serious-discussion

[fresh comet]

I'll see what I can do I suppose

[ripe needle]

FUCK

I'm here too much

[fresh comet]

or maybe I'll do smth math/physics related

[ripe needle]

Goddamnit

That just happened, I was regular active when I checked like 2 hours ago

[fresh comet]

you were regular active 20 min ago

lmao

even like 5 min ago

[ripe needle]

Yeah I haven't 100% decided yet, too many years where anything can change, but as of right now I'm probably going to grad school for stats then heading into industry to make money

[fresh comet]

oh I meant for a coding project

[jagged forge]

i love how comes from the stats server lol

[fresh comet]

but tbh it's true for my future career too

so

[plush arrow]

yoo anyone know when to use partial or regular differential ?

[ripe needle]

Just Stat Things

[jagged forge]

lol

[ripe needle]

Shouldn't the notation tell you? Or the problem?

[plush arrow]

i just wanna understand why we use it tho

notation works fine but the reasoning is what im looking for

[ripe needle]

Explain a little more

[plush arrow]

for example we use differntiation to get the value of tangents for every point ( for a function)

but what does partial differential do

[ripe needle]

Differentiation is for one variable, if you have multiple variables like (x,y,z) you can only differentiate a part of it (one variable at a time), that's your partial differentiation

[plush arrow]

oh

that makes sense

thanks

[tall nest]

🥤

[dire glen]

hey, is there a way to know the amplitude of a function from its fourier series?

I'm asking this because in the lesson they say that the integral of a square wave is a sawtooth wave. But what's the amplitude?

[dire glen]

you are right. But what if i don't know what function the fourier series approximate?

I should differentiate and find the zeroes and find the max and min ?

can i do that with a series?

I think this is a topic of fourier series analisis that i didn't studied yet but i've seen metioned .. ?

[glacial panther]

I just discovered something crazy

it turns out

x/sqrt(x) will always be equal to sqrt(x)

the radicand divided by the square root of the radicand is always just the square root of the radicand

you can legit just ignore the numerator

[dire glen]

yeah it's not obvious

[neat lintel]

This follows from the law of exponents

sqrt(x) is just x^(1/2)

[neat lintel]

Not true, you also have the total derivative

[neat lintel]

Except at x=0

[zealous garden]

Thanks Carla

I didn't wanna be the one

[rocky shuttle]

https://youtu.be/sALHC0GKyLA

[tropic mica]

Going to exam

Last time I slept was

Acc woke up Yesterday at 2am

Took 5x200mg coffee pill

Model student what can I say

[fallow zodiac]

help

[neat lintel]

https://tenor.com/view/gun-anime-sniper-scope-scoping-gif-17545837

[fallow zodiac]

wdym'

first solve my doubt

then

[neat lintel]

Too late to help ya bro...

[fallow zodiac]

https://discord.com/channels/268882317391429632/1228686948584001639 , heres the link

[fallow zodiac]

why

[neat lintel]

[fallow zodiac]

please

[neat lintel]

You'll be missed.

[fallow zodiac]

same bro

have only few friends like u

[solar hawk]

@shrewd loom

[shrewd loom]

frick no, ive been pinged to this place

hush or ill put u into an old persons home

they r coming to r house to pick u p as we speak

ur*

[ripe needle]

Yeah I was trying to guage their level of knowledge and what class they're in without going too deep into it.

[fervent pebble]

oooooh this one is good

[solar bronze]

#math-discussion message
@thorn matrix
Knowable: what can be known
Whole: that which is complete in itself; complete: that which lacks nothing for its existence, whether qualifiedly or not
Predicated: that which is said
Parts: that which is incomplete in itself; incomplete: not complete
Something: any thing whatsoever; any: qualifier meaning "one choice of"; thing: an abstract or concrete idea or being; whatsoever: as-is without need of qualifying.

[thorn matrix]

Your definition of something is circular

and these are just more Ill defined and vague terms

[solar bronze]

I have not used any circular definitions here

[thorn matrix]

Define a thing

[old oak]

No, you're avoiding circularity using infinite descent instead

You're defining vague notions using other vague notions

[solar bronze]

They are not vague; they are general. I thought this was a math server, but if you won't respond seriously to me, then I'm not interested in having this discussion with any one of you.

[cunning plaza]

People are responding to you seriously!

[old oak]

Yes, I was entirely serious.

[solar bronze]

No, they think I'm a toy to push around, clearly. That's the attitude that everyone has towards me right now it seems.

[old oak]

The way things are defined in mathematics is entirely different to what you're doing.

[cunning plaza]

If you take an Intro to Proofs class, you will get the same feedback, at any university.

[solar bronze]

Why? Why not take every question seriously, no matter how absurd it seems? Is the good that comes from doing that not obvious?

[thorn matrix]

You haven’t asked a question

[solar bronze]

Claim. Same difference implicitly.

Why does emotion have to get into the cold and logical?

[thorn matrix]

It doesn’t, but your system isn’t logical

[solar bronze]

No, it is logical, but you've convinced yourself its illogical before I've even written a single word. Apparently the word "syllogism" is meaningless here?

[thorn matrix]

What are your initial definitions

You are just doing infinite descent to define anything so it’s useless

You need to start somewhere

[solar bronze]

That isn't what I'm doing per se. That relies on the premise that everything reduces to circular definitions as the foundation when in reality the most fundamental definitions ultimately rely on some concrete reality or realities for their definitions.

This fact is the basis of things like Lingua Latina per se Illustrata, for instance.

[thorn matrix]

So what are your fundamental definitions

[shut cradle]

The problem is that you aren't able to define reality

[solar bronze]

Most fundamental, or what level exactly?

[solid snow]

I mean im not sure what youre trying to get out of this

are you trying to make your axioms for math?

[thorn matrix]

Fundamental

What everything is based on

What are your fundamental definitions

Fairly simple question

[shut cradle]

Without describing the sense in which your truths are fundamentally drawn from "reality" you effectively create them from thin air

[heady flame]

come on man, fundamental meaning not derived from any previous ones

[thorn matrix]

Arguably the most simple question one can make about a logical system

[solar bronze]

Yeah, but fundamental with regard to what? Being itself? I'm a Thomist, so that answers that implicitly. Fundamental with regard to mathematics? I mean I guess I can reiterate what I said in math discussion... so with regard to what are you asking for fundamental definitions?

[thorn matrix]

You define things in terms of other things yes? So what are the things that are not defined by anything else

[solid snow]

something akin to this

[shut cradle]

In a system of logic, any true statement can either be proven from the truth of other previously true statements or is inherently assumed to be true. Which are those inherent truths of your system?

[solid snow]

the logic operators can all be defined with truth tables

[thorn matrix]

Are we sure he knows what a truth table is

[solid snow]

let's not be dismissive

[cunning plaza]

To answer this question, it's because putting math on a rigorous basis was the big question of the 1800s into the 1900s. The math community is generally in agreement now with what constitutes rigorous math inquiry, after a long period of figuring that out. People have limited time, and not every seemingly absurd question is worth the time to ponder. There is some stuff at the higher level of math foundations that people are doing research in, but I'm not knowledgeable enough to comment on that.

[thorn matrix]

It’s a genuine concern, he seemingly hasn’t taken an intro to logic course so it might just be more confusing for him

[old oak]

This is exactly it

[neat lintel]

https://tenor.com/view/homelander-the-boys-gif-18572939

[solar bronze]

https://archive.org/details/dictionaryofscho00wuel/page/n15/mode/2up
If you go to the section "diagrams and charts", from there you can locate and browse "divisions of act and potency", "usage in regard to beings", "categories of being", "divisions of efficient cause", "chief divisions of certitude", "change and becoming", "divisions of concepts or ideas", "divisions of form", "senses of intellect", "some uses of material cause and of matter", "main types of principles", "divisions of propositions", "senses of reason and 'ratio'", "forms of reasoning, proof, and refutation", "main divisions of supposition", "some divisions of logical senses of term", and "divisions of unity, identity, and distinctions".

That should give an overview that answers the question adequately. I would post images, but I don't have permissions. You'll have to deal with the (quite frankly) silly notion of borrowing trivially copyable bits because of this wall known as copyright apparently.

[shut cradle]

Wouldn't a Thomist still fundamentally assume and fix at least one truth, which cannot be proven from any other? "Therefore it is contrary to the nature of an end to proceed indefinitely. Therefore it is necessary to fix one last end." - Aquinas, creator of Thomism

[solar bronze]

1. He reasoned from first principles; 2. you can't create philosophy, only acknowledge it

[thorn matrix]

What are the first principles

You haven’t defined first principles

[solar bronze]

Those things from logic which are intrinsically self-evident and common to all men who have the use of reason.

[thorn matrix]

So you do accept axioms

[solar bronze]

Yes

[thorn matrix]

So what is the problem with ZFC

[solar bronze]

I would have to investigate it to give you a good answer. I haven't studied it. If it contradicts the five ways in which ideas can be predicated: genus, species, difference, property, and accident, then the system is flawed.

Or more properly if it leads to metaphysical contradictions.

[neat lintel]

And why are those five ways correct?

Perhaps they are flawed and ZFC is correct instead

Never mind the fact that ZFC is unrelated to metaphysics

[thorn matrix]

Yeah, your logical system is not automatically the standard

[solar bronze]

Looks like I'll have to dig up some syllogisms and proofs. I'll have to get back to you on those.

[cunning plaza]

https://www.people.vcu.edu/~rhammack/BookOfProof/

I'm not linking this out of mockery. I think working through this free online book would be entirely worth your time.

[solar bronze]

Nice, thanks

[heady flame]

I mean when you accept the notion of axioms, I don't see what's the problem with math? Math has it's set of axioms it works from, and is self consistent afaik, now whether math as a discipline being based on these axioms has any bearing on what you perceive as real life (or anything else for that matter) doesn't matter, does it? It's a logical system like any other, just that a lot of people find it useful, right?

[solar bronze]

So this is based on ZFC, right?

Seems yes from a quick ctrl f

[thorn matrix]

Probably yes

[old oak]

Just to add to that, mathematics is mostly unconcerned with metaphysics or finding fundamental philosophical truths; it's a collection of methods developed to solve particular kinds of problems.

[neat lintel]

Probably doing more with peano axioms that zfc, but sure

[solar bronze]

I'm well aware, but a difference in definition for number has major implications for instance, or anything fundamental to math for that matter, like what I said about primes.

[thorn matrix]

We have a rigorous definition of number

[solar bronze]

From a set of axioms based on "nothing" according to eigenpuppet

I won't get into that again tho lol

[neat lintel]

The definition of number is done internally (and number as a term on its own is not defined). For number theory, we mainly deal with the integers, which are the group completion of the naturals, which are, in turn, well defined by the peano axioms

[thorn matrix]

You have a fundamental misunderstanding of the point of mathematics

[neat lintel]

That’s not what I said

[old oak]

And very nicely constructible using sets within ZFC

[solar bronze]

My apologies.

[thorn matrix]

We don’t care about where the axioms come from, they seem interesting and consistent so we study them

[neat lintel]

Please just read a book or two on this stuff before making claims about it

[heady flame]

I would argue that it's even impossible to reason about fundamental philosophical issues from a standpoint of mathematics, since it's reliant on a set of rules, but if you question even that foundation, it's hard to argue anything properly, but in my opinion using math there is worthless as it directly depends on what you're questioning. Now whether that's reasonable to say is dubious, sinceeverything is under scrutiny, including the logical dependency chains so to say in a lack of a better term

[old oak]

Would calling axioms "that which is self-evidently true" annoy you less?

[cunning plaza]

The entire, or nearly the entire, math community has agreed on what a number is, after a long period of of studying and figuring it out. People are not debating on the rigorous definition of a number these days. You can eventually study a book on Set Theory if you want to learn how a number is rigorously defined.

[heady flame]

Saying axioms based on _ is fundamentally flawed, the very definition of axioms is that they are not deduced, but assumed. Now whether assumed means assumed in everyday sense, or it means self evident, given by god or something fourth is irrelevant, they are the rules of the game.

[neat lintel]

Halmos has a very good 90 page introduction

[heady flame]

You can pick up and move a pawn 5 steps diagonally on a chess board, but people agreed to the rules of chess and call the game played according to those rules chess.

[solar bronze]

Well, I'm not exactly trying to make any definitive claims on this stuff right now because I don't understand them fully, and to make judgements in that way wouldn't be reasonable. The whole issue sparked from me trying to define "uncomposed" to define my idea of "general closed form" so I can be specific about what kinds of ideas I'm looking for, especially with respect to algebra and algebra relevant to my field as a software engineer.

[solar bronze]

Sure lol

[old oak]

Let's go with that then, it's the same thing.

The axioms of ZFC describe those properties of sets which we consider self-evident.

[solar bronze]

That's the original definition of axiom anyways

[old oak]

~~In particular the well-ordering principle, the most self-evident of them all ~~

[neat lintel]

Nah, that’s Zorn’s lemma

[old oak]

Zorn's lemma is neither evidently true nor evidently false

Unlike the axiom of choice, which is evidently true

[solar bronze]

Ultimately, I can't say anything at this point really. I've more or less allowed myself to be misled in the past by rather naive and surface-level understandings presented by various things I've just come across about different things, while right now, I'm making claims based on what I've been able to reason about numbers themselves from first principles, and accepting certain mathematical principles on faith as taught by public "school", so this endeavor of mine to actually learn mathematics will give me what I need to see for myself whether or not it is reasonable apart from actually making algorithm research much easier. The problem for me has mostly been finding a painless means of learning, and so far, I think what I've been given with this and spivak's calculus are quite stimulating and not at all like my experience with the public school system here in America.

[grand sapphire]

i feel like kurepa's principle is very intuitive equivalent of choice

[neat lintel]

Yeah, US public math education is not good. Books are the way to go 👍

[solar bronze]

Tell that to my old teachers 😒

[grand sapphire]

unfortunately you need foundation for it to be equivalent so sadly one can't teach it to undergrads right away

[solar bronze]

Honestly not sure how to cope with all the lost time from public school.

[cunning plaza]

Most people are not interested in diving deeper into math and high school math education reflects that.

[solar bronze]

You say that, but I reiterate that no one can appreciate what he neither understands nor loves

[cunning plaza]

Sure. It's hard to tell whether the time investment in learning a subject is worth it though.

Video games give a quick reward, where as learning math takes a long time.

[solar bronze]

I really didn't enjoy math, considering it for quite some time as mere knowledge useful only in a vacuum, until I got into finding a faster division algorithm, and then I became an addict for life with discrete math.

[solar bronze]

Quite a stark contrast, and it's a shame given video games are about as high level as anyone gets these days. Likely there's a small chance only those that get into speedrunning will ever find academic interests imo.

[neat lintel]

Why is speed running related to academics?

[solar bronze]

Well look at this, for instance: https://youtu.be/2x_pqyrf9lA

[cunning plaza]

If you dive deeper into math then I'm sure you'll find other things to love about the subject. But I encourage reading through the books first before making any profound claim. Just trust that the math community (which includes the book writers) knows what they are talking about while you ponder whatever question you have.

And when I say "read through the books", I also mean work through a good amount of the homework problems.

[solar bronze]

Also this: https://www.zeldaspeedruns.com/oot/srm/srm-overview

[cunning plaza]

Speedrunning is completely different from the subject here.

It is its own thing, it's great, I'm sure it can be studied academically. That's about it.

[solar bronze]

It's analogous to doing math for recreation

[cunning plaza]

Completely disagree. Maybe there's a few analogies but that's it.

[neat lintel]

That doesn’t imply that it’s equivalent and/or necessary for academic interest

[thorn matrix]

I’ve done some speedrunning and I can vouch it’s completely different

[solar bronze]

All I said was this. It's a potential gateway drug.

You watch any GDQ event for even five seconds and wonder what's going on and you're already going to go down a rabbit hole to find an explanation for why a certain set of actions produces a certain set of effects.

[cunning plaza]

Oh. Sure, I guess it's similar in that sense.

[solar bronze]

Such as "why does swimming backwards in The Legend of Zelda: The Wind Waker let me swim across the ocean at high speeds?"

TASes are even more clickbait

[thorn matrix]

Have you seen triforce% in oot

[solar bronze]

That's the video I linked lol

[cunning plaza]

Oh that speedrun. That's the best speedrun I've seen.

[solar bronze]

It's amazing 😂

and all this just because SRM leads to ACE

[thorn matrix]

ACE was found in Mario sunshine recently iirc

[solar bronze]

Cool

[timber burrow]

hello guys

what's different here from the first discussion channel?

[thorn matrix]

It has a 2 at the end

[timber burrow]

oh right

so it's a bit less active?

[old oak]

yes, for those of us who find the main one too fast moving

[timber burrow]

oh I'm gonna be here then

how are yall doing today?

^does this question fit better for the chill channel?

[fresh comet]

it's fine here

I'm doing okay today

[timber burrow]

how long have you been in this server?

[fresh comet]

well, it says on my profile

since July 31, 2023

[daring parrot]

Is khan academy or basic mathematics by lang a better refresher for math

[fresh comet]

why not both?

[icy void]

Is pure mathematics major, applied math, statistics or physics major better

For getting jobs

And money

[ocean harbor]

some people leave and rejoin back

like i was here in jan 2023 and i joined back in aug

https://media.discordapp.net/attachments/952271935620915225/1207700482760638464/image6.gif

[fresh comet]

oh I know

but I haven't left

[ocean harbor]

https://cdn.discordapp.com/emojis/1112022027847606383.gif?size=48&quality=lossless&name=catcombing

oh

I see

[cunning plaza]

I would guess statistics is the best out of those options for making money.

[leaden torrent]

applied math at one point was the highest-earning undergraduate degree in america, period

buuut thats biased by "applied math" programs being more common in higher-ranked schools

whereas "stats" programs tend to be offered by basically every school with a math department

so im not sure i'd trust that metric

in any case though, i doubt the difference in earnings potential between the two fields is that large.

if you learn to program you shouldnt struggle either way

[leaden torrent]

(iirc a bachelor's in applied math even beat out most graduate-level degrees, though professional degrees still beat it)

(no clue if those stats are still accurate, theyre from like 10 years ago)

[proud olive]

Only 10 years ago?!

I thought this was going to be like back in the 1960s or something

[leaden torrent]

applied math degrees did not exist in the 60s lmao

[proud olive]

Back when they were racing to construct those power plants

Were they just extra fancy engineering degrees back then?

[leaden torrent]

or just "math" degrees

the distinction of math into "pure" and "applied" is a very recent construct

back in the day, every mathematician learned a lot of applied stuff

you were usually expected to take a few semesters of physics

etc

and then you could specialize in pure stuff for your graduate degree if you wanted

but again they didnt conceive it as a pure-applied split like we do

instead it was more of a "theory" vs "techniques" split

[ripe needle]

Yeah I feel like every school is offering a degree or certificate in stats/data science and it's flooding the market. I'm not in that industry so idk how it truly is.

[cunning plaza]

Seriously. Data Science is the new hot degree these days.

[timber burrow]

Does discussion count as like showing a problem and discussing what would be your first instinct to do when solving it?

Like

What is yalls first instinct if I gave you this equation $$2x^2 + 6x + 9 = 7x \sqrt{2x + 3}$$

[fathom swallow]

A guy named Karolis

[timber burrow]

Or would this fit more as a help

[tired musk]

i need to study for my math finals whats an effective way to study math

[timber burrow]

When are the finals

I have no idea how to help you I'm just asking relevant questions

[minor current]

how to stop sucking at math

[fresh comet]

I ask myself that every day

[tired musk]

in like 3 weeks 😢

[timber burrow]

How do i stop sucking

[tired musk]

https://tenor.com/view/lebron-sunshine-lebron-james-sunshine-sunshine-lebron-you-are-my-sunshine-you-are-my-sunshine-gif-509896211431970290

[ocean harbor]

https://tenor.com/view/math-the-stanley-parable-numbers-fish-addition-gif-16937516

[mint patio]

Hey art people, what's that artstyle called out where like everything is colored out (uniform colors) except for some defining features of the focus? I don't have an example on me right now but like usually the background is one color and the silhouette is another color, sometimes there may be details added to the silhouette and each one of those will have its own flat color

But like there's no shading or attempt to make it 3D I don't think, no different shades of a color on the same 'section' or anything, it's entirely flat and matte

I know I've seen it in some Pokemon artwork for sure

[jagged forge]

https://www.youtube.com/watch?v=5B0UPtEpOQc

i'm addicted to this yt channel

[neat lintel]

@shrewd loom ping me here

[shrewd loom]

k

[neat lintel]

i gave u 10 points for stuff u leanred beford

[shrewd loom]

nice

ill prob ping u tmrw bc ill sleep soon

[neat lintel]

ok

[icy void]

Should i not major in math if i dont wanna end up in a programming job

Can it lead to jobs outside of programming/coding

[ripe needle]

Multiple people have already answered this.

[mortal vortex]

You can do math without it leading to programming

[earnest flax]

do programming without it leading to math (impossible)

[cinder zephyr]

That is not impossible

Every day I witness CS majors go great lengths to avoid any mathematical thinking

[earnest flax]

depends on the grade u are at cs

[cinder zephyr]

I see this at all levels (having graded for theoretical CS courses at a few different levels)

[cinder zephyr]

I'm mostly joking

[jagged forge]

mostly

[cunning plaza]

You don't need to do any math for many programming jobs

[earnest flax]

This could also apply for me

i know physics but i don't do the maths

[neat lintel]

Then you don’t know physics

[earnest flax]

fake physicist?

i mean, physics ain't 100% about math

as math can't explain everything in nature

can math explain chaos?

[cunning plaza]

https://en.wikipedia.org/wiki/Chaos_theory

[earnest flax]

did you just link me a site that says that applied math can't explain everything exactly, and that's why chaos can't be explained by math?

[cunning plaza]

No, there is a mathematical area called Chaos Theory, which frankly I haven't studied but I know it exists.

[earnest flax]

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.
^ literally a paragraph on the site

[cunning plaza]

Uh... okay? Is physics somehow able to explain that situation better?

[earnest flax]

math can't explain chaos because math and chaos are two separate things,

Math is an intricate system of perfect conditions that can always give the same result
Chaos is an unbalanced system of incalculable conditions that always results in different things

[earnest flax]

no, physics is based on math

[solar bronze]

Wouldn't solving $a(n+1) = a(n) + k$ algebraically be a proof of mathematical induction?

[fathom swallow]

Andrew Porter

[earnest flax]

but physics can explain chaos as a chance of happening, either it's below 100% or above 0%

an event will never take place 100% of times, doesn't matter how many calculations you put in it

[solid snow]

throw ball in air
ball falls

according to my calculations this happens 100% of the time

[earnest flax]

does ball fall in the same place? Yeah

[solid snow]

that's irrelevant to what i said

[earnest flax]

in reality there are way more systems instead of one singular system acting at one place

If you disregard these systems you're isolating terms so that your condition comes true.

[cunning plaza]

Using mathematical induction is a common way of finding a general formula for a recurrence relation like the one you have there.

(I think it's called a recurrence relation)

[solar bronze]

This by definition defines the set ${a(n)}$ with $n$ the $n$th element, but $a$ itself is indeterminate.

[fathom swallow]

Andrew Porter

[earnest flax]

like how physicists say "ignore air resistance" when talking about gravity

[solar bronze]

That may or may not sound confusing with my use of the word indeterminate 😅

[cunning plaza]

What is a?

[earnest flax]

Also, even at the system you said, there are ways to make your statement false

[solar bronze]

A symbol representing an unknown function or relation defining the elements of a set.

[earnest flax]

What if you're experiencing micro-gravity or 0g? The ball will never fall, it'll just shoot straight up forever

[cunning plaza]

So, something like:
$a(1) = 2$ and $a(n) = a(n - 1) + 4$ for $n > 1$
?

[fathom swallow]

TopDreg

[solar bronze]

Sure

afaict this algebraic relation I gave is equivalent to mathematical induction

[cunning plaza]

Then yeah, you could use induction to give a formula for a(n).

If you want to give a proof of mathematical induction, then you need to use the well-ordering principle.

[solar bronze]

Yes, but where is the proof for induction itself though I wonder

I'm not seeing where the well-ordering principle is mentioned in the book you gave me

Also, so far it just sounds like dialectics, but math edition

[cunning plaza]

which book?

Hammock?

[solar bronze]

Yeah

[cunning plaza]

Could you tell me what chapter?

[earnest flax]

If you calculate for such systems, your formula will be so complicated no one will be able to calculate anything with it

[cunning plaza]

And problem?

[solar bronze]

Are all the principles spread throughout or is there not a reference? I'm getting 158 matches.

[earnest flax]

you throw a ball, well, the wind speed made it go right, you calculate for wind speed, well, the thermical conditions made the ball go to another side again, you calculate for thermical conditions, well, the gravity changes the speed on which the ball goes to the ground and so on

[cunning plaza]

I'm not sure if the author proves induction in that book. I know Spivak does in his Calculus book or at least asks for a proof in a problem.

[earnest flax]

by the time you're done with your formula, there will be so many variables that it would be just better to throw the ball repeated times and just make an average of it's trajectory

[solar bronze]

Oh ok

[cunning plaza]

But if you want to try proving Induction, then use the Well-Ordering Principle: Every set of natural numbers has a smallest number.

[solar bronze]

Yeah right now I'm kinda just skipping around this text. Most of what I lack is terminology, axioms, and principles.

He's also kinda going in depth in places that I don't think need much more than the definition

[cunning plaza]

If you want to understand math more fluently then you need to practice the problems. You can't learn math without actually working through it yourself.

Everyone who is into math in this server is basically doing problems all day, every day (homework problems, research problems, etc.)

[fervent pebble]

what a truly ignorant take

[fresh comet]

tbf they’ve been spewing out things I would deem ignorant at best and nonsensical at worst all day

[cunning plaza]

Yeah I didn't feel a need to respond any further

[fervent pebble]

if math is an intricate system of perfect conditions that can always give the same result why am i so fucking bad at it riddle me this liberals

[fresh comet]

have you considered the possibility that you just have a major skill issue

(this is a joke don’t kill me please)

[fervent pebble]

too late im on my way to ur house

watch out...

[fresh comet]

[neat lintel]

Chaos theory, stop yapping and spend more time researching

[reef geode]

How cooked am I with my fall course schedule

Intermediate Spanish/3rd semester Spanish
Graduate level proof-based Cryptography
Linear Algebra I
Formal Languages and Automata

(Probably not but maybe)
Applied Regression Analysis

[peak tide]

doesn't cryptography require linear algebra?

[reef geode]

Yeah

The thing is, I do a lot of quantum computing research and work with linear algebra a lot

And I just recently entered this university and have to work through a couple things I already kinda know

For the credit

Linalg1 is one of those

And the Prof gave me the green light and my academic advisor is the one who initially suggested me to take the class

[earnest flax]

I was talking about math explaining 100% of chaos.

Not just a piece of it as chaos theory implies

[fresh comet]

I don't mean to be rude, but I feel like you've been explaining a whole lot of nothing for the entire day

[ripe wasp]

💀

[neat lintel]

5867uty jhfgvnbt

[fresh comet]

83274hriwe iehfowfrw

[earnest flax]

it's ok if that's your opinion but you'll never prove that chaos = mathematics and neither that mathematics = chaos, they need to be equal so that they can explain each other. They are distinct in a natural way, even tho you can find order and math in chaos, you'll never be able to fully explain chaos by math or math by chaos.

[visual breach]

Crank be creative and fun challenge: impossible

Lol

[neat lintel]

Keep yapping about things you don't know 🗣️

[fresh comet]

I have absolutely no idea what you're on about, but it doesn't seem well informed

[earnest flax]

well, it's possible to explain part of chaos by math, but not all parts of chaos are explained by math

[neat lintel]

Define chaos in a rigorous way

[earnest flax]

i alr defined it

[neat lintel]

You didn’t

[earnest flax]

?

[neat lintel]

‘in a rigorous way’

[earnest flax]

wdym by that? How can it be more rigorous than that definition 💀

[neat lintel]

Nevermind, You’re a waste of time. Blocked

[fresh comet]

why the sully? @mint patio

[earnest flax]

if it was that easy to define chaos with math then physicists wouldn't be having difficulties on explaining reality or even creating a theory that explains everything

[fresh comet]

lmao

[mint patio]

I don't disagree with Catgod

I just think that having to exclaim it, especially so aggressively, is a bit childish and silly

[fresh comet]

oh I see

[fair mural]

do you actually know anything about math or chaos or physics or are you just saying what you think they should be

[fresh comet]

in that case, I mostly agree

[mint patio]

Especially the "waste of time" part

[fresh comet]

Chaos is an unbalanced system of incalculable conditions that always results in different things.

is not rigorous

[mint patio]

BWH just sounds naive and inexperienced, trying too hard to talk about things they don't actually understand

Especially with that pre-university math role

Perhaps something to keep in mind when engaging with them

That doesn't make them a "waste of time"

[fresh comet]

I mean sure, but they're not going about this in the nicest way either

[cunning plaza]

Yeah I wouldn't call BWH a nice person with how they've been talking

[mint patio]

I haven't been paying attention to the rest of the conversation

Just happened to come in time for that 😛

[fresh comet]

it's been going on for at least 12 hrs now

lmao

[earnest flax]

i was talking about how math can't fully explain chaos but alr

[fresh comet]

well, not continuously

[cunning plaza]

If you're going to be a crank then at least be nice.

[mint patio]

The foundations for chaos theory are based in math no...?

[fair mural]

they seem less mean and more just insistent

[fresh comet]

there's nothing wrong with being a crank as long as you're willing to admit you may be wrong imo

[earnest flax]

yes, but they can't explain every part of it

[mint patio]

So what?

Why does that matter?

[earnest flax]

they can explain the start of chaos but not everything

[mint patio]

Math can't even explain math half the time

Who cares?

What is the purpose of saying that?

[earnest flax]

by your definition, what is the purpose of saying anything anyway

[mint patio]

That's not what I said at all

I have not provided any definitions either, please don't try to misconstrue what I say

[heady flame]

man are you serious, someone even linked you the wiki page stating that chaos theory is a part of math dealing with systems which are deterministic but highly sensitive to initial condition variations. you can have a perfect model of a chaotic system and still not be able to so anything useful with it, but thats not on math, thats a computing problem

[earnest flax]

is it a computing problem?

[sterile fable]

hi guys, does a non invertible matrix mean its determinant is zero?

[fresh comet]

yes

[earnest flax]

i never tought of it that way

[heady flame]

yeah

[mint patio]

It could be nonsquare, in which case the determinant isn't even defined

[fresh comet]

but in that case, it doesn't have an inverse anyways

[mint patio]

Yes

It's noninvertible

[visual breach]

But what about M_n(Z)

[sterile fable]

so theres this question they have asked us to find lamda of a matrix but the thing is that even if you plug any of the options its gonna be multiplied by zero

so how do i find lamda then

[mint patio]

By lambda do you mean eigenvalues?

[visual breach]

An integer matrix may not have inverse as integer matrix

[fresh comet]

you're right

[heady flame]

well take a prototypical lorenz attractor example of a chaotic system. it's perfectly well defined as a system of nonlinear differential equations, with perfectly well defined solutions (not in closed form but whatever) , the chaos arises from the sensitivity to initial conditions

[sterile fable]

what is hat

that

[mint patio]

Okay never mind then I think

[sterile fable]

i guess

[fresh comet]

damn I suck too much at LA

can't even answer right

[mint patio]

Me2 hgr

Higgins :3

[visual breach]

Noo

[heady flame]

2I comes to mind

[earnest flax]

maybe if you could just get every state of conditions you could predict it infinitely, no? (Like re-doing the test but with the condition met at the final of the test)

[neat lintel]

me but texas

[visual breach]

Yeah

[heady flame]

well that's what the diff eq tells you, how will you go about it practically is a different question

[fresh comet]

feel free to call me that if you like lmfao

it's a funny nickname for sure

[heady flame]

theoretically you can go through all of the initial conditions you care for and find the responses in some way, but it's not really practical imo

[mint patio]

I will :P

[heady flame]

depends on what you're doing concretely

[earnest flax]

for my concept of reality, applied math isn't fully right

which seems true

i mean, you'll never be able to determine the exact position of an object, just take an atom for example.

[heady flame]

i have several questions but ill summarise them into one

what the fuck

[heady flame]

that's on physics man

physics gives you a mathematical model, and i stress, a model, of reality

now how good that model is? depends on what you want to do, for me designing a buck converter i don't give a shit about quantum mechanics, if i were to design a high electron mobility transistor to use as a switch, I'd have to care about it

[fresh comet]

okay even if that's the case, what's your proposed alternative?

are we supposed to give up on math completely?

[earnest flax]

yes, many people get isolated systems to use physics at

[heady flame]

also, no you can't really determine a position of an electron, since its not a ball as far as physics is concerned

[fresh comet]

just striking down math as a discipline doesn't seem like a productive use of your time

[earnest flax]

I never meant that

[cold needle]

See the theory of distributions

[heady flame]

i mean i dont really get the problem, math applied to the real world (whatever that is) is a problem physics deals with, math exists independently of physics

[cold needle]

and quantum mechanics i guess too lol

[earnest flax]

we should be making a rule so that applied math is good to use once it calculates a percentage of reality (like 99.5% like reality) to use it on reality

[fresh comet]

[cold needle]

It already does that

in fact usually better than that

[earnest flax]

bc we will never have a mathematical equation that gives 100%

[fresh comet]

if math wasn't at least 99.5% accurate, we wouldn't be here

[heady flame]

let x, y be numbers of apples in distinct baskets A and B,

the number of apples in both baskets combined is given by x+y

????

[earnest flax]

if you know we can't explain 100% reality by math, why are we even trying to get a ToE out of that?

[heady flame]

how well does it approximate reality

[fresh comet]

...you're taking a shot at physics now?

[heady flame]

@physics

[sterile fable]

x -1 4
-2 0 1
-1 1 2
matrix of order 3 by 3 is not invertible then i have to find x?

[fresh comet]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[sterile fable]

i dont want the solution

😭

[fresh comet]

I mean discussion channels are still not the place to ask

[sterile fable]

the thing is if i do determinant = 0

[earnest flax]

i've heard they be trying to make a ToE of physics with math alone 😭

[heady flame]

find x s.t. its singular

[sterile fable]

x will just disappear

[fresh comet]

what should they be using then?

our feelings?

[earnest flax]

mainly concepts

[sterile fable]

oh singular isnt that just determinant = 0

[fresh comet]

...physics without math is not physics at all

[heady flame]

det=0 <=> singular yeah

[fresh comet]

conceptual physics can only take us so far you know

[mortal vortex]

It shouldn't
You need to set the det = 0 and solve for x

[earnest flax]

Reality never needed math to exist in the first place

[sterile fable]

but then x*0 would just be 0 when you find deterinant

[fresh comet]

math doesn't need reality either

[sterile fable]

hmm

[fresh comet]

I'm saying this as someone who does both math and physics lol

[mortal vortex]

^

[heady flame]

that's true, but physics is concerned with modelling reality using mathematics and experimental methods

[earnest flax]

why are you trying to determinate a non deterministic-reality with math, that uses a deterministic system

[finite inlet]

I feel like my toes are here…

[finite inlet]

Reality can still be accurately predictable with mathematics

the things that do that is a ‘model of reality’

[sterile fable]

OMG I JUST REALIZED MY MISTAKE

[heady flame]

not a physicist
ee here, close enough
i care about it since it's good enough for my purposecs
the same concept applies to physics, newtonian mechanics doesn't hold on relativistic velocities, yet it's used extensively, because its simple and it works for everyday stuff
when pushing the boundaries of physics, yes, you need to be more and more accurate, but in the end it'll always be a model

[earnest flax]

i'm confused

[sterile fable]

I WAS JUST CONSIDERING THE SOUTH EAST ARROWS OF SARRUS METHOD

😭

i forgot about the other arrows the north west ones

[earnest flax]

ik but to create a ToE of physics as they've said, they need something that isn't mathematical

[sterile fable]

XD

thanks

[earnest flax]

[heady flame]

when considering how an apple falls to the ground, vs. an orange or a brick, you'll notice they behave in the exact same way (dont come at me fluid dynamics people)

then you abstract stuff away and say

alright an object with a property called mass m

in a gravitational field G

[finite inlet]

We only predict the necessary details that we need of reality

[heady flame]

obeys this law of motion

is it accurate? depends on what you need. but it's a model, it explains particular physical phenomena abstracted away into math

[heady flame]

call it a model of everything if you like

[earnest flax]

well i actually stumbled across this problem, ToE can't be a scientific theory bc a scientific theory must be failable so it can be replaced and strengthened in the future

[finite inlet]

What does this even mean

[heady flame]

that doesn't mean predicting every single physical phenomenon ever to occur with infinite precision, that means to have a model which is self consistent and describes all of physics we know so far accurately

[earnest flax]

when you think about the failability of something that shouldn't fail, it breaks my little orangutan brain

[earnest flax]

idk, i just read an article about that, people who writed that must've been high on crack 😭

[heady flame]

maybe, but you should use this as a learning opportunity to look stuff up elsewhere

skimming through an article, especially on something you're not an expert on, is absolutely not going to give you any useful insight, and will probably lead you down a road of misconception after misconception

[earnest flax]

it was a concept created by Karl Popper

[heady flame]

falsifiability of the scientific theory

yeah

[earnest flax]

idk what this must mean

[heady flame]

how could one test a theory of everything depends on what it is

looking at a world where only optics and electromagnetism exist, a theory of everything would be the Maxwell's equations explaining optics as em wave phenomena

it's falsifiable, not a problem with it

[earnest flax]

i was talking about hypothetically if this theory just slapped all four forces of nature together

[heady flame]

now what the mythical toe entails and whether its even possible is a different question

[heady flame]

slapped together how exactly

that's the main problem

[earnest flax]

connect all of them

[heady flame]

yeah i know what unifying means, I'm asking about how do you expect it to be done

[earnest flax]

i won't give you the answer

[heady flame]

reading a paper on the toe, what would it look like

[earnest flax]

i was thinking about not only ToE

but something higher

ToE is made to explain everything in physics

something higher can explain everything in everything (physics,biology,chemistry,history,etc.)

[heady flame]

well i suggest you turn to philosophy, going further down this road is absolutely not a matter mathematics deals with

[earnest flax]

if you think ToE is hard, just imagine this one thing lol

[heady flame]

call it god, call it a theory of everything imaginable call it whatever you want

is it possible
i don't know
but more importantly
i don't really care tbh

[earnest flax]

i wanna go absolute anonimous on this topic

[earnest flax]

it's possible

[heady flame]

i mean try chipping at it, learn some basic physics at first i suggest

[earnest flax]

what should be the basic of physics?

[heady flame]

i mean that's just a baseless conjecture, but going down the rabbit hole of putting that on solid ground is an endless endeavour i don't care about

[heady flame]

basics as in freshman physics, not as in fundamental physics

mechanics, electromagnetism, thermodynamics, fluid dynamics, intro to quantum mechanics

[earnest flax]

like i said, endless complexity

[heady flame]

that's a nice starting point

[earnest flax]

is it crazy to think i know nothing about every topic you listed( as math ), but i also know everything about the topics you listed? (as concepts)

[heady flame]

yes, because you're full of shit

[fresh comet]

it's very common to have heard of a lot, but not to have learnt a lot

[flat harbor]

"knowing smth as a concept" is being a showoff abt smth ure actually unqualified to talk abt

mightve worked in ur friend group wont pass here

i recommend u focus on ur mandatory education

[earnest flax]

thats what makes me a fake physicist

[heady flame]

doesn't make you a physicist at all

of any kind

[flat harbor]

cranks at least usually have an undergrad education

[earnest flax]

it's a fake physics bc i know of all the rules, but i don't know any math of these rules

[heady flame]

come on, you should seriously open a book and drop the ego down a few notches

[fresh comet]

then what were you trying to get at this whole time??

[heady flame]

yeah and what does faradays law state

[fresh comet]

you don't know any of the math, but are claiming that using math to describe reality is hopeless?

[flat harbor]

it like. states electricity bros

[earnest flax]

Isn't this about how if you get sum conductors around you, you wouldn't be in a shocking experience?

[heady flame]

brrr electrons go fast

[heady flame]

no

[earnest flax]

yes?

[fresh comet]

...at least have some qualifications if you're going to make such a bold claim

[flat harbor]

i know abt terms
whats faradays law
u clearly mean faradays cage

[heady flame]

i mean you dont need math to make statements like this

[flat harbor]

faraday did it too

[earnest flax]

that's what knowing only concepts is

[flat harbor]

too bad u havent focused on ur mandatory education

[earnest flax]

just common sense but "better"

[heady flame]

the problem is conceptually its also wrong

[earnest flax]

how?

[flat harbor]

mofo is in deep

[heady flame]

conceptually you could say that an electromotive force will be induced across a closed contour as a result of an existence of a changing magnetic field going through it

[earnest flax]

that's faradays law? I didn't know it was actually that

[flat harbor]

ok i read a bit of the convo above and this rly makes me want to crush some ribcages already

[earnest flax]

What

[heady flame]

mathematically you would say is that the closed loop integral of the electric field is the negative of the derivative of the flux of the magnetic field through the area enclosed by the contour no i wont use latex

[heady flame]

yeah that's faradays law conceptually, now open a book on physics and actually learn it

[flat harbor]

"a theory of everything is impossible bc science needs to change with experiment" is the most moronic take ive ever seen

[fresh comet]

you've missed hours worth of content in #math-discussion earlier today

[flat harbor]

i was there

[fresh comet]

oh were you?

dang

[flat harbor]

for like a half hr of it

[earnest flax]

i've alr learned it partially 😭

[fresh comet]

yeah this has been going on for some time

[heady flame]

no you haven't i guarantee

[flat harbor]

i think everyone in chat should just be really rude and abrasive

thatll show em

[fresh comet]

lmao

I wouldn't recommend

[heady flame]

lol

[fresh comet]

partially isn't good enough though

if we only understood E&M partially, we'd be stuck in the 1700s

[heady flame]

man i wish i was able to learn em so quickly, i would've passed with an A with like 5 mins of studying

[flat harbor]

em rly is a cakewalk if ukno up to mm

2nd yr uni math

some wuld even say freshman

[fresh comet]

I can't read mm

what is that

[heady flame]

yeah i had to take em first semester, wasn't fun but it was doable

[flat harbor]

ukno like how i go mm this cake is nice

[heady flame]

LMAO

[flat harbor]

shuld i make it three ms for u from now on

[fresh comet]

only thing I can think of is math methods

[earnest flax]

i am on high school, expecting it to be hard, as i always heard of it from others that high school was hell, but when i reached high school i was depressed, no actual pressure on me.

[fresh comet]

but I don't think that's what you mean?

[heady flame]

math math idk

[fresh comet]

real

[flat harbor]

i was literally going mmm like thats how i type text hgr cmon

[earnest flax]

I'm expecting university to atleast press me a little bit so i could learn more

[fresh comet]

[heady flame]

naw man it's all handwaving conceptual talk

[flat harbor]

the interpretation works if its mathematical methods tho so lets say it id

[flat harbor]

im sitting in a qft 2 course barely knowing how to use gauge theory and the prof starts ranting abt supersymmetry

apparently like. dimensions bro. they like work out

[earnest flax]

the amount that i learn is based on how much i'm pressed

[fresh comet]

you can just learn more on your own though

[earnest flax]

as you guys saw by my physics, no pressure

[flat harbor]

uvd been pressed to stop talking and read on this server for a whole day now and ure still here so i doubt that

[fresh comet]

no need for a uni to put pressure on you

[heady flame]

trust me bro it works heres the algorithm to calculate shit bye bye

[flat harbor]

this is what ppl mean when they say public education fails u

[fresh comet]

perhaps

idk

[fresh comet]

...does that mean you've not been pressed at all? because it seems like you haven't learnt all that much :/

[earnest flax]

But how may i learn physics on a math server?

[earnest flax]

yep

[fresh comet]

well, there's a physics server for one

see #old-network

[flat harbor]

like i see korean education burning in the dumpster but at least children are PUBLICLY SHAMED and CONDEMNED TO POVERTY if they dont take their mandatory edu seriously

[earnest flax]

high school exerts absolutely no pressure on me

[heady flame]

tbh i really sucked in hs, i was a really problematic kid, uni slapped me in the face hard, now i know what it means to study lol

[flat harbor]

i slept thru half of hs

[fresh comet]

yeah so put pressure on yourself

[fresh comet]

I mean this is a lot of people yeah?

[earnest flax]

dats why im here?

[fresh comet]

myself partially included

[fresh comet]

yeah so, why're you going on about all of this nonsense

instead of actually studying 😭

[flat harbor]

wake up at 6/45, sleep
wake up at 8, sleep
wake up at 12, lunch, sleep
wake up at 4, POWERMODE
sleep at 6
wake up at 11/45, sleep

[heady flame]

idk how its like in the west, at least for the standards of my country i was on the brink of being kicked out, not going to school for months on end etc

nah wasn't fun at all

[fresh comet]

oof

[heady flame]

i have no idea how i wasnt kicked out lmao

[earnest flax]

You saw when i was talking at math-discussion channel about the formula i had to transform rational numbers as fractions

[flat harbor]

u werent and lived to tell the tale

[heady flame]

true

[flat harbor]

if ure a phys major then u are under good care,,.

[earnest flax]

Then that girl made me talk about how i'd prove that it has no fail 😭

[heady flame]

thank god its fine now

[heady flame]

please don't shoot me

im in electrical engineering

[flat harbor]

that is also good

[earnest flax]

when literally to prove it has fails you need to prove it exists a rational number that can't be expressed as a fraction

[flat harbor]

i knew someone who recently went into grad for uhhh signal processing was it idr

they only talked abt "lang algebra" with me idk why

[heady flame]

i rather enjoy it, especially the control theory/dsp/math areas, makes me sad i did poorly on my real analysis and complex analysis courses

[heady flame]

lol

dsp my beloved

[flat harbor]

ehh uni courses be damned

[heady flame]

yeah i complain and rant all the time but seriously its a blast

[earnest flax]

that girl was asking the impossible 💀

But she talked in such complex manner it took me a load of time to even realise that's what she wanted

[flat harbor]

u were yapping thru that entire convo

[heady flame]

what the fuck

[flat harbor]

pick up a book

go

[earnest flax]

it's because the formula makes a rational number become a fraction

like 5.999... become 54/9

[heady flame]

oh no its the 0.99999... = 1 thing again

[flat harbor]

i bought a book abt numbers with 0.99.. = 1 when i was like 12 and it was easier to read back then than reading what this kid is yapping abt rn

[earnest flax]

the formula just multiplies everything by 9 so the rational becomes divisible by 9

it's like assuming there is a 1 below the number but multiplying both the numerator and denominator by 9

[flat harbor]

so yea chat anything interesting going on

[heady flame]

stuck on 17-9 again

[flat harbor]

im stuck reading smth

[fresh comet]

the door slam lmfao

as for me... idk

I'm not up to anything ig

[flat harbor]

u shuld think abt quantum things then

dont be a jaded loser like me

read.. gottfrieds qmech... smell the roses

[fresh comet]

gottfried?

I've not heard of that one

lemme see

[flat harbor]

it might not be a friendly first read of qmech

[fresh comet]

better or worse than Shankar?

[flat harbor]

but u dont need a friendly first read if ukno how to solve diffeqs and know linalg

i havent read shankar gimme a sec

[fresh comet]

I mean I've thrown myself into the fire before

I can do it again

[heady flame]

would you recommend it to learn about some basic qm for semiconductor physics (man i still don't know howa a bjt works lol)

[flat harbor]

mmmmm

i actly didnt pay attention for the semiconductor part of the solid state course i took last yr

but it didnt use any concepts beyond whats in griffiths

[flat harbor]

i think the two are similar

if i had to choose in particular tho

[heady flame]

fair enough, i'll give it a shot regardless, will see how i do haha

[flat harbor]

id say the last chapter of gottfried is amazing

many books kinda shy away from talking abt fundamentals

shankar looks like it has a lot of good discussion upfront

[fresh comet]

I see

okay, downloading Gottfried rn

[flat harbor]

i think qmech is definitely like

Intensively studying over the course of a year

*worth is meant to go somewhere in that sentence

[fresh comet]

I see

I'm pretty sure my uni uses Cohen-Tannoudji, which I've heard a lot of complaints about

from seniors and such

so I wanted smth diff

[flat harbor]

never heard of that one

[fresh comet]

yeah bc it's bad according to everyone I've asked lol

[flat harbor]

ug books are all similar id beliebe

gottfried has a lot of discussion abt fundamentals upfront as well iirc

[fresh comet]

that makes sense

I'll take a look at Gottfried

[sterile fable]

how would change in mass effect a stepper motor

[wraith holly]

can someone explain to me what ^^ means cuz im looking online and it doesnt seem to give me a straight answer. i saw something saying its tetration but i just wanna confirm so i know what im looking at

[tacit magnet]

³b=b^b^b its the tetation notation

[fair mural]

^^ is also tetration notation

[wraith holly]

so if i wanted to notate b^b^b i would say b^^3

[north topaz]

@odd narwhal Why do you sound Scottish

[finite inlet]

I saw it and it was kinda dumb

kinda was a light word, actually….

[woven basalt]

he's Scottish

no wait i think loch was scottish not him

[north topaz]

He isn't I think

[woven basalt]

the username he has rn is i think his name which is scottish

he told me once

ok wait he might not be

i checked the chats and he said that its pronounced the way scots pronounce loch

so doesn't really mean hes scot lmao mb

[north topaz]

You can find out where he's from from watching the YT channel in his bio

[minor current]

how to stop sucking at math

[woven basalt]

oh alr lol didn't know that

wait i dont see any channel link in his bio

[scenic pond]

⬞

[sturdy vector]

dont stop sucking

[solar bronze]

Is there a term for the case in which there exists $f(p(x)) \neq p(f(x))$ for the individual functions $p$ and $q$ such that $p(f(x)) = x$ and $f(q(x)) = x$?

[fathom swallow]

Andrew Porter

[fresh comet]

this seems like an oddly specific property

[solar bronze]

wha

[river moon]

perhaps you're just looking for an f which is a right inverse of p and also f has a right inverse which is q?

[solar bronze]

I'm asking for the names of p and q if there exist any already

[fresh comet]

left and right inverses of f me thinks

[solar bronze]

Or is anyone opposed to calling them inner and outer inverses?

[fresh comet]

it’s usually left and right afaik

[solar bronze]

weird

[fresh comet]

because p o f = id and f o q = id

[solar bronze]

Bruh moment

[fresh comet]

(assuming they all have the same co/domain)

but that doesn’t really change their names regardless

[solar bronze]

Those names are awful. Common L in math.

[fresh comet]

???

how is it awful

[solar bronze]

Inner and outer seems to be more intuitive for what it is

[fresh comet]

well I mean, there’s function composition notation you know?

[solar bronze]

"left and right" is merely intuitive with respect to that notation for function composition

[fresh comet]

It’s the more common notation

[solar bronze]

Next, you'll tell me I need to say Oil-or-Macaroni constant instead of logaroharmonic limiting difference constant

[fresh comet]

what?

[solar bronze]

Unfortunately it seems to have rubbed off a bit in computer science. I still have no clue what a Red-Black Tree is. I always forget.

[cunning plaza]

Inner and outer would be confusing to me. Left and right inverse is accepted and easy to write.

[deep mango]

Its just bad because you dont know if its in terms of the expression or the diagram

Idk how inner and outer is more confusing than something thats actively ambiguous

[cunning plaza]

Oh? Maybe I'm wrong then. I thought left and right was the generally accepted terms for dealing with an inverse.

[solar bronze]

Right... back to solving $a(n+1) - a(n) = k$ without mathematical induction...

[fathom swallow]

Andrew Porter

[cunning plaza]

I am confused on why you would not want to use a tool to solve a problem.

[deep mango]

They are accepted thats true

I just think its ambiguous

[solar bronze]

I want an algebraic means of solving algebraic problems, and reason for proofs.

[deep mango]

Whats a here?

[proud olive]

Whats wrong with induction?

[deep mango]

If a's defined inductively

It might not be possible

Since you have to "get out of the inductive definition" somehow

[deep mango]

Sometimes its just nice to understand multiple distinct proofs of a fact

[proud olive]

A direct proof would basically just turn into a more detailed version of a proof by induction

Ig you can do a proof by contradiction

[solar bronze]

Well I've defined that we have some $A_n = {a(n)}$

[fathom swallow]

Andrew Porter

[proud olive]

They're a bit less intuitive for me but the still ofc can be made sense of

[deep mango]

Depends a ton on what An is

[solar bronze]

Just an arbitrary set defined by some arbitrary operation or set of operations $a$

[fathom swallow]

Andrew Porter

[deep mango]

You can ofc do it superficially since induction is equivalent to N well ordering

Transforming any proof by induction into a proof by contradiction

[solar bronze]

Well like I said...

[deep mango]

(Let n be the smallest number such that P(n) doesnt hold, then P(n-1) holds, we use that to conclude P(n))

[proud olive]

Fully possible to do this with proof by induction

[solar bronze]

I'm aware

[deep mango]

Then again, it depends on An. Some Ans are defined algebraically. Some are defined inductively. Some geometrically

However you define An should be your goal for how to write a proof imo

[solar bronze]

Whatever means "any and whatever" is what $a$ and $A_n$ are, though I'm not sure to what extent that's rigorous or not and what the rigorous equivalent is.

[fathom swallow]

Andrew Porter

[deep mango]

If An is defined in terms of Ak for k < n, it's not going to be possible. No matter what you do, you need to use induction to "unroll" the definition somewhere.

If you means something like "An is the nth partial sum of a series"

Then that can often be done without induction

And there are typically nice algebraic proofs, or nice analytic proofs, or nice geometric proofs. But no one size fits all technique

[solar bronze]

Wait, maybe I'm just stupid. $a(n)$ is just an arbitrary sequence of numbers (which defines a set, and $n$, an index into that set).

[fathom swallow]

Andrew Porter

[deep mango]

(After all, many series are already written in their simplest algebraic form)

[solar bronze]

However $a$ also implicitly defines the rule for that sequence.

[fathom swallow]

Andrew Porter

[solar bronze]

(via the recurrence relation)

[deep mango]

Ok, so you have some sequence a(n) defined by an algebraic formula applied to n, and you want to prove something about every term in the sequence?

[deep mango]

Recurrence relations are inherently inductive which is what i meant here

[solar bronze]

I want to be able to solve for arbitrary $a(n)$, and also prove that the steps are sound and true.

[fathom swallow]

Andrew Porter

[solar bronze]

Like one idea I've been messing with, if you catch my drift here, is: $a(a_{index}(n) + 1) + n = k$

[fathom swallow]

Andrew Porter

[deep mango]

Hmm

[solar bronze]

Here's where I'm at so far. This likely won't all be rigorous in terms of wording. (see "List of Recurrence Relations in Order of Complexity" folder) https://www.desmos.com/calculator/kohqgsfpoq

[sturdy gulch]

"e and pi are transcendental" mfs when i show them xln(x) - x = 0 and sin(x) = 0

[fresh comet]

well those aren't polynomials...

[neat lintel]

sin x is a polynomial with veeeeeeeeeeeeeeeeeeeeeeeeeery high degree

[fresh comet]

real

[sturdy gulch]

also that's the joke lmfao

[fresh comet]

I see

I'm not particularly good at detecting jokes

[empty saddle]

im doing data analysis right now in python and this feeling is so great when things just work together, do you know what i mean?
it is so cool that packages like uncertainties just exist and work nicely

[latent edge]

holy shit I should call the nobel prize peeps for this

this is some cutting edge math right there

[neat lintel]

[fluid terrace]

I need help with quadratic functions

[visual breach]

It also in R[[X]]

[sleek pagoda]

If I wanted some spherical geometry where all of euclids axioms are true beside the 5th one, does a half sphere work

[sour temple]

im going to get a summer job for 2 months to buy FL studio and the rest of the money will be used to buy Minecraft and Geometry Dash on my laptop

[north topaz]

The problem with a half-sphere is that you can't define lines properly

On a full sphere, the line going through 2 points can be extended all around the sphere

Whereas you cannot extend lines indefinitely on a half-sphere

You've contradicted postulate 2

[north topaz]

And so the line will pass through the same point infinitely many times: you can keep going around and around the sphere infinitely

[raven plaza]

I'm wondering if this actually violates postulate 2

I don't know Greek but it seems some people interpret it as requiring the line be extendable "indefinitely" while some don't

[old oak]

You could always do the open half-sphere

[raven plaza]

This too

What does "indefinitely" mean

Infinite length?

Actually how do lengths work in Euclidean geometry

[heady flame]

i presume it means without any arbitrary limits imposed

[raven plaza]

I don't think it is required that straight lines be locally geodesic right

Oh but if we change length then circles change too

[crimson geyser]

I'm wondering if this actually violates postulate 2

[main delta]

Ok, so you have some sequence a(n) defined by an algebraic formula applied to n, and you want to prove something about every term in the sequence?

[quasi roost]

hoffe dir geht es bald besser ☹️

[solar bronze]

What is the fastest converging series known for any given function that cannot be expressed in elementary functions? Highest I've at least heard is quadratic convergence.

Is something like exponential or factorial convergence possible?

[solid snow]

there is no fastest converging series

[solar bronze]

Not the question

[neat lintel]

Mfw

What is the fastest converging series…. ….functions?
Not the question

[solar bronze]

The fastest converging series known

(uniformly convergent)

[neat lintel]

‘there is no fastest converging series’ implies that you know the existence of a series that converges faster than the fastest converging series known thus making the new series the fastest converging series known

The fastest converging series for pi is just pi

[solar bronze]

Yeah... how about a limit bruv. With all due respect, I didn't ask to get a joke answer.

[neat lintel]

fast converging limits are more interesting

[solar bronze]

Yeah, but what else converges non-trivially except things that have non-trivial limits

[finite inlet]

somewhat analogous to the series, the limit of pi as x approaches pi converges to pi really quick

[heady flame]

i mean whatever series you cook up i can just take and multiply each term by 1/n
yeah its not the same series but it will converge faster

if that's what you're asking

[neat lintel]

https://www.researchgate.net/publication/276483614_Fast_Converging_Series_for_Riemann_Zeta_Function I found this and it looks interesting, I don’t think I have the capability to understand it enough though

[solar bronze]

First, I will disclaim I don't fully understand limits. Now then. You have some $f(x)$ approximated by some limit $\lim_{y\to A} g_n(x, y) = f(x)$ that exists for unknown $A$ with $g_n$ being the set of approximations that differ by convergence where $n < n+1$ means $g_n$ converges slower than $g_{n+1}$. What is the fastest known $g_n$ of all $g_n$ of all the known $f$?

[fathom swallow]

Andrew Porter

[solar bronze]

Bruh how is $g_{n+1}$ getting formatted like that

[fathom swallow]

Andrew Porter

[solar bronze]

BRUH

[heady flame]

you might want to take a look at this wiki article, i believe this is what you're asking about

https://en.wikipedia.org/wiki/Rate_of_convergence?wprov=sfla1

that being said, there's an example given by numerical integration, and you can always just use a higher order integrator to speed up convergence if i understand this correctly, although im most definitely not well versed in numerical analysis

so take this with a grain of salt

[solar bronze]

Interesting

Yeah some series I've seen don't seem to be useful for numerical approximations as much as they are just useful identities in particular instances.

I'm also of the opinion that for transcendental functions, a limit involving constants is preferable to even a rapid uniformly convergent sum or product as I only have to adjust a constant to get more accuracy.

I look forward to learning more about limits presumably in Spivak

[heady flame]

i took a closer look, it's not the order of the integrator but the "timestep" which is affecting convergence, but i believe in general this answers your question

as far as i understand, there's no hard cap on the order of convergence, and also as i said, for whatever function you take the power series definition of, i can force it to converge quicker by multiplying each term by 1/n, and calling it a different function with a faster converging power series

[heady flame]

preferable in which way? if you don't care about numerics, I don't think this matters, it's just aesthetics

then again please take what im saying with a massive grain of salt, im not a mathematician, i just happened to use quite a bit of math results

[solar bronze]

Well take a limit of the exponential function for instance: $e^z = \lim_{n\to\infty} \left(1 + \frac z n} \right)^n$ as opposed to using its taylor series directly. Use that to get something fast within some range of values, and then exploit properties of the exponential to go from a small subset of values to the entire domain as just one possible idea. $n$ can be some arbitrarily large constant.

[fathom swallow]

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

[heady flame]

and also, please for the love of god learn limits properly before learning further results from calculus, because they are the foundation of the rest of calculus

concrete example - talkimg about series, series are defined as a limit of partial sums up to N as N tends to infinity

[solar bronze]

I can't type

[heady flame]

im not sure this is correct, as n can't be a constant, since you're taking the limit as n tends to infinity

say for example n=1000, what does $\lim_{1000 \to \infty} 1000$ even mean

[fathom swallow]

мосар свадбе и сахране

[heady flame]

i appreciate the inquisitive questions, you should keep asking questions, although i don't think its productive to go that much further with questions until you're solid on the fundamentals

[solar bronze]

Mosar, porzalujsta...

[heady flame]

oh shit i assume this is supposed to be russian

[solar bronze]

Yes because am pleb without Cyrillic keycaps

[heady flame]

im not russian :D
although to be fair i speak russian a little bit

I'd like to learn it properly, I quite like Russian, it's a nice sounding language to me

[solar bronze]

One thing I've been working more towards in general is away from the numerical and magnitudinal to the symbolic because it has the same accuracy and preservation of information as just doing things by hand without need for approximation.

Problem is implementing the various ways to compare at least, and I'm not sure what else is necessary to make a purely symbolic approach work here.

That is to say, for any arbitrary $f(x)$, I need a way to know when $f(x) < f(y)$; $f(x) > f(y)$; and $f(x) \equiv f(y)$.

[fathom swallow]

Andrew Porter

[solar bronze]

You can imagine how that might be a lot cheaper if $f(x)$ is perhaps $\Gamma(x)$

[fathom swallow]

Andrew Porter

[heady flame]

One thing, I believe this shouldn't be equivalent, but equals, since you're talking about numerical values, although they're written in general symbolic form

[solar bronze]

I'm not always certain on what the best notation is in cases like these 🙂

[heady flame]

That being said, you would need definitions of binary relations of comparison

That's a quite a bit out of my range as far as my understanding of math is concerned, but i do recall my algebra professor talking about this in passing

[heady flame]

Excuse me, it's a relation, not a binary operation

[solar bronze]

I've tried this already with some simpler things like symbolically comparing $a^b$ and $c^d$, it holds that $\ln(a^b) = \ln(c^d)$, and if we have some approximation of $\ln x$ such that it retains its comparative properties, then instead of representing $a^b$ and $c^d$ as magnitudes and directly comparing two potentially massive numbers, I can use the approximation to compare them.

[fathom swallow]

Andrew Porter

[solar bronze]

Though ideally we would have something that just gives the smallest two comparable integers in base 2 which are 0 and 1 as the inputs to some compare instruction.

Then again, I guess, using Iverson bracket notation, what I need in general for symbolic computation is things like $[x<y]$, $[x>y]$, and $[x=y]$?

[fathom swallow]

Andrew Porter

[heady flame]

I mean if you delegate comparison of two numbers to their images under monotonous functions you're just moving the goalpost of defining the relations of order. That being said, it's quite commonly done to take a log of large numbers (and generally if you're comparing functions on a large range), that's the idea of a log scale. An example from my field would be the Bode plot, concretely the amplitude/frequency plot

[heady flame]

I don't know anything about Iverson brackets, can't help you with that one. Perhaps there's something on Wikipedia?

[solar bronze]

Iverson brackets as an operation yield 1 iff its input is true and 0 iff its input is false.

[heady flame]

To be fair, me talking about monotonicity of functions doesn't make sense without defining the ordering relation in the first place, I'm speaking from an intuitive position, which is absolutely not rigorous at all

[heady flame]

Fair enough

[solar bronze]

I'm speaking intuitively as well.

[heady flame]

shit i can't post a screenshot

regardless, you might want to take a look at relations

[solar bronze]

I'll get there eventually

For now tho, back to thinking about how to define literally every idea ever, and what else my dictionary needs for that.

[heady flame]

Good luck

[surreal sapphire]

notice that to even define rate of convergence you need a metric and that results will depend on the metric

[heady flame]

considering he said he wants to get through math from the axioms up i think it will be a while until he gets to metric spaces lol

[surreal sapphire]

eh, a standard class on real analysis will start with "what is a number?" and define metric spaces in a week

[heady flame]

man i hate my analysis class, we jumped pretty much straight into limits after about 2 hours which i slept through

tbf its engineering so its to be expected to be lousy

nope im lying i just took a look at my textbook

apparently we started with cardinalities of sets, defining functions and into sequences

i really should learn analysis for real now that i care about it lol

[viscid thicket]

really?

[glass peak]

And then there’s my uni, where you do 2 analysis classes before you ever touch metric spaces because… who fucking knows

[fresh comet]

fwiw I haven't formally touched metric spaces either

and it's been 2 semesters of analysis

[viscid thicket]

right?!!

mine you'd have to go to introduction to topology iirc

[neat lintel]

does anyone here work in finance or graduate witha finance major? im looking to ask a few questions

[glass peak]

they used to do metric spaces in analysis but now its its own course for some reason

But eh, was an easy class, just praying the exam isnt awful]

[stone fulcrum]

I'm doing a project in option pricing, dunno if that helps

Also, have questions of my own lol

[next blade]

maybe rather than asking to ask, just ask your question and see if anyone answers

[narrow zealot]

is anyone here a aerospace nerd

[neat lintel]

https://tenor.com/view/peter-griffin-perhaps-family-guy-thinking-gif-13587558

[neat lintel]

Are you in graduate school

[stone fulcrum]

Well, not exactly. I'm almost done with my masters, but it's a dual Bachelors and Masters 5 year programme

[neat lintel]

What r u studying

[faint escarp]

Hey guys, I will write my bachelor thesis this semester about applications in persistent homology. Do you know something cool which I could write about?

[latent edge]

!noadvert

[quasi jetty]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[neat lintel]

duck wanted to join and he cant do dms due to parental controls or smth

[latent edge]

what are you doing to hyzae smh

send me da link

in dms

[sleek pagoda]

the problem with the sphere is that there are multiple lines that go through opposite points

I thought removing the bottom would get rid of that

Would the real projective plain work

[delicate swift]

Where is

Help

[sleek pagoda]

I can't post an image

Below the introduction section in the side of the server

There is the Math help section

The instructions are in #❓how-to-get-help

[storm sage]

The real analysis course here doesn't define a metric space until the end of the semester

Which I think is standard of a lot of the textbooks I've seen

Besides Rudin

[jagged forge]

hmm. all i know is rudin tbh

[fresh comet]

my real analysis course didn't define a metric space, period

it was two semesters too

but, we'll see them in a topology course soon

[surreal sapphire]

well, its standard in europe

[young quartz]

there aren't any people here doing analysis or algebra?