placing a knight on any square of a regular 8 by 8 chessboard. Grigor moves the knight first. 
(b) Hui and Grigor alternate moving the knight, but they can only move the knight to squares that it has never been to before.
(c) The player who cannot move the knight anymore loses. With the correct strategy and perfect play, either Hui or Grigor will always be able to win. Who has the winning strategy?

i need a hint

a small one

anyone??

[odd narwhal]

#❓how-to-get-help

Since this seems like a game theory question, maybe #proofs-and-logic would be better

We don't really have a channel where game theory fits well

[neat lintel]

i never knew that was a channel here

[tender musk]

@solar hound Are you done with your website and can you send a URL if you are?

[solar hound]

I'm not done with it

[tender musk]

RYC for moderator! Yes!

[solar hound]

I still think it needs more

Before I can confidentally release this version of the site

[tender musk]

Is it close? Or do you have a beta version?

[solar hound]

It's close

But I still don't want to release it until it's 100% polished

[tender musk]

Can you update me when it is finished?

[solar hound]

If you want, a previous iteration of the site is available, but it's no-where near as good

[solar hound]

If I remember lol

[tender musk]

Yes, do you have a URL?

[solar hound]

https://number-time.web.app

But this is the previous version

It's not the remade version I'm working on

The new version will be so much better

[tender musk]

That is still very cool! Good job!

[solar hound]

Thank you.

[tender musk]

Can I dm you to keep with updates? (I don't know why but I feel invested now.)

[solar hound]

Sure ig

[cyan goblet]

when is $\phi$ vs $\varphi$ appropriate

[fathom swallow]

anamono

[cyan goblet]

because (as far as im aware) i have yet to see phi denote anything other than some variable

[deep mango]

Meh, interchangeable

[cyan goblet]

dammit

[deep mango]

Angle, homomorphism

[cyan goblet]

oh true phi is angle

forgot

[jolly tulip]

@cyan goblet different notations are basically picked according to conventions and preferences. Just be consistent and do not mix them together

[cyan goblet]

kk

same thing for $\epsilon$ and $\varepsilon$ too then?

[fathom swallow]

anamono

[deep mango]

Umm

I would just never use epsilon and always use varepsilon

Tbh

Absolutely only use varepsilon for your usual small epsilons

Some people forget to and they are evil

[cyan goblet]

oh

i dont wanna be evil

[coarse grotto]

[deep mango]

I define \eps as a macro for \varepsilon

[cyan goblet]

would i be stupid to just renew command \epsilon to \varepsilon

[deep mango]

Thats fine too

I just use a lot of epsilons so i want it shorter

[cyan goblet]

dope ty

[jolly tulip]

Yes

[fluid rapids]

https://drive.google.com/file/d/13pSWodNyMOYezARejViz5rBww1QBgGD1/view

very good video

[deep mango]

[gritty copper]

[vast surge]

This URL looks like a virus and I'm afraid to click on it.

[dawn bridge]

i clicked

@fluid rapids what's this

[ripe wasp]

wtf is this

[neat lintel]

just another troll vid

[bright hill]

how do you guys take notes? (especially when self-teaching)

if you don't, why?

[fluid rapids]

i don’t lol

every time you learn something try explaining it

and word it so that you can fluently explain

this proves mastery

[bright hill]

that actually the reason why I take notes

[potent valley]

I feel like notes never work for math

like ever

[surreal sapphire]

i dont write notes, but i do scratch work

[fluid rapids]

the truth.

[deep mango]

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

[bronze pelican]

I love how this sentence is in the video description of a WIRED video

[deep mango]

lmao

it's actually a very fun video

if you're expecting nothing of any depth

[ancient flame]

lmao

she didn't even explain pi

"ratio of circumference to diameter" is not mentioned at all

like why is that not the first thing you say

[hybrid rune]

Is folland good to prepare for QR exam in real analysis?

[bronze pelican]

Yes but who fucking wrote this video description

They just took random questions from quora and stuck them in the description

[deep mango]

lol

those were literally tweets in the video

(including the anabelian topology one)

[bronze pelican]

Ok didn't get to that point yet

[empty root]

Does anyone know why the line integral definitions of divergence and curl aren't taught often

I think they're far more intuitive and don't depend on your coordinate frame (this is particularly important because you learn curl and divergence in so many different coordinate frames).

[mellow moon]

You need to be well aware about Differential geometry, differential forms, exterior derivative and Stokes' theorem to make a full meaning of an adapted intrinsic formulation

But yes

The same goes for surface integrals (Stokes theorem)

[empty root]

We have some slighly non rigorous proofs for divergence and curl tha work wihou differential geometry

t on my keyboard has broken

[coarse grotto]

my uni uses folland for the real analysis course meant to prepare you for the qual. I would say that it prepares well (but this is university dependent)
I’d say picking up something like royden or stein-sharkarchi might help you if you see a concept in practice exams that isn’t covered in folland

[tiny marten]

yeah folland is used here too

and people advise stein and shakarchi, etc

i think that one rudin text does both too

i used it a little for my complex analysis class

[limber thunder]

our uni uses it for our PhD analysis courses too

[uncut socket]

@austere hazel Kinda wish people would look up resources on stuff they don't understand first, because I literally Googled "point slope to slope intercept form" and that was one of the first results

[austere hazel]

google is by far a very uncommon common sense skill, i've found

[uncut socket]

Same, and people need to Google first

[austere hazel]

yes, yes they do

[uncut socket]

Literally all my solutions, I Google first

[hybrid rune]

My university also uses folland but I don’t like it

[neat lintel]

so is reading

but sometimes people want to be told by a person rather than read and it’s understandable

[long matrix]

The mysterious thing is the process of reading still occurs via discord

[frozen merlin]

my courses provide pdf lecture notes, so the only thing I do is write up a big list of all the significant theorems/propositions for reference

so that I can look up a theorem in my 5-page book of theorems instead sifting through the of the 50 pages of the book/lecture notes, where most of the space is filled by explanations/examples/proofs

[ripe wasp]

i write notes

down of formulas and ideas

but mostly its just to get the topics into my head

i literally never look at them again

after writing them

[rancid meadow]

this video was really bad

i dont know if it is wireds fault or the presenter but god nothing of substance was said

didnt even explain pi

yet wrote down that awful looking identity

odd behaviour

all the comments that are like "im a math major and this is so true " make it worse

also opening with that clip of her being like "you don't need this"

[ember fog]

Hello I'd like to ask for tips on dealing with math anxiety, I just read a report on it and it seems I perfectly fit the bill. Any recommendations on starting my journey? I mostly have to do it alone without the help of an educator. I feel really intimidated and scared and I know it's ridiculous.

I really want to love math but fear is overshadowing it

[deep mango]

you good my guy

no fun allowed

[rancid meadow]

this is the kind of stuff highschoolers point at and say hey look i dont need to laern this

idk i think its bad if u r in an authroity positon to say that without any qualifiers lol

[neat lintel]

hi

i just opened up a poll and asked people to pick a number from 1-10

[fair mural]

[neat lintel]

[long matrix]

-9

[uncut socket]

Pi

[sly vale]

Given discussion, dx

[long matrix]

dx < 1 rip you

[sly vale]

1.000...001 then 🙄

[fair mural]

reminder that you said -9

1+dx

[long matrix]

1-10 is -9

[sly vale]

Yeah

r/woooosh

[fair mural]

shut it shuri

[long matrix]

1 < -9 < 10

ig

[sick burrow]

I'm not sure how helpful this will be, but my suggestion would be make sure you're not viewing struggle as a sign of failure

The only people who haven't struggled with math are people who've never seriously done math

[steep mountain]

i would suggest getting good

[sick burrow]

So when something isn't making sense right away or you're struggling to solve a problem, don't beat yourself up about it

Because that happens to literally every person who studies math

[ember fog]

I'll try my best to rethink how I deal with struggling, all my life I've been in a top class with super smart kids and things just came so naturally to them. Wasn't far off that I thought I was failing for my pace

I also thought only smart kids like them could do it

I've been trying to use math this way, I'm redirecting my impulses towards learning math

[steep mountain]

well im sure things come more naturally to terrance tao than to me when studying analysis but thats just a depressing way to move forward and enjoy things in life

[sick burrow]

My take on talent in general is that the most significant "innate gift" for a pursuit you can have is enjoying it

[steep mountain]

i think its very natural to feel this way and i feel this way too sometimes but you have to realize that there is more important things to focus on for your own well being

if you feel sad by someone being better than you math is not it
there is people here in hs who are already better than me lol

[sick burrow]

The way to get good at anything is by practicing it a lot, and the main obstacle in the way of practice is it takes a lot of time and it's tedious as fuck if you don't enjoy the thing you're practicing

[steep mountain]

just find what you enjoy about math and focus on that
thats how you build passion about it

and as he mentioned

[cyan goblet]

so in my experience the environment of "i need to match the super genius kids around me" tends to lean someone towards the "nonstop study to catch up" kinda thing

[steep mountain]

practice makes perfect

[cyan goblet]

which then is flawed because

when you nonstop study, your efficiency actually goes 📉

[ember fog]

Fuck

[cyan goblet]

so then even when you indulge in something interesting, you have that same pattern

so take breaks and explore other hobbies too

[ember fog]

I've spent my whole life in that latter group :')

[cyan goblet]

for example, i like to do gardening

[sick burrow]

imo the main thing that the "talented" people have is they really really like the thing they're doing

So they spend a lot of time on it

[cyan goblet]

so when i've studied for a while i'll just go outside and touch some dirt or someting

[sick burrow]

And get a lot of value out of that time since they really enjoy it

[cyan goblet]

so you can focus on math if you'd like, but be sure to enjoy a lot of other things too

[steep mountain]

ye he is right
if you're passionate about something you'll probably do better than most people 95% of the time lol

[cyan goblet]

that way youll develop a healthy relationship with math, with your work ethic, and with yourself

[sick burrow]

And that time commitment is what ultimately matters more than any "innate ability"

So the takeaway here

[steep mountain]

i made that number up but you get the point

[ember fog]

I want to fall in love with math but it feels like I've gotten on the wrong foot and have a wrong view on it, hence the fear

[sick burrow]

Is that if you care about being good at something enough to put the time it, you will get good at it

[cyan goblet]

https://www.youtube.com/c/3blue1brown

rediscover

[ember fog]

Yes i love his channel

[cyan goblet]

3b1b does a good job at illustrating the beauty of math

[steep mountain]

takeaway is do it with passion or not at all

[ember fog]

I'm really inspired by him, he's the reason why i want to relearn and confront my math anxiety

[cyan goblet]

dope, then the next step would be to slowly start introducing yourself to new math concepts

or relearning ones that you may not have a clear understanding of

[sick burrow]

Or to put it another way, the mentality of "I want to do X but I don't have the talent for it" doesn't make sense because wanting to do the thing is what talent is primarily made of

[cyan goblet]

i am being extremely realistic

by saying that you cannot achieve perfection through nonstop study

and will instead hit burnout

[sick burrow]

I think anyone can be really really good at almost anything if they put the time in to practice

[cyan goblet]

time commitment yes, nonstop commitment no

[ember fog]

That's kinda what I'm scared of finding out, what if math isn't the right fit for me

[steep mountain]

what most people seem to forget about einstien and newton is that

[cyan goblet]

and im not saying this person has to go and become the next einstein or newton

[ember fog]

Me giving 100% into doing it

[steep mountain]

they really loved physics lol

[cyan goblet]

im giving them a chance to just discover something new

[cyan goblet]

i mean, simplest answer is jus that it's not

[steep mountain]

there is a reason they invest that much time into it

[cyan goblet]

and there's a lot of things outside of math that may be something you love

[sick burrow]

Some people have insane gifts, but the only thing that kind of gift lets you do that you can't without it is become one of the best in the world

[cyan goblet]

and it won't be a matter of "you weren't born with great math skills", it's just that math isn't a great fit for you

[sick burrow]

With the right amount of luck

[cyan goblet]

and that's okay

[steep mountain]

i'd like to believe its just that they are "born different" but they simply had passion and some talent and they worked hard to improve upon it

[cyan goblet]

i would love to do wildlife conservation but i tried volunteering at conservation centers and it wasn't really my thing

so if you've got the free time, go out and explore math

and if you like it, great

and if you dont, it is what it is

if you decide that math isnt for you, you will walk away with a valuable lesson

[sick burrow]

There's no point worrying you're not Euler if you aren't aiming to be Euler

[cyan goblet]

you won't have "wasted your time" pursuing something you wanted to get better at only to discover you dont like it

you will have instead learnt the lesson that sometimes you have to test the waters before you dive into them

[sick burrow]

The takeaway here

Is that there's no sense in worrying you're not "good enough"

[steep mountain]

the only reason you need to do math is to love math

[sick burrow]

Because you are good enough at math to be however good you want to be

[ember fog]

What if I learn to love it so incredibly much but my skills don't fit to do it

[sick burrow]

I'm saying that is nonsense

[cyan goblet]

^

[steep mountain]

i 2nd that

[cyan goblet]

there are plenty of ways to reach a goal if you truly love it

kinda why this server exists imo

[ember fog]

That's reassuring

[sick burrow]

Loving it so incredibly much is what it means for your skills to fit to it

[cyan goblet]

https://www.youtube.com/watch?v=byNaO_zn2fI

this is a nice little video

[ember fog]

6 hours

[cyan goblet]

10 minutes long, and pretty good

[sick burrow]

I wish I could study for 6 hours

[ember fog]

I can do all nighters when I really need to but i know that's not healthy

[steep mountain]

bunny i walked into uni with barely any calculus knowledge and no proof writing skill beyond hs geometry or anything beyond hs really and i can tell you that im in my 2nd year rn and i am doing really well in very hard subjects because i love doing it lol

[ember fog]

Oh oops i havent tried doing math for 6 hours but in general for school i do 6 hours of self study

[cyan goblet]

adding onto what james said

[sick burrow]

What are you taking rn james ash

[cyan goblet]

over 50% of incoming students to harvard's CS department walk in with no prior experience of programming

actually i think it's greater than 50

[steep mountain]

metric spaces ,bilinear algebra,probability,calc 3, intro graph theory, odes

[sick burrow]

Ok but also Harvard 🤮

[steep mountain]

yes in 1 sem

[sick burrow]

Holy

Is this the not liberal arts college experience

I've never taken more than 2 math classes in a semester

[steep mountain]

lmfao its not pleasant but i manage

[charred mortar]

Yeah that is fast

I feel like that’s a fairly universal experience tbh

The more in-depth you go the more you realise how much there is to really know

[steep mountain]

indeed

gotta love the aha moments

[deep mango]

[ember fog]

Thank you everyone, truly. I'll keep trying. I hope to fall in love with math as I learn more about it.

[deep mango]

the best part about math is the grueling parts

when i'm having fun, something's wrong

[stone valve]

does anyone have any good resources on 3d vectors

coz im struggling a bit to learn it properly

a yt playlist would be v helpful

[cyan goblet]

https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function

video library talking about vectors and matricies in 3d space

• some other stuff

[deep mango]

computations build character

[stone valve]

any other's that directly focus on it?

[cyan goblet]

not sure if know of any resources that explicitly focus on 3d vectors

[stone valve]

oh

[cyan goblet]

perhaps some linalg books?

#books-old

[errant furnace]

[stone valve]

hm ok

??

[neat lintel]

[wise vigil]

What why is that so true lol!

[wise vigil]

Almost as expected

[daring zinc]

anyone here bilingual?

[devout nacelle]

Yes

[surreal sapphire]

not being native english speaker moment

[devout nacelle]

I don't really know if I qualify as bilingual

[ripe wasp]

yeah

[devout nacelle]

Since I still have to use very limited amount of English off screen

[surreal sapphire]

hm?

[devout nacelle]

But my primary forum for interactions has been screen for a long time

I mean

[surreal sapphire]

bilingual means you speak two languages

[devout nacelle]

I don't really "speak" English a lot

[surreal sapphire]

certainly you are able to

[devout nacelle]

Verbally

I'm definitely okay with text

[surreal sapphire]

ok, i have no idea what it means to 'speak' a language

[devout nacelle]

Yeah at least for my CV I can pretend I'm proficient with English

[surreal sapphire]

when the interviewer switches to english mid conversation

[devout nacelle]

Interviews for internships have been an actual metric for me to gauge how far I can hold a conversation in English

[surreal sapphire]

its really weird for me to talk english with other germans

im rather comfortable talking english but i never know how much they understand

[devout nacelle]

Aah

[surreal sapphire]

it was super weird in school

[devout nacelle]

I just start supersonic rapping in English

With the onus to understand on the listener

[surreal sapphire]

time to go to the US for a year

[devout nacelle]

[toxic schooner]

[devout nacelle]

:

[toxic schooner]

manan no

fuck off

😭

tho i would say u are ok at speaking in english

[devout nacelle]

"okay" might be a fair description, yeah

I still feel some nervousness meddles with what comes out of my mouth

[toxic schooner]

its pretty diff with me

i start speaking and then i start stuttering coz my mouth cant keep up with my head

[surreal sapphire]

you will learn quickly once english is the only way to communicate with people around you

[toxic schooner]

and then i get nervous

i can usuallly overcome it, but at times it becomes

[toxic schooner]

true

[surreal sapphire]

my final highschool year we visited london and some guy in my class was robbed

and unable to talk with police or wtv

so i had to do it

[toxic schooner]

Ooo

[devout nacelle]

Yeah, that's true

[toxic schooner]

talking with natives is a good way to learn

[devout nacelle]

[surreal sapphire]

ye, there were almost no natives in london

[devout nacelle]

Lmao

[surreal sapphire]

i asked two shop owners for the phone number of the police

they did not know

[devout nacelle]

[surreal sapphire]

i asked a "policeman" giving tickets to cars

he gave me the wrong number

[devout nacelle]

Bruh

[surreal sapphire]

so yeah, this was quite the odyssee

[devout nacelle]

[toxic schooner]

lmao

[surreal sapphire]

anyways, in the end we had to visit the embassy

and this dude had to finally talk with someone

and he talked in really not great english

and the other guy noticed and told him to just talk german its fine

[toxic schooner]

[surreal sapphire]

moral of the story: look after your belongings in foreign cities

and learn english

[toxic schooner]

i look after them in my own home

[toxic schooner]

and i think i know english

will be good to go

[devout nacelle]

😭

[devout nacelle]

Can you get by with German officials talking in English?

[surreal sapphire]

no idea

my guess would be no

if you are nice you can probably get hold of one who speaks english well enough

there are lots of people in germany not being able to speak (any) german

problem is they dont speak english either

[velvet dagger]

What do they speak?

[neat lintel]

russian ?

some arabic speaking minority too afaik

[flat harbor]

wendish

[velvet dagger]

Makes sense

[flat harbor]

tongue of the wends

[velvet dagger]

Actually... idk if this is in Germany or Austria

But apparently there's a rarely spoken language called kandis (spelling?)

Oh I think it ends with eszett

kandiß

[flat harbor]

whats

[velvet dagger]

And it's in Austria not Germany

@flat harbor hmm?

[neat lintel]

why are you reacting with random emotes

[velvet dagger]

I don't know

Shawshank do you know of that language?

[neat lintel]

i dont

[velvet dagger]

You seem... more familiar than my American ass

[flat harbor]

then you should ask what kandis is

[velvet dagger]

Ah

[flat harbor]

go ahead

[velvet dagger]

blo what are you doing

I don't get it

Anyway Shawshank wanna know about it?

Bruh what's with this memeing

#chill

[neat lintel]

about kandiß ?

[velvet dagger]

Yea

[neat lintel]

sure

[velvet dagger]

Kandiß dick fit in yo mouth

I'm sorry

[flat harbor]

yooooooo

[velvet dagger]

Witness the master at work

[flat harbor]

immense pain in my lower intestines

[velvet dagger]

Anyway my degeneracy aside what's up? I haven't seen you around the server much before Shawshank

What are you interested in?

[neat lintel]

I am new here yes, i came here initially to get help with finite automata concepts here

[velvet dagger]

Oh nice

I should know more about mathematical CS tbh

[neat lintel]

yes im interested in CS too, low-level concepts

[toxic schooner]

good thing i didnt ask about it and read the messages below

[neat lintel]

not strictly CS actually

more on the applied side

[velvet dagger]

Shyshu you actually inspired one of my better jokes

You remember that one time we were having the convo about Jotaro?

[toxic schooner]

the gnome one?

[velvet dagger]

Not a DN joke I mean like

The antagonist in Jojo

Loooong time ago

[toxic schooner]

i dont really remember no

[velvet dagger]

Oh

[toxic schooner]

my memory is filled with random ass chemical equations i cant remember stuff well

[velvet dagger]

Well you know that scene where he's walking to that other guy?

I forget his name

But he's like oh come as close as you want

[neat lintel]

i randomly asked here about anyone knowing haskell, someone pointed towards mniip and i saw his github and now I randomly ask about binary exploitation stuff from him in #chill

[velvet dagger]

You're the one who showed me that scene

[toxic schooner]

i havent seen jojo or any anime other than dr stone for that matter

are u confusing me for someone else

[velvet dagger]

I mean neither have I but that famous scene with that one guy

Anyway so

[toxic schooner]

[velvet dagger]

It's a 3 part joke

First you ask them to translate "God" into Italian

[surreal sapphire]

there are lots of turkish speakers and now also arabic

[velvet dagger]

The goal is to somehow build up to a convo about how French numbering makes literally no sense

[neat lintel]

sababa

[surreal sapphire]

there is a german-russian minority too but its not that many

[velvet dagger]

ANd get them to say "dix neuf" (the number 19) in French

[toxic schooner]

hmmmmm
that does sound somewhat familiar to me actually

[velvet dagger]

Aka deez nuts

[toxic schooner]

[velvet dagger]

But you have to build up to it so it's not sus

So here's how it would look like, let's say I'm the one getting you here

Shyshu how do you say "God" in Italian?

[toxic schooner]

dio

[velvet dagger]

Dio like deez nuts

[toxic schooner]

[velvet dagger]

FUCKING SUBVERTED LET'S GO

[toxic schooner]

thats really nice lmao

[neat lintel]

its borderline offensive

[toxic schooner]

these are offensive internet memes, yeah

[velvet dagger]

Hmm, inappropriate I'll grant, I hesitate to say offensive

But wow I had to work really hard for that one there

[toxic schooner]

i knew u were building up to a deez nutz joke the moment u said god in italian

[velvet dagger]

Tru hence why I was hoping that you'd think it'd take longer by telling you the punchline

Reverse reverse reverse psychology

[toxic schooner]

i chose to go for it, coz i would feel bad for not letting u have it

[toxic schooner]

[plush cloud]

i have kinda dumb question but want to see ur answers

not homework related

but math related

if there is infinite numbers between 0 and 1, how are we able to reach number 1? when all decimal places are resetted to 0

like numbers would be 0.xxxx where x /= 0, but then all xs will become 0 when it reaches 1?

that means the infinity numbers between 0-1 came to an end?

[charred mortar]

We can’t really “reach” 2 in that sense

There’s no notion of “the next number” once we introduce decimals, as far as I know

[plush cloud]

i meant 1 instead of 2 sry

[flat harbor]

real numbers dont rly exist

[plush cloud]

bruh wat

[devout nacelle]

Reach in what sense?

I can write 1 and "reach" 1 in a sense

You most certainly can't start "counting" from 0 and reach 1, enumerating each real number in between

[plush cloud]

in other words, how does number 1 exists when its infinitely numbers away from 0

[surreal sapphire]

i dont see how this is an obstruction

you should be more worried about the fact that all the numbers between 0 and 1 exist

[plush cloud]

whats the first real number greater than zero

[surreal sapphire]

first?

[plush cloud]

the first real number to satisfy > 0 condition

[surreal sapphire]

there is none

[devout nacelle]

There is no such real number

Suppose x were to be such a real number

Then x/2 would be less than x and still greater than 0

Contradicting the fact that x was the "first" such number

[plush cloud]

im so confused

[devout nacelle]

It's okay, the idea can take some time to absorb

If you like to think geometrically

Your "first" real number would come to the right of 0 on the number line, right?

Now since these two points are not one and the same, there's some distance between them

[plush cloud]

i understand this. but i think number 1 depends on 0 somehow

[devout nacelle]

Pick any point lying on this segment

And you now have a smaller number

[devout nacelle]

Depend how?

[ripe wasp]

it basically means for any number you choose as close to 0 as you want, you can always choose a number closer to 0

[plush cloud]

conceptually

[flat harbor]

real numbers are supposed to not make sense if u try to count them

[plush cloud]

i think its existence cannot be understood without understanding zero

[flat harbor]

thats why theyre literally called uncountable

[long matrix]

someone drop the tortoise paradox here

or was it hercules

[plush cloud]

😭

[flat harbor]

bb ub but if the turtle can always b bhh b then how can hercules win ?.?/??

[surreal sapphire]

the tortoise paradox is not about uncountability

[devout nacelle]

I can assure you the way real numbers are "constructed" is consistent and devoid of paradoxes as far as we know, but it takes some technical machinery to understand how they come into being from simpler numbers (rationals).

[flat harbor]

its abt misinterpreting the idea of tasks

[long matrix]

yh

[surreal sapphire]

the error is assuming that a sum of infinitely many numbers is necessarily infinite

[long matrix]

the question seems less about uncountability

and more about how an infinite number of points have finite measure

[abstract mason]

@rationals have that property too right?

[surreal sapphire]

there isnt really a question here tbh

[abstract mason]

oops. newbie here. i meant to sddress sean

[devout nacelle]

I think I can vaguely sense the problem here but can't give an explanation unless Lam is familiar with limits

[flat harbor]

the concept of Convergent Sequences did not appeal to the common greek

[long matrix]

that paradox would probably

[devout nacelle]

Maybe Lam wants to think about discrete jumps starting from 0 that will eventually lead to 1

[surreal sapphire]

there is some problem, but i think lam just needs to think a bit more, identify their issue and come back then

[plush cloud]

i know some of it

[long matrix]

clear some things up

[surreal sapphire]

people unloading their knowledge will be semi-helpful

[flat harbor]

if smth just doesnt feel right and is very confusing

[devout nacelle]

Yeah, fair enough

[flat harbor]

smtimes helps to just put it on the backburner

[devout nacelle]

Throwback to me realising Cantor's proof of uncountability of reals actually makes sense months after seeing it for the first time

[flat harbor]

i had a crisis abt epdel the first time i learned it for abt a month

came back to it after a year and it was a lot clearer

bc of the simple fact that the more ukno the more u see

[devout nacelle]

My epdel crisis will never end

[flat harbor]

it will end once u actly commit to finishing ranal

stop being so math promiscuous

[plush cloud]

is 0 a part of 1?

[ripe wasp]

wdym

[devout nacelle]

"part"?

[abstract mason]

intersecting conversation. so there is not a way to explain this without getting deeper in more advanced math? btw hello, i just joined and know some calculus and some discrete math.

interesting

[devout nacelle]

Hello K-Son!

[flat harbor]

hello ❤️

[plush cloud]

can number 1 exists without 0s? for me i think 1 is the sum of zeros like 0.x + 0.y = 1

[flat harbor]

ure not talking in a way that makes sense

[devout nacelle]

Exist in what sense?

[plush cloud]

idk how to explain:((

[devout nacelle]

I can declare a set {1} and say 1 exists (foundations cranks please steer clear of this remark)

[flat harbor]

read some stuff on how the reals are defined

and try to pick up how math ppl express it

[devout nacelle]

holds the urge to rec Tao's Analysis 1

[flat harbor]

mana

i will commit extrajudicial violence against u

[surreal sapphire]

just historically the invention of 0 comes (way) after the invention of 1

the number 1 is just some abstraction of a collection of 1 thing

[devout nacelle]

Good point

[flat harbor]

u just need to broaden ur idea of what "number" means

[plush cloud]

alright my head is heated, that’s enough math for today bye!

[flat harbor]

finally

[flat harbor]

take some rest pal

[toxic schooner]

[bright hill]

you mean forgetting theorems is normal?

fuck that actually makes sense

[frozen merlin]

while you're learning them? definitely

(for me)

[somber abyss]

examinations provide formula booklet for a reason

u just need to know how to apply a theorem in our school, they give u the formula for it in a formula booklet

[frozen merlin]

nice username

[somber abyss]

thx

[frozen merlin]

if you're doing a maths course then you'll probably want to know the exact statements + proofs of the important results for the exam, but while you're learning it's very normal to forget these things

[bright hill]

do you think knowing how to replicate those proofs correctly is important for a self learner?

[frozen merlin]

depends on the theorems, sometimes a proof is really central to the idea

also depends on if you're learning maths for its own sake, or to apply to something like engineering

[bright hill]

I see

thanks for the insight!

[modest rune]

It is ultimately most important to understand the big ideas behind these proofs rather than the details

The big ideas might inspire you when it comes to proving other things, and the details you can always look up

But if you don’t know the big ideas, you might not even think to look at them

[hollow flame]

ive always wondered... properties that are inductively demonstrated to be true in finite cases, why does that not necessarily transfer to infinite cases?

[ancient flame]

because infinity behaves weirdly

[hollow flame]

i can maybe understand for uncountable infinity

but like..
if you have a normal number in a given base, right? youre guaranteed to find every sequence of finite length somewhere in its decimal expansion

[modest rune]

iirc normal is about the frequency with which the digits appear

[devout nacelle]

Objects that are not finite often have "infinite" room to wiggle around, and that dramatically changes the applicability of results.

[modest rune]

not the guarantee that every finite pattern shows up

you can have very regular normal numbers in that case

am i misremembering

[hollow flame]

normal and transfinite then

not transfinite

[modest rune]

Transfinite?

[hollow flame]

transcendental

like, what we assume to be true of pi

[modest rune]

I don't think that is strong enough to guarantee what you want

[hollow flame]

because yeah if thats the definition of normal then some fractions are normal

"If a number is normal, no finite combination of digits of a given length occurs more frequently than any other combination of the same length"

from wikipedia

[tiny marten]

normality is an interesting property, i usually think of it dynamically

[toxic schooner]

[hollow flame]

thats literally the definition

maybe this was a bad example lol its the first one i thought of

how about like literally anything from group theory

like idk fundamental theorem of abelian groups

not that you can do that inductively

[modest rune]

Every finite number is finite. Proof: Let n be finite. Then n+1 is finite as adding 1 to a finite number will still be finite. Thus every infinite cardinality is finite.

[hollow flame]

i guess

[modest rune]

Let A be a finite set. Then A has no proper subset of cardinality A. Proof: supposing this is true for sets of cardinality n, assume a set B of cardinality n+1 has a proper subset S of cardinality n+1. Then we may remove a point from this subset from B, and we will have a set B-x with a subset S-x both of cardinality n and with S-x proper

Therefore no infinite set has a proper subset of the same cardinality (which is a contradiction)

[hollow flame]

i mean at that point you may as well just appeal to like

zfc

[modest rune]

?

those are both counterexamples

they aren't even that complicated

If you want the real reason this works

[hollow flame]

that you cant construct a set containing itself as a proper subset, thats a consequence of the literal definition of a set

as distinct from a class

[modest rune]

That is not what I did

In ZFC every infinite set has a proper subset of the same cardinality

For example, you can remove 1 from the natural numbers

you still have a countable subset

but its proper

[hollow flame]

oh i misread

[modest rune]

The real reason this does not work is that an inductive proof gives you an algorithm to get a proof of the fact for any fixed n by just starting at the base case proof and working up

This terminates and therefore gives you the desired proof

There is a process called transfinite induction that can be used but it requires an extra step to get around this issue

[hollow flame]

makes sense

i think maybe invoking like zenos paradox makes it clearer

like i wouldnt say that it terminates

[modest rune]

terminates was a bad word to use, the point is you have some way to "get at" each n

whereas you can't "get at" the infinite case

[hollow flame]

but that an infinite number of finite steps will not "reach infinity"

you need additional machinery, like a limit or an infinite set

[modest rune]

that is essentially how the transfinite process works

You have two things to show, namely that if the statements holds for a then it holds for a+1, and if it holds for all such a then it holds in the limit. then you can reach all the desired ordinals

[alpine kindle]

you can reach every ordinal

i think

[hollow flame]

what about the smallest ordinal that is not the limit of a countable collection of ordinals

[alpine kindle]

isn't that omega?

because N isn't finite

[hollow flame]

oh right

how about countable

[alpine kindle]

uh

hm

[untold sapphire]

this would be the first uncountable ordinal

omega_1

[hollow flame]

i guess it would be the supremum of a collection of countable ordinals

i guess im imagining that there must be some level where transfinite induction would break down because you need a meta "all such a" sort of thing

but not necessarily, if its general enough

[modest rune]

every ordinal is either a limit or successor

[plush venture]

Nice dog

[untold sapphire]

yep

this collection itself is necessarily uncountable btw

[hollow flame]

right

[untold sapphire]

of course one doesn't have to choose a countable increasing sequence of countable ordinals to take the supremum, one could just take the set of all countable ordinals and take its supremum, it's not necessary to "get there" with a countable sequence

[tiny marten]

the magic of the supremum

[hollow flame]

but you do need a set

[untold sapphire]

ya

[hollow flame]

so you couldnt take the supremum of all ordinals

[untold sapphire]

no way jose

[hollow flame]

which i guess is obvious lol

[untold sapphire]

Well you can read this the other way too

your argument proves that the ordinals don't form a set

because suppose they were a set; then you could take the supremum, and this would be an ordinal greater than all ordinals in the set, a contradiction

[tiny marten]

$sup_{\omega}{\text{all ordinals }\omega}=X$

[fathom swallow]

LoLDongs

[tiny marten]

boom

got any other problems for me

just solve for x

something something, supremums always exist

[hollow flame]

oh thats why i said you cant take the supremum

because the ordinals dont constitute a set

how else would you arrive at "you cant take sup(all ordinals)"

[untold sapphire]

Well, what I think you're saying is

1. The ordinals don't constitute a set.
2. Therefore, it doesn't necessarily make sense to take the supremum of the class of all ordinals.
   And what I'm saying is:
   Hmm, I'm not convinced; how do you know that the ordinals don't constitute a set?
   Well, you can prove it by running the argument in the converse direction.
3. If a collection of ordinals is a set, it has a supremum, which is also an ordinal.
4. But the collection of all ordinals has no supremum. Ergo, it is not a set.

[tiny marten]

[hollow flame]

[untold sapphire]

(I guess the larger point here is that I don't know how to prove "the ordinals don't constitute a set" without assuming "every set of ordinals has a supremum", but I do know how to prove "every set of ordinals has a supremum" without assuming "the ordinals don't constitute a set")

[hollow flame]

no cap

[sick burrow]

I mean the set of all ordinals would itself be an ordinal

Since that's how ordinals are defined

But then it wouldn't contain itself

[untold sapphire]

Sure, one might assume that for the sake of a contradiction.

(Here I am assuming that "being a set" is part of the definition of an ordinal.)

[sick burrow]

I mean is that not just a proof that there is no set of all ordinals

I mean also if there was then couldn't you use that to get $ZFC \vDash ZFC$

[untold sapphire]

Yeah, you're right.

[cinder flume]

I got to the conversation just right now

[fathom swallow]

Worst Geometer NA

[untold sapphire]

I don't think I know what you're trying to say here.

[modest rune]

So the issue I think is that if one constructs the ordinals in a reasonable way (say, VN ordinals) then you observe that you can take any set of ordinals and union them to get a new ordinal that is no smaller. You also observe that the successor operation is necessarily larger. Then you assume you could take the union of all ordinals. Then this is a new ordinal, larger than all others. But that ordinal +1 is larger, which is a contradiction

[cinder flume]

Is the question to prove that there is no universal orjinalini set?

[hollow flame]

something something too large to be a set

[cinder flume]

Ordinal

[untold sapphire]

You can edit your posts nevzat. Haha.

[sick burrow]

Well there's a proof that if k is an ordinal then the collection of all sets of cardinality less than k is a set

iirc

[untold sapphire]

Yes, this is known.

[cinder flume]

Isnt this burali forti paradox that you guys are talking about

[sick burrow]

So if K was the largest ordinal then that would give you the set of all sets

[cinder flume]

Again, I got to the convo late

[sick burrow]

Hence set model of ZFC within ZFC

[untold sapphire]

Yes, it's closely related to that nevzat, but each person here is I think bringing their own comments and questions, there's no one single issue to be resolved

[sick burrow]

Or really just whatever contradiction you want to derive from the set of all sets

[untold sapphire]

Hahaha. This is the strangest proof I've heard that the class of ordinals is not a set but I guess it works, in theory.

Assuming one takes Godel's incompleteness theorem and the apparatus of model theory for granted

[sick burrow]

Yeah

There are much easier ways to form a contradiction from the set of all sets

Just comprehension into Russell's Paradox for example

[hollow flame]

i was about to say

you dont need to assume godel

[sick burrow]

The godel thing is somewhat intuitive to me though

[untold sapphire]

Sure, whatever floats your boat

[sick burrow]

Because of the whole inaccessible cardinal giving you a model of ZFC thing

[hollow flame]

wait back to the sup thing how would you show that the class of all ordinals does not have a supremum

[sick burrow]

Add 1

[hollow flame]

would it just be like
because the sup would have to be in the set?

[untold sapphire]

Yeah, basically. Or sup+1, whatever it is to make the proof work

[plush venture]

Nice dog

[untold sapphire]

Far out, man. Thank you.

Her name is Summer.

[tiny marten]

summer is a good pooch

[neat lintel]

[limber oracle]

who's more of a daddy

newton or euler

i say newton but my friend says euler we're in an argument

[static loom]

euler was legitimately a dad, newton never had kids

[limber oracle]

whattt

well imean euler does defo look like a dad

[charred mortar]

Newton was kind of a huge dick from what I’ve read about him

[fair mural]

yeah

[little vine]

Newton said on his deathbed his greatest achievement was dying a virgin