serious-discussion

[winged token]

yes

[tall badge]

ye p much as u say

[tall badge]

itd be nice to show K within P but ye

[winged token]

am I getting the notion across?

oh true

okay so T maps from C[0,1] to C[0,1] but it also has the property that P maps to K

and K is a proper subset of P

😭 got thrown in the deep end of functional analysis and im fightingbro

[tall badge]

whats ur question

[winged token]

nothing i understand now

[arctic plinth]

hi

can someone help me on my calculus subject?

I'm really struggling rn

[honest veldt]

#calculus

or #❓how-to-get-help

[neat lintel]

i need help

[wind nest]

jus be patient

everyone in the help channel is volunteering

[visual hatch]

correct

[rain dome]

I feel that the definition of prime numbers is wrong but because we are so use to thinking in base 10 it might just influence the way we think of primes. So I’d like to argue that 2 is not a prime number because it’s too small. The question is now to make 2 artificially larger by picking a base smaller then the number in question. Using a base I believe of .5 would be sufficient enough to make 2 large enough to show that 2 indeed is not a prime number

I also believe 3 to be too small so I think the first prime number should be 5. What are your thoughts?

[fair mural]

[surreal sapphire]

can you point out where in the definition of prime number the base is mentioned?

[little vine]

A number is the same size no matter what base it's in

Also, why does it matter that 2 is small? Why is 5 large enough?

These numbers are elemental, that's why they are special

Nothing to do with their magnitude

[wispy dune]

its bait

pretty sure thats a copypasta from some crankpost on reddit

[inner finch]

lmfao

i love this

[neat frost]

The definition of prime numbers has nothing to do with the base you’re expressing the number in

[neat lintel]

Knock Knock

[neat frost]

Are you a delivery person?

[neat lintel]

Amoeba is the powerhouse of the cell

[neat frost]

Firstly, no

Secondly, biology

[charred mortar]

ah it's copied from r/numbertheory

[dapper star]

guys

i need a teacher

pls

[charred mortar]

#❓how-to-get-help

[wanton tartan]

Yesterday I saw a mug that said V-F+E=0

Took me a sec but it was incredible

[nimble jetty]

Wait, a base of .5? How would that even work?

[frozen merlin]

I guess abc.xy in binary would be yxc.ba in base .5

[sleek wing]

Base 2 but you reflect everything about the

Wow

I see how it is

[frozen merlin]

too slow? more like wew slow

[neat lintel]

yeah, this is Euler's characteristic. Here equal to 0 instead of classical 2

[toxic schooner]

[little vine]

Omg it's so obvious and I didn't see it

[odd narwhal]

Ohh that's cute

I'd like a mug like that

[toxic schooner]

its obvious?

[odd narwhal]

Specifically, the joke is that a torus has 0 euler characteristic

[toxic schooner]

[neat lintel]

ah. I missed the joke

[little vine]

I JUST UNDERSTOOD THE JOKE

BC THE TORUS IS A MUG

[odd narwhal]

Yes

It's a genus 1 surface

[toxic schooner]

1 DONUT= 1 COFFIS CUP

[toxic schooner]

that just means it has one "hole" right?

[odd narwhal]

Well not exactly

I mean, roughly yes

[toxic schooner]

i was told that genus of any surface is kinda related to the number of holes it has

[fair mural]

i watched that one vsauce video am i a topology expert yet

[odd narwhal]

well, that's an intuitive description of that

but it's not exactly 100% when you move to more abstract spaces

[toxic schooner]

i see

[rotund aspen]

What will be (a+b)^2

[modest rune]

It’s not compatible with the usual ways a topologist thinks about holes

Arguably the torus has more than one alresdy

But for a surface this definition of # of holes is reasonable

[rotund aspen]

I can give the explanation.

[toxic schooner]

ic

[rotund aspen]

It is the first identity of algebraic expression
(A+b)^2 = a^2 + 2ab + b^2
Will be the answer.

[leaden torrent]

thanks for interrupting the convo with random high school algebra facts.

where would we be without you?

[rotund aspen]

Oh sorry
By the way what was going on I'm new.

[fair mural]

the funny thing is that you didn’t even give an explanation

[fair mural]

[rotund aspen]

It has no explanation as it is a formulae

[modest rune]

That is not true lol

[rotund aspen]

Ok mate, sorry for the interruption.

[leaden torrent]

(a+b)² = (a+b)(a+b) = a(a+b) + b(a+b) = a² + ab + ba + b² = a² + 2ab + b²

its just applying distributivity twice.

[leaden torrent]

the steps shown are literally exactly what i did, yes.

[rotund aspen]

Yes mate exactly correct

[leaden torrent]

???

i am going to have an aneurysm

[rotund aspen]

Ok

Bye

[modest rune]

you know i dont get to see you talk about math much nami but you really are good

[leaden torrent]

i know, my skills are unmatched.

[fair mural]

praise nami for explaining hs math

[neat frost]

Hs math?

[neat lintel]

[little vine]

Way to kill their young enthusiasm

[neat lintel]

Unbelievable

Let's ban @neat frost

[fair mural]

you should know not to interrupt though

it’s common sense

[little vine]

It's discord

[neat lintel]

No it's not

[neat frost]

Bruh who even are you?

[neat lintel]

Can we all agree slurp is a bitch

[neat frost]

[fair mural]

why are you being so rude

[neat lintel]

I'm rude? Slurp is rude

[neat frost]

[neat lintel]

[leaden torrent]

knock it off @neat lintel

and dont random ping people

[rotund aspen]

I got it now that

You are 2nd Einstein

[fair mural]

[neat frost]

Nono it’s fine I know him

[neat lintel]

?

[neat frost]

He’s actually sitting next to me rn

[leaden torrent]

if you dont want to cause misconception, then dont say things like "who are you"

anyway please go to #chill to shitpost

#❓how-to-get-help

[fair mural]

#❓how-to-get-help

darn it

[median zinc]

It's actually ban because quiz

¯_(ツ)_/¯

[neat frost]

Yeah I understand, and I apologize for that

[leaden torrent]

wait is it just me or is that question terribly worded

i dont think it can even be solved

[stable ginkgo]

You get help if youre in a quiz

Lol

[median zinc]

uhh what

[neat lintel]

https://youtu.be/-ZE2Iv-8tsA

This is cool

[sick burrow]

This channel is peak #chill rn

[rancid skiff]

anyone got a chegg account i can use for a question please

[deep mango]

[neat lintel]

just wondering can i go for math after studying engineering in some other country, but they take me not based on my HS record

[jade crane]

When is winds of winter gonna come out

Been waiting since middle school for the book to come out but I guess never

[cyan lake]

Yo

[real sigil]

Hey

[jade crane]

Hello Kotoboki

[sick burrow]

why

is Windows so insecure

like why is it

that when I install a program

I basically have to give it the permission to take root access if it wants

and then trust that it'll not fuck me over

[steady gate]

Hey guys, do you know a websive for practice problems or having like a practice test?

I tryed seaching in google, sometimes I find good free pdfs of them but not always

[ancient flame]

khan academy

if it's like algebra or calculus or smth

[steady gate]

And something with like, a real life exam?

they are actually pretty good

butI think some pages give you like real ones

[ancient flame]

they have exams goo

too

[steady gate]

Well since their exams are different every try i guess should work

thanks

[limber thunder]

something something bad kernel design use linux

[rotund aspen]

Means?

[fading pulsar]

ayo can someone help me with stats

is anyone here a stats pro

[pearl moth]

it depends on your expectations

[fallen knoll]

i just joined this server and idk where to go. can someone help me w this problem

[odd narwhal]

Welcome! Please take the time to read the #rules and then go to #❓how-to-get-help to find out how to get help

[neat lintel]

Guys no english, philosophy, or politics server is helping, can anyone help with puting this in plain digestable english. The methods of business in colonial days were loose and slack to an inconceivable degree. The movement of industry has been all the time toward promptitude, punctuality, and reliability. It has been attended all the way by lamentations about the good old times; about the decline of small industries; about the lost spirit of comradeship between employer and employee; about the narrowing of the interests of the workman; about his conversion into a machine or into a “ware,” and about industrial war. These lamentations have all had reference to unquestionable phenomena attendant on advancing organization. In all occupations the same movement is discernible in the learned professions, in schools, in trade, commerce, and transportation

[pearl moth]

sounds like engels

[neat lintel]

yea dude, they are giving this shit for SAT now

[pearl moth]

well, to me it's perfectly digestable english

but my undergrad degree is in political science, so really that's like half the articles i read for class for two yeras

[neat lintel]

damn, now i understand. but can you help put this shit into a more simpler worrds, like i don't understand the general jist of this

[pearl moth]

yeah, and then i went to law school 🙂

i think they estimate you read a thousand pages a week in law school

it certainly seemed like it

[neat lintel]

so you write that license agreement that no one reads?

[pearl moth]

no, i left law school in second year for a job offer

[neat lintel]

good

but can ya summarise that for mee

[pearl moth]

i don't really regret that decision

i could, but.... not really wanting to

[neat lintel]

can you just generalize it

[pearl moth]

also, my writing level is about the same as that passage, so it's unlikely you'd be any better off

[neat lintel]

you don't have to write a research paper on that

[pearl moth]

but but but that's the fun part, writing the research paper!

[neat lintel]

like "author says capitalism bad, cause bad things"

[pearl moth]

well, that is a not entierly inaccurate summary

[devout nacelle]

A very rough gist of this is that in an attempt to increase workplace output/efficiency, the loose and slack nature of workplace environment has been gradually replaced by large scale industries that dehumanised the workers and destroyed the employer-employee relationship. The same trends can be seen in fields like education, transportation, etc. too.

[neat lintel]

lmao no dude, the author i actually arguing for capitalism, but it seems as he is also mentioning how people see negative things in it

[pearl moth]

well, i don't have the full context

[neat lintel]

wait, should i post the full paragraph?

[pearl moth]

and @devout nacelle's summary is a good effort that i don't feel like improving on

[neat lintel]

i see his summary, but his summary conflicts with the author... atleast i think, because of the context... maybe

[pearl moth]

the language feels like late 1800s or early 1900s

[neat lintel]

yea because of less context

[pearl moth]

yup, published 1881

[devout nacelle]

I think the author is bringing up these points only to sabotage them, because they start the core with "it has been attended all the way by lamentations about the good old times..."

[neat lintel]

The advance of a new country from the very simplest social coordination up to the highest organization is a most interesting and instructive chance to study the development of the organization. It has of course been attended all the way along by stricter subordination and higher discipline. All organization implies restriction of liberty. The gain of power is won by narrowing individual range. The methods of business in colonial days were loose and slack to an inconceivable degree. The movement of industry has been all the time toward promptitude, punctuality, and reliability. It has been attended all the way by lamentations about the good old times; about the decline of small industries; about the lost spirit of comradeship between employer and employee; about the narrowing of the interests of the workman; about his conversion into a machine or into a “ware,” and about industrial war. These lamentations have all had reference to unquestionable phenomena attendant on advancing organization. In all occupations the same movement is discernible in the learned professions, in schools, in trade, commerce, and transportation. It is to go on faster than ever, now that the continent is filled up by the first superficial layer of population over its whole extent and the intensification of industry has begun. The great inventions both make the intension of the organization possible and make it inevitable, with all its consequences, whatever they may be. I must expect to be told here, according to the current fashions of thinking, that we ought to control the development of the organization. The first instinct of the modern man is to get a law passed to forbid or prevent what, in his wisdom, he disapproves.

[pearl moth]

william graham sumner, "War and Other Essays", 1881

i'm certain i've read some of his stuff for class, his style feels very familiar

[neat lintel]

the author is basically arguing for capitalism, but in someplace says that there is some restriction of liberty there, which can cause some people to look at it negatively, but after all capitalism is what gives us the comfort of life and much more

but i am specially confused about the lamentiations part

[pearl moth]

welcome to late 19th century prosody

[neat lintel]

like what is he trying to say there?

[pearl moth]

you should try reading court opinions from this era, they're interminable with overstuffed language

"verily forsooth, we should proceed forward from this place until we again return to the peace and pleasure of our hearthfires"

which means "let's go home now"

"lamentations" basically means "weeping"

[devout nacelle]

Oh I thought you passed on your subs

I gave up after "universals"

[pearl moth]

the author was using it here to speak belittlingly of the opinion he is deriding

basically, this guy really dislikes engels, and is strawmanning engels' position so he can mock it

[neat lintel]

hmm

wtf is engles

[pearl moth]

it's not a terribly wrong summary of engels, but it's expressed in a very derogatory way that facilitates his goal of mocking socialism

friedrich engels?

[neat lintel]

wait you aren't talking about my passage are you?

[pearl moth]

yes, i am

your passage is by a noted late 19th-century American classical liberal who really hated Marx and Engels

[neat lintel]

its by William Graham Sumner,

[pearl moth]

indeed, i mentioned that

[neat lintel]

youre a search engine, has anybody told you that?

[pearl moth]

you're in my wheelhouse, i was a political science major in college

it's been 25 years, but there's still stuff i remember

and yes, i did some research. google is not hard to use

franklyt i didn't care for this stuff, i was more into election theory, comparative political science, and the interaction between law and politics, but you can't completely ignore these people

[neat lintel]

so basically the author likes capitalism, but he is mentioning the opposing views, and he is stating them, and then mocking them/ arguing against them and later arguing that since capitalism gives us much more good Drip and comfort, so we kinda have to sacrifise some liberty and other things to actually be able to live a good life. but if we want the good old socialism/comunism(idk the diff) then we should be willing to sacrifise some good DRIP and comfort

basically that, the bolded part i mentioned

is him stating the opposing views

[pearl moth]

more or less, yes

[neat lintel]

good, great.

[pearl moth]

he's trying to argue against the Marxian notion that capitalism is exploitative of workers

[neat lintel]

ye kinda looks like it, since i read the whole passage

[pearl moth]

and that instead capitalism is better for workers than the alternatives

[neat lintel]

alright thanks, ill look at it, and further derive answers from that

[pearl moth]

he's one of the many people of this era who had trouble squaring his racist and classist attitudes with the notional belief that "all men are created equal"

[neat lintel]

did he own cotton fields?

[pearl moth]

no, he was a northerner

[neat lintel]

ohh

[pearl moth]

professor at yale

[neat lintel]

thats weird

[pearl moth]

what, that a northerner would be a racist? everyone was a racist in the 1880s

[neat lintel]

ye, youre right

later everyone changed their opnions i guess

the civil war

north and south

[pearl moth]

i'm from indiana. in the 1870s, indiana passed a law that prohibited black people from living in the state without a white sponsor, and encouraged any black people livijng in indiana to move to africa

and indiana was fairly middle of the road for post-bellum politics

there were still sundown towns in indiana and illinois through the 1950s

and those are in the north

[neat lintel]

“The movement of industry has been all the time toward promptitude, punctuality, and reliability.” is this saying that industry is moving forward in the right time towards quality/accuracy and reliability?

[pearl moth]

it means that this author wants you to associate these morally positive qualities with industrialists

also, what exactly is the difference between "promptitude" and "punctuality"?

this article is not intended as an informative essay

[charred mortar]

promptitude sounds like it should be done really quick, compared to the on-time notion of punctuality

[pearl moth]

it is an opinion piece, a persuasive essay that is intended to convince you that free-market capitalism good, socialism bad

[pearl moth]

fair

keep in mind the american obsession with, well, industriousness

that's not new, it goes back to america's calvinist 17th century roots

[neat lintel]

one question has given multiple sentenses and is asking which is supporting capitalism or critisising the opposite views

“Now the intensification of the social organization is what gives us greater social power.” this line clearly states that CAPITALISM GOOD.

[pearl moth]

he's arguing for a well-defined class hierarchy in society

not necessarily for capitalism,. although capitalism tends to foster classism

again, arguing against Marx, who supported a class-free society with no division between workers and owners

[neat lintel]

but the line, "industry has been moving fast in the right time towards quality and improvement" also hints at positives, like it mentions the evolution of industry, but it also had some positive attributes in this

[pearl moth]

again, the purpose of that line is to associate three generally-accepted virtues with "industry"

it's a rhetorical device, not actually a reasoned argument

[neat lintel]

yea but Khan academy says that, “These lines indicate the author’s beliefs regarding the natural evolution of industry and society, but they do not discuss the importance of choice and organization that the author is most concerned with.”

[inner finch]

isnt there a place in africa where they deported slaves once they freed them or something

[pearl moth]

liberia

[neat lintel]

so is this a good argument line? i am trying to pin point what exactly is giving me the right result for the quesion./ like which line provides best evidense

[pearl moth]

i'd argue that it's more in support of the importance of hierarchy, and thus classism. it's not explicitly support for capitalism. it also reveals that the author is fundamentally a psychopolitical conservative, which also explains his disdain for universal suffrage

[neat lintel]

yea i get that

[pearl moth]

i have no idea what the rubric for your assignment is

[inner finch]

being unironically against universal suffrage

[pearl moth]

and i'm drawing in a lot of scholarship to comment on this, including quite a bit of fairly recent work (like Joss and Heidt)

[neat lintel]

but it is asking for best evidence for this question Q10: Based on the passage, it can be inferred that the author would have been most critical of those who.
Correct choice is B: Condemned the capital state.

[pearl moth]

i thin kyuou can support that position, probably, yes

of course as someone who studied law, i can argue the opposite as well 🙂

[neat lintel]

but from both lines i pointed, which one is the best one?

[pearl moth]

dude, i'm totalyl not going to answer that. you have t odecide what you think is the best and then make your case for it.

there's no right or wrong in this area, there's just opinions, and everyone's got at least one

[neat lintel]

SAT is weird, it wants you to pick one even though if you think outside, the answers could be multiple

[neat lintel]

alright

[pearl moth]

is this multiple guess, or a writing assignment?

[neat lintel]

multiple choice

[pearl moth]

ugh, stupid test

[neat lintel]

only a single choice from both those above is right

SAT is different from the normal classroom discussions

[pearl moth]

are we talking the college admission test, or some other thing called "SAT"?

i went to high school in the 1980s, i have no idea what people do now

[neat lintel]

you have to not make any judgements and just pick the one that it is restating or redemonstrating in the passage, but as humans we tend to think more deeply, so we end up making our own judgement calls and pick the wrong chpice

[pearl moth]

i mean my son is in hight school now and my daughter graduated last year but i didn't pay all that much attention

[neat lintel]

yep

Its a waste of time

[pearl moth]

we had questions like that on the LSAT, but the line was much clearer

[neat lintel]

ill tell you literally NO test could actuallllllllllly test for what its trying to test for

[pearl moth]

the test is testing how good you are at being selectively dumb

[neat lintel]

its weird shit

[pearl moth]

honestly, i think it's testing how well yhou've internalized the dogma of Modern American Capitalism

[neat lintel]

selectively dumb?

[pearl moth]

at not questioning capitalist dogma

if you haev anty socialist leanings at all, this passage will piss you off

and i think they're deliberately writing the questions so that those with socialist tendencies will get it wrong

college board is not remotely an apolitical entity

[median zinc]

Nothing is apolitical

[neat lintel]

i did another test other then SAT, and there was an "inteligence section", and the question was, "pick the odd one out" and there were different fruit/vegetable(idk) names, so basically you were supposed to choose the one which was different than the rest. so i choose the one with the different color than the rest, and i got it wrong because we were suposed to choose the one which didn't have seeds while the rest had seeds

NOW HOW TF is that an "INTELIGENCE" Test

[charred mortar]

those intelligence sections are often arbitrary in terms of what they're looking for

[median zinc]

It's a binary classification problem

With multiple models

Pick any

[neat lintel]

what are you talking about?

[pearl moth]

that's a conformity test

it's testing whether you think like the test writer

questions like that punish people who are unusually creative, who are indecisive, or who are neurologically atypical

[median zinc]

That looks like a reasonable thing to me

[neat lintel]

and how is that supposed to help? considering humans are very complex beings, mood, nutrition, environment, sleep, sences and MUCH MORE could steer how a person thinks about something at a given movement. we are not robots. at one place and time i could answer it like the test writer and at another time i could answer differently

[median zinc]

People fear what they do not understand

[pearl moth]

also those who have a greater degree of subject-specific knowledge than the test writer

[median zinc]

The closer you are to a robot, the more use you provide.

The more you operate outside of acceptable parameters, the less useful you are.

[pearl moth]

it's intended to make it harder for socially maladjusted individuals to get into college

[charred mortar]

Yeah it’s not necessarily meant to actually help the person being tested

Or to gauge their actual ability

[pearl moth]

they're to measure your social utility as a worker drone

[neat lintel]

This sounds like some venture capitalist would say about his workers

[median zinc]

They wouldn't say it out loud

[pearl moth]

who do you think the college board works for? it's not you.

[charred mortar]

Just to check whether you can fit certain checkboxes so you can mindlessly slave away in the future

And to not question certain values that are deemed essential

[median zinc]

You can't continue like a slaver in the modern era by using the labels "slaver," "taskmaster" or anything similar

[charred mortar]

True, you need to rebrand

[neat lintel]

the main reason i want to do engineering is because of its creativity

[dawn falcon]

中国共产党万岁！

[neat lintel]

lmao

and i am being tested on not being creative

[pearl moth]

indeed. sucks, doesn't it?

think outside the box, but not too far outside the box, please.

hell, i'm a cynic, you should ignore me and just be the best version of yourself you can

[neat lintel]

i do see that but i feel like i have already figured out many mental things at my core

[pearl moth]

but, yeah the purpose of admissions tests is to predict how likely you are to (a) graduate and (b) be a "good contributor to society" after graduation, so that admission slots are not wasted on people who won't go on to increase profitability for the corporations that will own them after graduation

[neat lintel]

like now i am more relaxed, now all i need is action. to bring my actions on the same wavelength as my beliefs and goals

[neat lintel]

but whatever, I got to get into college, experience shit, work on things I am passionated about

work isn't bad, all you need is a balance in life. balance is literally everything.

not too salty, not too sweet

it often gives me a chuckle, when people argue if comunism, socialism, or capitalism or blah blah blah is good for society. i don't think there is any right or wrong thing, just find the right balance, and everything will workout

like have free health care to some extent while letting people own property

[pearl moth]

i won't disagree with that

but i'm a pragmatic liberal, not a ideologically-motivated radical

[neat lintel]

Speaking of being the best version of yourself, i have this on my wall

[pearl moth]

snrk

[neat lintel]

whats snrk

[pearl moth]

onomatopoeia

[neat lintel]

okay now wtf

this is it i think

[neat lintel]

Yes

[neat lintel]

The beta/alpha male thing came from a study on wolves, the author of which later retracted the claim.
Just another misunderstanding

[neat lintel]

yea but i am talking in a meme sense

[median zinc]

Where my gamma males

or eta males

[neat lintel]

i only got so much wall space

[neat lintel]

I'm not fluent enough in memery

[inner finch]

me when the alif male

[neat lintel]

well, sometimes memes do have something deeper in them if you look for it, like look at giga chad, as 'Know your meme' youtuber beautifully put it, "...but what makes giga chad real to us is what he symbolizes, a man that is in complete harmony with himself and the world around him."

and i guess don't be alpha because it will get into your ego, don't be a beta because it will give you an inferiority complex. just try to be the best version you can

[neat lintel]

Something like alpha/beta male most likely doesn't exist

But I agree with the message, don't try to tell yourself you're one of those. Well, this applies to anything, really

Too much sense of identity and you become delusional

[neat lintel]

yea because sometimes we get too lost into being "something" that you loose your core values and beliefs. you loose who you are

both of us came to the same conclusion

great

Yep.

[neat lintel]

btw it has actually happened to me before that I lost who I was. but thankfully I have recovered.

People learn through their mistakes

Good job on recovering

yea, but one thing i hate is when people try to engage/do something but when it fails or they don't like that thing anymore, they think they wasted their time

everything is a learning opportunity, one thing leads to another, like a domino

well, now you know you don't like that thing

Sometimes it really is a waste of time

It doesn't matter if it's already done though

[neat lintel]

fine, with somethings I can agree, but now you know something you didn't. and if you had not done it, you would have been regretting

[frail sail]

Bro I don’t understand this shit….why doesn’t the kinetic energy of gas molecules not depend on their MASS!? Like how can it only depend upon temperature when temperature itself doesn’t even depend on mass!? Please help me understand this I’m going crazy

[neat lintel]

would mass be factored in via the r-value?

[frail sail]

U mean the R =8.31J/mol*K constant?

[neat lintel]

Yeah so operating off the fact that PV=nRT describes many properties of many gasses often, and T should be proportional to kinetic energy of the gas at rest

[frail sail]

Yea but…I still don’t get it on the overall level…like isn’t temperature really a function of velocity and k.e. a function of both mass and velocity?

[neat lintel]

You would likely be better served by a physics helper, consider that n would be proportional to the mass of the system as well

[frail sail]

Hmm I do understand it now a little bit…but it’s still hard to get a complete picture…

I mean like…in the original equation of k.e.=3RT/2 Na…both R and Na are constants that won’t depend on mass. Then how is any quantity in this formula related to mass itself?

[neat lintel]

n is the number of mols of the substance, and the number of mols of the substance is proportional to mass via molar mass

[frail sail]

But we don’t use n in the k.e. formula right?

[neat lintel]

I'm not a physics expert I would recommend contacting someone in physics, interrogating your book a bit more closely, or conducting an experiment faithful to the values you're trying to predict

[frail sail]

Hmmm..but thanks for the help

[brave hollow]

well in maxwell boltzmann distribution you have the square root of mass term in denominator in r.m.s velocity (which is what you use when talking about average kinetic energy)

[little vine]

Why do we use rms?

I used to know the reason but I forgot

[toxic schooner]

rms as in root mean square speed?

[little vine]

Yeah

[brave hollow]

because we are taking average of kinetic energy so we will use the mean of v^2
but if you want to convert this to velocity in some way you would have to take the root which will give you rms

[sick burrow]

Aleph male

Alpha male Aleph male Aleph_0 male Omega male

QED Alphas are actually Omegas

[ancient flame]

just finished pi day at my school

sold out of pizza, almost sold out of pie, and we pied 4 teachers in the face

fun af

[toxic schooner]

[sly vale]

pi = 3.10 confirmed

[ancient flame]

yes

[empty temple]

Ha!

[empty temple]

Too inaccurate

[sly vale]

Hmm?

[fading pulsar]

Any stats pros here

[strong cipher]

yo

[frail sail]

Yea exactly…but when u substitute Vrms as root(3RT/M) in the k.e.=1/2 m Vrms^2 formula then the mass contribution cancels out
That’s the problem I’m facing that of course mass does contribute in k.e. but in 3/2 RT/Na which quantity is it that will be affected by mass?

[pearl moth]

n

[frail sail]

n?

[pearl moth]

is the quantity affected by mass

[frail sail]

Sorry i confused the formula a bit…I meant 3RT/2Na

[brave hollow]

if you were to magically increase the mass of all the atoms while keeping the same velocities, then the temperature would increase so that is where the change would happen, also every other term except for T is a constant here

[pearl moth]

of course, increasing the mass of the atoms without decreasing their velocities would increase their kinetic energy

the conclusion should be that heavier atoms move more slowly at the same temperature, which is, oddly, true

[long matrix]

inequation 🤔

[neat frost]

[long matrix]

solve this equality

2x = 4

[neat frost]

i disagree

[neat lintel]

-2(i^2)

[sick burrow]

Let $f: \mathbb{R}[x] \to \mathbb{C}^{<\omega}$ be the function that gives the roots of a polynomial over $\mathbb{R}$. Then we have the solutions as follows
\begin{enumerate}
\item $f(2x-8)$
\item $f(-3x+10)$
\item $f(2x-8)$ (not sure why this is listed twice)
\item ${y: y\geq f(-2x+35)}$
\item ${y: y\geq f(-8x+16)}$
\end{enumerate}

[frank orchid]

Hey….
Uhhhh can a graph be out of scale
like if a graph has 7 notches and you only have 6 numbers
and you need the 6 at the end…
can it be out of scale like that or do you just have to ignore the end part?
or add more notches

[long matrix]

🤔

[fathom swallow]

Banach N Amington

[long matrix]

this is sus af

[pearl moth]

wtf?

[mint patio]

LMFAO

Stan Gamma

[sick burrow]

(jokes aside #❓how-to-get-help)

[long matrix]

i cannot verify it even is correct

[pearl moth]

what is this asking you to do about f?

[long matrix]

the last few ones are sussy

[sick burrow]

the last two are right I'm pretty sure

[long matrix]

if u say so

just cus we have linears you can write this smh

[pearl moth]

f's codomain is finite sets of complex numbers, is there even a partial ordering on that?

[sick burrow]

there's a slight abuse of notation here

[long matrix]

slight

inequality on sets, imagine

[sick burrow]

in that f returns finite tuples of complex numbers

but here it'll only return singletons since the equations are linear

[pearl moth]

sets, not tuples

roots aren't ordered

[sick burrow]

well presumably f picks some ordering

[long matrix]

aoc needed?

you cant just do that

[sick burrow]

since its codomain is finite sequences on $\mathbb{C}$

[fathom swallow]

Banach N Amington

[long matrix]

imagine f(0)

we surely need aoc

no we definitely need aoc

[pearl moth]

ok, that allows for repeated roots to be distinguished, too

[sick burrow]

f(0) isn't defined

[long matrix]

what

[sick burrow]

huh

[pearl moth]

f(0) can't be defined

not on that codomain

[long matrix]

0 in R[x]

[sick burrow]

right the roots of that is all of C

[long matrix]

yeah i agree with this

[pearl moth]

$R[x] \cap {0}$ ?

oops, forgot the slashies

[long matrix]

aoc if we want f(0)

[sick burrow]

you mean $R[x] \setminus 0$

or wait no

[long matrix]

R[x] - {0}

[pearl moth]

that too, i'm tired

[fathom swallow]

Banach N Amington

[sick burrow]

$R[x] \setminus {0}$

[fathom swallow]

Banach N Amington

[sick burrow]

or just R[x] - 0

[pearl moth]

finite sequences is the one that makes the most "sense" but now we're introducing an arbitrary order of roots

[sick burrow]

yeah

wait how is $X^{<\omega}$ defined again?

[fathom swallow]

Banach N Amington

[pearl moth]

finite sequences of element sof X

[long matrix]

finite tuples

[sick burrow]

right

but like explicitly

[long matrix]

U_{n in N} X^n

?

[sick burrow]

yeah

[pearl moth]

i think that's the same, yeah

[sick burrow]

so in that case the n=1 case still wouldn't technically be a a singleton

it would be the ordered pair (1,root)

wait no

(0,root)

not just the root alone

[pearl moth]

why 0?

[neat frost]

$0$ is so ambiguous. It could be so many things
\begin{itemize}
  \item $0$
  \item $1$
  \item $\{0\}$
  \item $\begin{pmatrix}0&\cdots&0\\\vdots & \ddots & \vdots\\0&\cdots&0\end{pmatrix}$
  \item $x\mapsto0$
  \item $\varnothing$
\end{itemize}
It's pretty sus

[sick burrow]

1={0}

[pearl moth]

we do overload 0 a wee bit

[neat frost]

Im def missing a few

[pearl moth]

oh, we're doing zermelo-fraenken now?

[long matrix]

0 = {}

[neat frost]

Ah yes

[sick burrow]

or I guess we don't have to

[pearl moth]

oh, we've moved on, my bad

[neat frost]

tbh ive never seen 0 used to denote the empty set, but it seems understandable, so im including it

[long matrix]

0 = {0} is sus

ZFC?

or whatever it was

[neat frost]

Uh

[sick burrow]

I'm just so Foundations brained that that legit felt like the most natural definition

[long matrix]

0 = {}

1 = {0}

2 = {0, 1} = {0, {0}}

...

[neat frost]

My LA prof used 0 to denote the trivial vector space

[sick burrow]

since then you just say X^Y is the set of functions from Y to X

[pearl moth]

i think i've seen that usage.

also for the trivial group (the one with one element)

[long matrix]

interesting, you have enlightened me one step

[neat frost]

Anyway, $0=\{0\}$ and $0=\varnothing$ so $\{0\}=\varnothing$, so their cardinalities are equal, meaning $1=0$

\hfill$\blacksquare$\par

[long matrix]

0 = {0} is sus af

0 = 1

[sick burrow]

consider the multiplicative group on R. This is commutative, so we denote its identity by 0 as is convention. Then we have 0+1=2

[neat frost]

Why no hfilling D:<

[neat frost]

there we go

[sick burrow]

stop typing in the programmer boxes

and start typing in TeX

[neat frost]

wdym?

[sick burrow]

I mean

bleh

you are using TeX I guess

but the programmer boxes make my eyes glaze over

[neat frost]

what are programmer boxes

like code blocks?

[sick burrow]

like this

yeah

[neat frost]

what do you want me to use

[long matrix]

noobs```

[sick burrow]

|| _ _ _ _

---

---

---

---

_ _ _ _||

[long matrix]

//code blocks are the best
console.log('hello world uwu')

[sick burrow]

||_ _ _ _||

[neat frost]

$\gamma\sigma\mu\ \alpha\bR\varepsilon\ \tau h\varepsilon\ \eta\sigma\sigma\beta$

[fair mural]

ew

regular h

not hbar

$\hbar$

[neat frost]

hbar is uglier

[fathom swallow]

quantum

[long matrix]

Is there a \greek command

[sick burrow]

$\mathbb{ur cringe}$

[fathom swallow]

Banach N Amington

[long matrix]

nice

$\mbb{U SUCK}$

[neat frost]

$\mathcal{ur cringer}$

[long matrix]

is there a \greek

D:

[neat frost]

for what?

[long matrix]

turn my english letters into greek letters

[neat frost]

$\varsigma$

[neat frost]

so like \greek{abc} -> \alpha\beta\varsigma?

[long matrix]

yh

[neat frost]

uh

[long matrix]

isnt it \gamma

[neat frost]

maybe someones made it

oh

you mean like

[long matrix]

\alpha\beta\gamma baka

[neat frost]

actually translate

in order

[long matrix]

what else could i mean

[neat frost]

i thought you meant like in looks

[neat frost]

like this

[long matrix]

yes

well not like that

[neat frost]

[long matrix]

ok ok

smh

[fair mural]

greekify

[long matrix]

u bad grekek

[neat frost]

uh

[long matrix]

i dont think so, prolly have to define yourself

[neat frost]

yuh

ask plante

[neat lintel]

$A:$ Wrecked him? Damn near killed him!

[fathom swallow]

Lysh

[ancient flame]

I solved a polynomial system of equations

would not recommend

[mint patio]

damn like

x + y = 2
x - y = 0

Like that? :o

wow ur so smart and cool and poggers gmod

omg

[honest veldt]

gmod don't do it again

You might hurt yourself

[ancient flame]

lol

[paper yew]

\greek command

[sick burrow]

how is Obsidian so good

I've never fell in love with an application this quickly

I'm writing up notes for model theory

I've never been good at taking notes for math which I think fucks me over in my reading courses

since the lack of lectures and graded homework makes it too easy to move too quickly and skip important details

so I've just been starting from the beginning and trying to make a full web of all of the important definitions theorems and proofs I've done so far

[last oxide]

I thought you meant minecraft

[frail sail]

Ohh I get it now

Tysm

[sick burrow]

I mean I'm just jotting things down and connecting them where it seems reasonable

I've also been using it to jot down some worldbuilding ideas for a ttrpg I plan to run someday

honestly the graph view kinda gamifies it in a really nice way for me

I mean it's fun to see my graph grow

note taking is honestly cool because I don't have to think as hard

[jade crane]

[sick burrow]

since I'm just writing down and organizing things I already know vs learning new things

[jade crane]

I don't take as much notes anymore just because of that lol

during lecture I mean*

Sometimes I'm just scribbling stuff down I end up not thinking as much

[sick burrow]

yeah this is all out of lecture

as I said my main issue is with reading courses

[jade crane]

oh ok I agree lol taking notes is great then

[sick burrow]

a combination of trying to move too quickly and not reviewing the things I've done

with classes, lectures and homework fill most of that niche

but taking notes is cool because it takes a lot less work than progressing further

but is still valuable in helping me cement my knowledge and review details I may have missed the first time through

and the result of this is I have a way to do math that doesn't require me to go into maximum mental overdrive

reading and understanding math takes a lot of effort and I don't always have that much focus available

[jovial ember]

I posted it there

[frail sail]

Lol

[charred mortar]

Wonder what the mean actually is

Obviously going to be very skewed, but am curious about how much

[neat lintel]

mean basically means average

[pearl moth]

federal reserve data puts it at around $750,000

[visual hatch]

Are you stupid?

[pearl moth]

base has no impact on primality. a number is prime no matter what base you write it in

[candid cypress]

idk how you dug that up but its a copypasta from r/numbertheory

[pearl moth]

lol

trolls abound

[visual hatch]

Thank you

[pearl moth]

that's very reminiscent on all the nonsense about the "infinite nature of pi" that permeates the intarwebs

[surreal sapphire]

there is no reason to dig up that days old copypasta, especially not to insult op

[pearl moth]

although now i'm curious about what base early greek mathematicians used

there's an old greek counting system that is essentially base 30, if i recall correctly

[surreal sapphire]

they had a numeral system similar to roman numerals

but they did not write down too many numbers in their mathematics

and if they did, probably in "plain text"

[tender tulip]

If you know calculus:

By the mean value theorem, for a function f(x) that is continuous and differentiable over X = [a,b], there must exist a c in X such that

f’(c)(b-a) = f(b) - f(a)

Let F(x) be the signed area under the curve of the interval [a, x] (integral) [or for any initial value for the interval]. The derivative of F(x) is just f(x). Thus. f(a) - f(b) is the area under f(x) over [a,b], and F’(c) is just f(c)

Thus there exists a c in [a,b] such that

f(c) * (b - a) = Area

Which is essentially what the average is

[charred mortar]

But what about those pesky super discontinuous functions

[tender tulip]

I said continuous and differentiable

[charred mortar]

Can’t use your beloved MVT then huh

[tender tulip]

Wait a second. Hmm

“Antidifferentiable”

like for example, integrating over floor(f(x))

we can still find the integral nonetheless

[charred mortar]

I guess if you just pretend everything’s lebesgue integrable

[tender tulip]

and there still might exist an f(c)

that’s for continuous functions. Then you just say that there exists some constant C instead of f(c)

Honestly f(c) only matters if you want to say a c exists which isn’t important here

[fair mural]

lol just say integratable

[charred mortar]

I don’t think antiderivative existing and integrable are necessarily the same, even for lebesgue or whatnot?

But do correct me if I’m wrong

[steep mountain]

my uni just decided to have this dumb fkin plan to delay the sem 3 exams (6 math courses) to be done after semester 4 (which also includes 6 math courses) because workers and teachers went on strike 🙂 meaning we'll have the sem 4 finals then have a break to restudy sem 3 material and im not asking for advice im just stating this out of anger thank you for listening to my rant 🙂 i cant wait to explain to grad schools why my grades went down

[tender tulip]

It would essentially be integrating over a domain that is a function of x

The domain is the output of the function

[tender tulip]

hey funny man you know about math

is a homeomorphism literally just a map between different topologies of a set

[surreal sapphire]

no

[tender tulip]

I don’t get how we can jump from the basic definition of a topology of a set to notions of continuity and limits

Like for example the real numbers, how do we define a topology on it around some number such that there are infinitely many neighborhoods around it

[surreal sapphire]

by using the metric?

[tender tulip]

just saying the neighborhoods such that every element of the open subset’s metric is less than delta?

[surreal sapphire]

the open delta balls form a basis of the topology

[tender tulip]

Metric spaces just allow us to apply “conditions” to these topologies right?

[surreal sapphire]

but you also have a general definition of open set in metric spaces

[long matrix]

metric spaces are topological spaces

[surreal sapphire]

metrics give you a topology

[tender tulip]

what

[long matrix]

continuity can just be defined on top spaces

[surreal sapphire]

why are you learning topology if you dont know at least some metric space stuff

[charred mortar]

w.r.t. the antiderivative/integrable question, does the function $f(x) = 1$ for $x \in [0, 1]$ and $f(x) = 0$ for $x \in [-1, 0)$ not have an antiderivative over its domain?

[fathom swallow]

ab

[long matrix]

theyre scanning definitions...

[tender tulip]

I’m not actually looking it up lmao

[surreal sapphire]

well, dont do that lmao

the (first) prototype of a topological space is a metric space

[charred mortar]

since besides the origin $F(x) = |x|$, but like obviously $F$ is not differentiable at the origin

[fathom swallow]

ab

[long matrix]

u havent done analysis or have u

[tender tulip]

Haven’t

I assume a metric space is just a set with an operator that outputs a positive real number (so we have an infimum that’s if they’re equal, and a notion of order)

[surreal sapphire]

check darboux's theorem ab

[long matrix]

the bare minimum of understanding this stuff is intro to proofs kinda stuff

[charred mortar]

oh yeah the derivative also has to satisfy IVT

[surreal sapphire]

i agree that the notions of integrable and "has an antiderivative" are different

[tender tulip]

can a metric space have a metric that maps into an arbitrary ordered set such that the lowest member of this set is what equivalent elements are mapped to?

[long matrix]

i keep seeing dodgy/questionable interpretations

[tender tulip]

I’m a dumbass so I’m not surprised

[long matrix]

ur not, u just refuse to learn properly

[surreal sapphire]

metric spaces dont have "a notion of order"

[long matrix]

intro to proofs first is highly advised

[tender tulip]

That’s not what I mean

[charred mortar]

you mean the distance function mapping into any ordered set?

[surreal sapphire]

also i have no idea why the word infimum appears

[tender tulip]

I used the wrong word

That’s if it was a subset of which it isn’t. Just the lowest element

[tender tulip]

I mean, essentially for metric space s, the metric is d: S x S -> K, where K is the ordered set, and if the operation is on equal elements, then it’s mapped to the “least” element in K.

The order is for a sense of “closeness”

[surreal sapphire]

you can do memes like this, but

if you have trouble understanding the topology of R, you should probably stick to the normal definition for now

[tender tulip]

“The topology” is what confuses me. Is R the set/field, and we chose a topology for it, I assume with conditions for these open sets that have to do with metric

[long matrix]

you dont seem to understand the motivation for these notions...

[tender tulip]

I don’t.

[long matrix]

you wont if u just suck up definitions

[serene parrot]

Your question is confusing to begin with

[long matrix]

what learning stage r u at rn

from our last conversations i feel u need to understand fundamentals first

[surreal sapphire]

R comes with a standard topology from its metric

[tender tulip]

Idk

[surreal sapphire]

R is more than just a set or even field

[long matrix]

you need to be reasonably confident in intro to proofs - like the set theory and functions stuff

and so that you can unravel definitions

and understand set builder notation

[tender tulip]

All elements (maybe of another set if it’s a subset) such that [condition]

I know set builder

[serene parrot]

Have you done any proofs before

[long matrix]

Then check up the defn of a metric space

[tender tulip]

Proofs in what way. I’ve done “basic” mostly informal proofs

[long matrix]

and see if u understand what an open ball is

[serene parrot]

Proofs as in proofs

[long matrix]

and then open set

[long matrix]

you should also try to write stuff formally

[tender tulip]

This is the only way I can think of a metric space being useful with topology without looking it up.

Around some element x of R, we create a topology such that every open set that isn’t empty or R has elements that have a metric (to x) that is less than or equal to some “radius”, and just calling the subsets that include x as neighborhoods. From here idk how to get to a notion of “infinitely small” around x

Besides the fact that these topologies with a smaller “radii” are “subcollections” of ones with larger radii

Can we just make the radii as small as we want, or say that there exists a topology like this for as small as a radii as we want

[long matrix]

you need analysis...

[tender tulip]

Yeah.

[surreal sapphire]

its very hard to parse what you are saying mizalign

[serene parrot]

You know triangle inequality?

[tender tulip]

yes

[surreal sapphire]

like, i have to put in a lot of interpretations on my end to make sense of this

[tender tulip]

||a + b|| =< ||a|| + ||b|| which is strict only if they’re equal

[surreal sapphire]

you should probably follow shuris recommendation

[tender tulip]

Fucking stupid discord syntax

i understand basic epsilon-delta shit (there is a 1-ball in the domain around some point x_n such that f(x) maps this 1-ball into the image such that it is a subset of a 1-ball around the limit point)

Of course the image ball has radius epsilon, which we “know”

[tender tulip]

This is a really stupid definition, mainly because I came across a similar form by accident when drawing how complex functions map circles

But not much beyond that and the general application of it

I don’t know the words for a lot of ideas so I mostly stick to ones that have words

[charred mortar]

I third shuri's recommendation

[long matrix]

i cant follow u

[charred mortar]

the analysis people have basically considered these sort of questions, in a way, and formulated some very good and precise definitions for these things

[long matrix]

the definitions of terms need to be precise

in words or in symbols

but precision is key

[long matrix]

For example, this is what I remember for continuity

(interval notation)

[charred mortar]

people like Cauchy/Weierstrass and whatnot have kinda done all the hard work of figuring out good definitions, and modern authors have made textbooks to explain these definitions and what you can get from them

[tender tulip]

I’ll order a book then lol

[tender tulip]

Fairly straight forward

[long matrix]

But after understanding a defn

a book will hopefully say why its a useful notion

which leads back to your Qs on metric and top

[tender tulip]

My first real “proof” was with the limit of x^n with x being a member of the positive reals less than 1 (or more specifically, less than some maximum X less than 1 so I can have a bound)

which I wanted to avoid logarithms/exponentials due to the fact that I like Bernoulli’s inequality

[neat lintel]

[tender tulip]

I understand why a metric will be useful but I’m wondering why they specifically map to R+, and not like Q+ which still has an infimum 0 in Q, but is also ordered and has infinitesimal elements (multiplicative inverses of “infinitely” large numbers)?

Actually wait

[surreal sapphire]

its just more general

[tender tulip]

So that’s just for convenience

[river linden]

limits wouldn't be nice in Q, if d(x_n, y_n) -> K then K may not be in Q

actually I think cauchy sequences would completely fail

[tender tulip]

Limits then require a metric or topology, then creating circular fuckery

[river linden]

circular? how

[tender tulip]

idk it just seems like limits depend on metrics or topology for their definition

Which I’m trying to define a metric that doesn’t require one itself

[river linden]

metrics don't require limits... where is it circular

[long matrix]

We define a metric in order to have a notion of limit

where is the issue

That is a motivating factor.

[rose dock]

I believe they're saying how the construction of the real numbers by cauchy completion requires the notion of a limit, which requires the notion of a metric, which requires the notion of a real number.

[surreal sapphire]

i believe this is most definitely not what they are saying

[tender tulip]

It is exactly what I’m saying

[surreal sapphire]

well, it is not true

[tender tulip]

Can’t we just use the notion of “making epsilon as small as possible” by saying epsilon is a member of the rationals but just 1/n for some large N

[surreal sapphire]

see any analysis book on how the construction works

[tender tulip]

[devout nacelle]

You can work with a metric mapping to rationals and I think it would still work

In fact that's how Tao did it in Analysis 1

It was only after he constructed reals that he started using real valued epsilon bounds

[surreal sapphire]

i meant he metric on Q only takes on rational numbers

[devout nacelle]

Oh

[surreal sapphire]

and then you construct the reals no problem

[tender tulip]

Also can you bullshit set builder notations for collections

[devout nacelle]

Yeah, I don't understand where you find it to be circular Mizalign

[tender tulip]

I thought if the metric has to map to the positive reals, then you need to construct the reals, which needs the notion of a limit of sequences (Cauchy), which feels like it needs the notion of a metric to understand convergence

[devout nacelle]

You can map to positive rationals too

See chapters 4 and 5 in Tao's Analysis 1

[surreal sapphire]

you dont need the notion of limit to construct the reals

thats kinda the point

you add limits to sequences that "want to" converge

unironically tao probably best suggestion

[devout nacelle]

I'll share the pain

Need new comrades who rant about how they wasted a year and learnt no analysis

[tender tulip]

Sequences that only use the 4 operations on the rational field, correct

[surreal sapphire]

hm?

[tender tulip]

what exactly is the “textbook definition” of a sequence

Just a mapping of some infinite set S to N?

Sorry

N to S

[devout nacelle]

Yes

[tender tulip]

Then how do we say that a sequence diverges mathematically

Without metrics ofc

[surreal sapphire]

you need a notion of convergence

divergent will mean "not convergent"

[tender tulip]

I implied the converse

Just not diverging

Because that implies that there does exist some limit of it doesn’t diverge

Because this isn’t projective, the notion of the limit “leaving the set” confuses the piss out of me

[surreal sapphire]

what

you dont need "a limit" to talk about convergence

[tender tulip]

Fair enough

But once again how do we say a sequence is convergent

Or say that a sequence of rationals doesn’t always converge to a rational

[surreal sapphire]

i dont know what this is supposed to mean

[devout nacelle]

It's not as much about limit leaving a set as it is about the order properties inherent to Q by the virtue of its construction

[tender tulip]

I was thinking about limits which don’t matter

[surreal sapphire]

in Q you use the notion of cauchy sequence

[tender tulip]

It’s construction is as an ordered field I thought

[surreal sapphire]

and you need the notion of null sequence

[tender tulip]

The definitive ordered field

[tender tulip]

never heard of that term

[surreal sapphire]

then you can define limits in the usual sense

and every cauchy sequence will converge to a limit

and everything is nice

[tender tulip]

O O OH

[devout nacelle]

Yes, defined as equivalence classes of certain pairs of integers

[surreal sapphire]

but like

this is the main problem

[tender tulip]

i still don’t get classes but I’m eventually going to have to learn them

[surreal sapphire]

Q has sequences that "want to" converge, but cannot because the "limit" does not exist in Q

[tender tulip]

That’s what I was about to say

[devout nacelle]

I'm also emphasising again that upto constructing R, you never have to use R

[surreal sapphire]

one way to fix this is by replacing the notion of converging to a limit by the notion of cauchy sequence

[devout nacelle]

Your metric can be a map to non-negative rationals

[surreal sapphire]

and use this to "fill in the holes"

[devout nacelle]

At least when you're constructing R

[tender tulip]

I have a question though

[surreal sapphire]

and the notion of cauchy sequence (and null sequence which is also needed) work with the metric mapping into Q (which it does anyway)

[tender tulip]

Do we specifically define how the operators + and * “mess” with the ordering of the field

[tender tulip]

Null mapping I assume maps to 0

[surreal sapphire]

null sequences converge to 0

[tender tulip]

Not mapping

Sorry sequenced Jesus fuck I am losing it

[devout nacelle]

You mean translation invariance of order and all that?

[tender tulip]

Yes

[devout nacelle]

Like a<b implies a+c<b+c

[tender tulip]

Actually moreso

Multiplication

Addition preserves order

[devout nacelle]

I think they become emergent properties in case of Q once you fix the definition of order

[tender tulip]

The definition of order probably boils down to reflexivity, transitivity, and that last one

[devout nacelle]

In retrospect they are defined in a way that will make the ordered fied properties work out

[tender tulip]

Hm ok

it’s just that why is a =< b then -b =< -a come out of it

Actually

Wait

Nvm

[surreal sapphire]

because we chose the right definitions

[frozen merlin]

thought of the day: the one-point compactification of Q is the same thing as the projective line over Z

[tender tulip]

Also quick question

uh how do we describe a specific group in general based off of its properties

[devout nacelle]

Definition?

[surreal sapphire]

first you describe it as a set and then you describe the group operation

[tender tulip]

Alr

Is the order of the group the cardinality of its set

[devout nacelle]

Yes

Generally we are not very specific when the group is infinite

We just say it has infinite order, not really like, aleph_0 or anything fancy

[tender tulip]

I’ve never actually heard of aleph

I usually just say countably or uncountably infinite

[devout nacelle]

Yeah, I've never seen that being distinguished in case of groups of infinite order

Maybe because most of the interesting cases are finite groups

[surreal sapphire]

[tender tulip]

Which my dipshit definition is if it’s countably infinite, you can describe it as a 1-1 mapping of N to the set such that each individual element in the image set has an element in the domain set

[surreal sapphire]

lagranges theorem is only useful in finite groups really

[devout nacelle]

That's the definition, yes

[surreal sapphire]

but you have still things like isomorphisms of groups become isomorphisms of sets

[devout nacelle]

Basic group theory is a corollary of Lagrange

[tender tulip]

For like the integers: countably infinite because you can define f(n) = (-1)^n floor(n/2)

[surreal sapphire]

and they preserve order (also of elements)

and so you might use this to easily see that certain groups cannot be isomorphic

[devout nacelle]

That's the generally accepted definition Mizalign

[tender tulip]

Ah alright

Didn’t know lol

Okay so uh I get what a set is

what the fuck is a class generally

also is the power set, or topologies, actually classes, families, collections, whatever the fuck a set of sets is called

[surreal sapphire]

something that might or might not be a set

[tender tulip]

[surreal sapphire]

its usually used informally

the powerset is a set

topologies are sets

[tender tulip]

That sounds like holding a stick in one hand and a detonator in the other hand in a minefield of paradoxes

[devout nacelle]

Class can be used to refer to any collection of objects, and such a collection need not be a set in general

[surreal sapphire]

everything you encounter in daily life is a set

[toxic schooner]

[devout nacelle]

I am a set

[surreal sapphire]

or you can transform your statements into statements that are actually about sets

[toxic schooner]

u are the set that procrastinates on LA for 2 years manan

[tender tulip]

Then what about equivalency classes

[surreal sapphire]

all sets

[tender tulip]

Every set that satisfies a condition?

[surreal sapphire]

😵‍💫

[devout nacelle]

Equivalence classes are sets, the term is different

[tender tulip]

[devout nacelle]

If R is a relation on a set X, then the equivalence class of an element x in X is defined as the set of all elements in X that are related to x by R, i.e., {y in X: (x,y) in R}

[tender tulip]

WHY IS IT CALLED A CLASS THEN

[surreal sapphire]

germans

but its just a word

[devout nacelle]

Yeah

[tender tulip]

a a a a a a

[surreal sapphire]

the word isnt formally defined in ZFC even (?)

i never use this word in my daily life

[devout nacelle]

Equivalence class?

Or just class?

[surreal sapphire]

class

[devout nacelle]

Yeah

[surreal sapphire]

oh

i misunderstood the confusion

100 years back the words class and set meant the same

[blazing pawn]

I think they were introduced by Frege or something

Yeah

[surreal sapphire]

they were both used informally

[blazing pawn]

Some logician working way before there was a distinction between set and class, and before set was standard

[tender tulip]

set theory sounds like paradox hell

[blazing pawn]

[devout nacelle]

It's probably not, but the definitions are subtle

[blazing pawn]

Nothing about this is paradoxical

Its just a choice of words

[tender tulip]

Alright

Topology of the discrete topology of a set

[surreal sapphire]

a red herring need not be red nor a herring

[blazing pawn]

Idk what you mean by that mizalign

[tender tulip]

quick question

Is the union of a topology and another topology another topology

actually I’m gonna think about that

[devout nacelle]

Yes, it's a cute exercise

[tender tulip]

Actually there exists topologies for every set, so yes you can have topologies of topologies

topologies are just sets for a set that have conditions like being “closed” under finite unions or intersections

[surreal sapphire]

topologies are just glorified semi-lattices....

[tender tulip]

Honestly when I first heard of topology I didn’t expect it to correlate to set theory

Wikipedia

Jesus

actually they’re all relations

[devout nacelle]

Partial, total and well order are the only things I've had to meaningfully encounter so far

Strict partial order probably drops reflexivity

Same for strict total order I guess

[fair mural]

how would topology not connect to set theory lol

[charred mortar]

Most things are connected to at least some basic understanding of set theory

[sick burrow]

Yeah. The whole point of set theory is that you can build the rest of math within if

[tender tulip]

At first I thought it related to just “shapes and objects”

Nah it’s just a branch of set theory

[neat lintel]

It sorta is

Its hard to formalize topology without set theory though

[long matrix]

Stuff studied in topology can certainly be visualized.

[neat lintel]

It isnt really a branch of set theory. Set theory is the language that topology gets communicated in most easily

[long matrix]

But topologies outside of the spaces we are familiar are less easy to visualize. And we certainly want to be rigorous when talking about these rather than handwave 'this thiis this looks like this this this'.

Set theory is a tool we can use.

[misty smelt]

funnily it is also the case for probabilities

[neat lintel]

Its the case for a lot of math and I think it would be cool to use other languages otherthan set theory to communicate the proofs

[misty smelt]

mmh

why that ?