serious-discussion

[echo dragon]

who's good at graphs pls dm me i need help

[lunar spear]

Whats good

[leaden torrent]

@echo dragon please dont multipost.

[echo dragon]

srry

[still vortex]

Hi

[modest rune]

fwiw in the grand scheme of things

using extra energy to cool yourself is probably a pretty reasonable thing to do

there are much worse wastes of energy and you making yourself uncomfortable isn't going to do anyone all that much good

unless ur worried about the cost of electricity in which case its a different convo I guess

[sick burrow]

What is a good free video editor

[arctic grove]

filmora is pretty nice

[neat lintel]

If you're a mobile user like me, inshot is the one I prefer the most

[bright hill]

I would tell you but I'd get in trouble :)

[arctic grove]

why did i get sullied

darq why did u sully me

[bright hill]

filmora sucks bro

it's like a video editor for mobile

[flint kayak]

?

[bright hill]

but for pc

[bright hill]

please read #❓how-to-get-help

[arctic grove]

[flint kayak]

sorry

i'm new

[bright locust]

Did you not read #rules

[uncut socket]

Tough major

[molten tartan]

most def

[uncut socket]

I did EE

[sacred forge]

hello

[river spire]

why say this instead of saying the conclusion is true / probable

[lunar spear]

How come my phone be falling on concrete and nothing

but the floor at home and this shit breaks

[tawdry falcon]

f

[wild lantern]

An deductive argument can have a false conclusion and still be valid

It depends on the truth of the premisses.

[chilly coral]

Validity vs soundness

[wild lantern]

"If I am Mozart, then I am spaghetti. I am Mozart. Therefore I am spaghetti." <- A valid argument with a false conclusion.

[storm sage]

you can say that

"the conclusion is true given that the premises are true"

and then "the conclusion is probable given that the premises are true" for the second one

they probably just used the word "impossible" for emphasis

or I dunno

I'm not the author

[severe depot]

Is it worth me retaking year 12 to do a level maths I want to do economics at uni?

[storm sage]

you can learn the math in uni

[limber thunder]

or just review year 12 maths by yourself

that's a better time investment than retaking anything

[storm sage]

yeah I wouldn't retake unless you have serious gaps in other subjects too

[molten tartan]

I did high school algebra in college. It was remedial and didn’t count towards my degree, but now I’m finishing up the last of my math in my electrical/computer engineering degree. Also Khan Academy is the shit, if you want to practice high school level math.

[river spire]

yeah I i've heard this definition too, it just seemed odd for the author to write it this way so I thought there might have been more reason to it other than trying to look swag

[neat lintel]

@opaque sail what if the linear terms are < 0 doesn't that give a even smaller number

[opaque sail]

since we're minimizing their squares the minimum is when they're 0

[neat lintel]

oh

well

what did u get finally by that method?

[atomic fiber]

@opaque sail how would making the square terms 0 give us the minimum

[opaque sail]

completing the square twice gives $(y+1.5x)^2 + 0.5 (x-2)^2$

[fathom swallow]

Tom

[opaque sail]

then the smallest this can ever be is 0 since both terms are >=0

and we can get both to be 0 with x=2,y=-3

[atomic fiber]

Ohh so it is two perfect squares

[neat lintel]

interesting

[cobalt vigil]

y is maths so big

[surreal sapphire]

we have been doing it for like 4000 years

[quiet geode]

a set is infinite if and only if it may be placed into one-to-one correspondence with a proper subset of itself

i dont get this

[sleek wing]

Try doing it with a finite set

[quiet geode]

I mean i get the idea

but

im uncomfortable

[leaden torrent]

which direction is unintuitive to you?

i think this is a really good characterization of "infinite" personally

"infinite" means individual elements dont really matter for the "feel" of the set

[sick kite]

That is the sexiest intuition for infinity I've ever heard

[quiet geode]

idk how to explaim

[vivid halo]

yeah I mean it feels weird because somehow a proper subset should be "smaller"

so it's weird to say that a proper subset has the same size as the original set

[quiet geode]

Why must a set be infinite just because of some property of finite sets?

[vivid halo]

but this is fine for infinite sets

this isn't about finite sets

or rather, it's saying finite sets are exactly the sets where you cannot do this

[quiet geode]

nice

[vivid halo]

like idk take the set of natural numbers {0,1,2,3,...}

[quiet geode]

now im even more confused lmao

[vivid halo]

take the proper subset {1,2,3,...}

there is an obvious bijection between these

say adding 1 to go from the first to the second set

since there is a bijection, these sets have the same size

but one is clearly a proper subset of another

[quiet geode]

is it like that because you cant prove it otherwise

[sick kite]

Meaty what's infinity - 1

Or for that case

Infinity- any finite number

[echo dragon]

does anyone how to make any of the following? pareto chart, histogram , frequency graph, sector graph, stastical display if so dm me please

[old fox]

textbooks vs video lectures, which one do you prefer?

[charred mortar]

I generally go for books

video lectures make me lose focus in the first minute

it's mostly just a me thing

[toxic gale]

Books for me as well. I like being able to reread the same proof over and over again to understand it and skip some examples that I find tedious.

[naive chasm]

i have very (VERY) short attention span, so books

[storm sage]

linear b

[silent moat]

Someone from there I assume sent me a message (have no idea why?) and then left right away.

Is that common here

[leaden torrent]

they have been banned

[silent moat]

Oh ok

The question is why would they have thought I could have been helpful

Or if they do that to everyone

[leaden torrent]

they sent it to a lot of users unprovoked

[median hill]

Wtf that man dm’ed everyone or what?

[leaden torrent]

hence one of the reasons why they were banned

[toxic gale]

This reminds me why I have DMs turned off.

I have no idea how anybody could think that it is socially acceptable to DM someone asking for help out of nowhere just because they are members of a math server.

[naive chasm]

change

my

name

@polar panther

[vivid halo]

[naive chasm]

i dont like that

at all

im gonna cry

the online harassment is too harsh

[neat lintel]

[naive chasm]

https://tenor.com/view/disney-plus-disney-sad-sad-eyes-sad-face-gif-15549594

[celest ferry]

hyyy guys

[wind igloo]

Hello friends

Is anyone active?

[surreal sapphire]

quite many people have the active role

[vivid halo]

how come most people talking have the active role?

[fervent pebble]

probably bc they're all nerds

[prime plover]

omg there were 13337 online.

[fervent pebble]

sounds like a sign to go and pirate some things

it's not exact but close enough

[prime plover]

i taught my professor how to pirate math books yesterday. I was suprised he didnt know

[fervent pebble]

doing the lord's work

[fervent falcon]

Any tutors around

?

[mint canopy]

#❓how-to-get-help

[cinder musk]

teach me

please

[prime plover]

idk what the rules are here, ill pm

oh nvm then

[cinder musk]

thats the website?

i assume

[vivid halo]

You’re not supposed to talk about that here

But yeah

🙂

[cinder musk]

thanks

😃

[leaden torrent]

yeah our rules wrt piracy are basically just, "dont get the server banned"

we do not care what you do personally, but please dont link pirate sites or explain how to pirate things or openly advocate for piracy or anything like that

[ancient flame]

🏴‍☠️

[prime plover]

Not even advocate piracy! dam, i feel oppressed 😦

[leaden torrent]

discord global rules

[prime plover]

jk ofc

[hollow ginkgo]

That only applies to digital piracy, right?

[leaden torrent]

discord's tos does not distinguish

it says "stolen goods"

i believe this means it technically applies to nautical piracy as well

so uh, dont advocate for that either.

(theres also a generic clause against any sort of illegal activity, which would also apply)

(but thats less funny)

[rotund cove]

every time i make a algebra mistake b/c of my handwriting i rage so hard im about to smash my computer. i fucking hate math i cant take it anymore

[neat lintel]

work on your handwriting instead of damaging your property

[rotund cove]

i want to choke u

[neat lintel]

get to know me a little better before you go there

[cold needle]

lmfao

[summer sandal]

I once pulled up my old algebra 1 workbook and man my writing was big af. mx + b will take up 1/3 of single page.

A big reason I hated doing row reduction on nxn matrices for n = 3,4 for a while in high school.

[tall badge]

4x4 matrices

[summer sandal]

Yep. Me and matrices were best friends before LA. Projection matrix, view matrix, model matrix. My three favorite matrices.

[tall badge]

before la

[toxic gale]

I had the opposite handwriting problem. I used to squeeze a 5 by 5 matrix into a single line.

[tall badge]

scary

[clever knot]

I would be interested in seeing someone fit a 5x5 matrix between two lines of normal paper

[rotund cove]

do any of u actually remember this

or do u just start from this

(eq10 is a special case of the latter one)

where the parametric curve r(u, v) can be just described as z=g(x,y)

i feel like it would be a lot faster if i just remembered the special case one but unfortunately im autistic so i can't remember this kinda stuff

[neat lintel]

most would start from the second and derive the first, it's less to remember that way

a bit more work (to go from 2 to 1), but at least the work is straightforward

[rotund cove]

ok that's good to know

i bet geniuses remember every line written on a textbook ever tho. that's how they solve hyper autistic problems

[neat lintel]

every line?

[rotund cove]

they probably remember every line in every proof

[vivid halo]

no, but it's much easier to remember how to derive it from something more general

[rotund cove]

is that the generalized one

[vivid halo]

yeah

[rotund cove]

i haven't gotten to that yet. and i probably never will (im glad)

[vivid halo]

it's certainly nicer than memorizing complicated formulas

[rotund cove]

that's true my memory is bad so it's easier to start from ez formulas

[clever knot]

I see but really hard to see the scale without a reference object. I suppose I'll take a look at a piece of paper

But indeed small

[summer sandal]

I am impressed. Well I don’t see any rational numbers.

Lol I am dumb.

[clever knot]

Beauty of digital is infinite pages and space

[summer sandal]

You know what I mean.

[toxic gale]

More scale I guess.

[charred mortar]

that'd be impressively frustrating to read for me

[toxic gale]

Oh even that is too hard for me to squeeze. I'd write it inline as a/b instead of \frac{a}{b} though.

[toxic gale]

I feel bad for putting some of my teachers through that phase.

[summer sandal]

You know what’s worse doing row reduction in latex.

[toxic gale]

That is pain yeah.

Even more pain before I learnt to make a matrix command.

Had to do the whole begin and end bmatrix shenanigans.

[charred mortar]

now I just say "check it yourself on Mathematica"

[clever knot]

Okay

[wooden widget]

noice

[sage remnant]

Anyone got work sheets with tasks/ridles

[proud olive]

The hottest equation of them all

[brittle socket]

That's nice handwriting for that size tho

[chilly coral]

Yo why don't the complex numbers have order? Like, I could easily define an order a + bi < c + di if [a < c] or [a = c and b < d], and this order is consistent with the real number ordering. Why did the people who made complex numbers arbitrarily decide "nah these will be an unordered set?"

[dense belfry]

There isn't an order compatible with the field structure

[leaden torrent]

for example, with your ordering, i would be positive [0 + 0i < 0 + 1i]; but then we have a positive number * a positive number that produces a negative number

since i*i = -1

[chilly coral]

Yeah, I realized that after posting lol. I forgot to check if order is still "preserved" under field operations, which it isn't

[leaden torrent]

you can order any set however the hell you want

when we specifically say "ordered field", we mean the order works with the underlying field

otherwise we just have 2 totally disjoint structures (an order and a field structure) on the same set

which is like, fine, but not really mathematically interesting

[chilly coral]

How do we know, though, that there's absolutely no possible ordering that's "compatible" with the field?

[leaden torrent]

do cases

suppose i > 0; then the proof i gave above works

i cant = 0 or its not a proper ordering

so suppose i < 0

then -i should be > 0 (since it's a negative times a negative), same problem

[chilly coral]

Fair enough

[leaden torrent]

there are more big boy ways to prove this fact, but no need to nuke mosquitos here

[dense belfry]

Lol I was trying to do this via that theorem about R being the unique archimedean complete ordered field

[leaden torrent]

though one of these facts has the far more interesting statement: the real numbers are the only complete ordered field (up to isomorphism)

[dense belfry]

Don't you need archimedean for this?

[leaden torrent]

that is to say, if you have an ordered field (i.e. a set that's a field, with an order compatible with its field structure) and it's "complete" in the sense that every nonempty subset with an upper bound has a supremum in your field, then that field is isomorphic to R

[leaden torrent]

nope

[dense belfry]

Oh every complete ordered field is archimedean

[leaden torrent]

right

i mean i guess you technically do in the sense that

its a corollary lmao

but yeah you dont need it in your hypotheses

[chilly coral]

BRB gonna look up what isomorphism means

[leaden torrent]

oh i thought youd be familiar with the jargon

[dense belfry]

[leaden torrent]

uh it just means "the same up to relabelling" basically

like

the numbers might be labelled differently but the "arithmetic" behaves identically

(and there exists an invertible function to "convert between" the labellings)

[mint canopy]

Not true. Non-archimedian examples exist.

[leaden torrent]

really?

[mint canopy]

E.g. the hyperreals

[leaden torrent]

am i having a dumb moment

[dense belfry]

Yeah I wasn't sure

[mint canopy]

The universal property is rather that it is the smallest complete archimedean ordered field

[dense belfry]

Before

Lol

[chilly coral]

I'm familiar with very sporadic jargon as a result of being self taught and not learning courses in the proper order lol

[mint canopy]

I'm not totally sure if it's the unique one, let me think about that

[leaden torrent]

i am confused by your example of the hyperreals

how are they complete

[dense belfry]

Lol

[mint canopy]

Am I mistaken in thinking that they have the LUB property?

[leaden torrent]

they do not

[mint canopy]

My mistake then!

[dense belfry]

I'm unsure actually

[mint canopy]

Yes in fact I can see that upon reflection

[dense belfry]

If they do

[leaden torrent]

suppose you have a LUB

take an infinitesimal less than it

thats an upper bound less than your LUB

sirens start blaring

the apocalypse commences

[dense belfry]

Okay yeah

[mint canopy]

I'm trying to think if lowenheim–skolem can be used to show that larger such fields exist

I don't think so

[dense belfry]

No the theorem statement was correct

As nami said it

Lowenheim skolem only works for first order

[mint canopy]

Yes, but I was thinking about whether or not that property could be expressed as a countable 1st order theory

But in fact it can't

At least I don't think it can

[leaden torrent]

i mean, we just showed it fails for the hyperreals, no?

which means it cant

[mint canopy]

Uh, this is different Namington

[leaden torrent]

oh

okay namington truly having a dumb moment

[dense belfry]

What are you trying to show then

The theorem that nami said is correct

[mint canopy]

The idea that I had is you could use Lowenheim–Skolem to produce an ordered field of a larger cardinality than R, but I don't think that's the case

[dense belfry]

If you Google it

[mint canopy]

Yeah I did google it, thanks Emma

I was just, you know, thinking

[dense belfry]

The hyperreals are a larger ordered field

Have you read stuff about the hyperreals?

[leaden torrent]

i mean yeah the point is that this shows that the LUB property isnt a first order property

[dense belfry]

I've read most of Goldblatts lectures on the hyperreals

[mint canopy]

The hyperreals are elementary equivalent to R, this much is true, but I was not talking about the hyperreals in the idea I was just talking about

And yeah I agree Nami

[dense belfry]

But that's my only real exposure

[leaden torrent]

sure but the point is that the hyperreals contain all true first order statements about R

i might have that statement slightly off

but its morally correct

[mint canopy]

I did just say that the hyperreals are elementary equivalent to R, yes

[leaden torrent]

okay then you must be talking about something else, sorry

[dense belfry]

The hyperreals are stronger than just fol

[mint canopy]

No I am talking about the same thing lol

[dense belfry]

At least in the better constructions of them

[leaden torrent]

i mean in this sentence:

Yes, but I was thinking about whether or not that property could be expressed as a countable 1st order theory

[dense belfry]

Where you expand your universe by adding names for things

[mint canopy]

Yes, and we resolved that question :)

[leaden torrent]

k

namington not smart

sorry

[dense belfry]

So the hyperreals are a strong counterexample

To completeness not being expressible

[mint canopy]

Yes, we've been through this

[dense belfry]

Oh I was adding I thought

Because you were saying infinitary fol before

[mint canopy]

Aaaaaaaaaaaaaaaaaaaaaaaa

[dense belfry]

And I think what I'm saying covers infinitary fol

Lmao

[mint canopy]

Yes! We've discussed that!

[dense belfry]

I am allowed to explicitly say things

[mint canopy]

I just don't know why you're repeating things

[dense belfry]

Because it wasn't clear that that's what was said?

So I am clarifying

[leaden torrent]

hey, did you know the reals are the only complete ordered field up to isomorphism?

if we're in the spirit of repeating things

[dense belfry]

Anyway what is your wider interest in the hyperreals?

I'm interested in them because I'm trying to understand the transfer principle better

[mint canopy]

I'm not interested in the hyperreals tbh. They came up when I was studying Los' theorem and I haven't studied them since.

[fading zealot]

Where can I read about providing seeds for replicating randomly generated results?

[dense belfry]

Are you a mathematical logic student?

[mint canopy]

I did a couple of modules on mathematical logic but my main focus is in algebra.

[dense belfry]

Oh cool

Do you know about algebraic approaches to logic?

[mint canopy]

I am aware of boolean and heyting algebras

[dense belfry]

Do you know anything about intuitionistic logic?

Sorry if this is too many questions

[mint canopy]

I do, I've done a fair bit of Coq

[dense belfry]

Oh that's neat

[mint canopy]

It's cute, but it doesn't fill me with hope for computer-aided proof

[dense belfry]

Agda seems lit tbh

[mint canopy]

I messed around aaaaagggessss ago with agda

I don't remember a lot about it

I hear set theorists like it

[woven whale]

agda sounds like an ugly dog

[loud rivet]

Silver DA

[near dragon]

Hi there

[mint canopy]

Silver DA?

[loud rivet]

Agda

[mint canopy]

LMAO

[vocal roost]

Question: Is there a good reason why we should have the distinction between natural numbers and integers?

Background: Debate about 0 being a natural or not and im fucking tired of it.

You can't get any good google result nowdays and i'm contemplating my life choices.

[mint canopy]

They are simply different sets and you often want to use them for different things. In that 'debate', people were trolling you bc the question of whether or not 0 is natural is not helpful.

[vocal roost]

and apperently my brain is starting to hurt

because of this trolling

[ancient flame]

integers include negative numbers

natural numbers do not

0 may or may not be considered natural but it is always an integer

[vocal roost]

Right, but what would happen if we just erased this border

[ancient flame]

wdym

what border

[vocal roost]

call them all integers, and dispose of the label "natural"

Why cant this be done?

[ancient flame]

but sometimes we want only the positive numbers

it's convenient to just say N

[mint canopy]

So we'd just call the naturals the positive integers. Woo well done

[ancient flame]

or you could adopt a notion like $\bZ^+$

[fathom swallow]

gmod

[vocal roost]

Well

it's what you would've done right? @mint canopy

[ancient flame]

kind of like how the positive reals are often denoted $\bR^+$

[fathom swallow]

gmod

[ancient flame]

idk it's just historical stuff that has lead to this point

[vocal roost]

How in the world can I avoid this 0-conversation

I just spoke to people and then they came in and disrupted it

[ancient flame]

you can't

you will always have to deal with it

[mint canopy]

Whenever it matters, you just ask: "hey, are you defining 0 as a natural" and then you reply "ok" to whatever the response is

[vocal roost]

we should have a pin saying: "0 can be natural/non-natural depending on context."

but nobody reads

the pins

[mint canopy]

nah

[vocal roost]

and now im being compared to Feynman for just saying that "No, 0 is natural!"

[mint canopy]

Hahaha

[ancient flame]

...

[mint canopy]

Sorry nesy, you were not being compared to feynman. Quite the opposite actually.

That was another joke.

[ancient flame]

any time I use N I always say whether or not it includes 0

[vocal roost]

what

a damn pain

some members of the server can be, when you want to communicate

[deep mango]

I say N and then let context dictate it

If I reference 0

Then 0 is in it

If I dont reference 0 being in N, it's not

Or like

It probably doesnt matter

[ancient flame]

bruh

hi ryc!!

[vocal roost]

Apperently im being trolled because im not using your level of mathemathical language

[tall badge]

if i wanna write 1/n then my N doesnt include 0

other situations my N does

[deep mango]

And then if I say {1/n : n in N} I obviously dont mean N with 0

Yeah

Lol

[vocal roost]

to the people that troll me

[tall badge]

get sniped ryc

[vocal roost]

they complain i disrupt conversations but...

they do it too

[mint canopy]

I think it's worth saying it explicitly sometimes like

[vocal roost]

it's like a cycle of hypocricy, and im in it

[mint canopy]

It's the difference between N being a monoid or just being a semigroup

and like

yeah that doesn't matter very often

[pure sun]

The thing that’s important about N is the other side of it

[mint canopy]

but

like you should mention it if you're talking about monoids or semigroups!

[vocal roost]

what

what other side?

[pure sun]

The fact that it goes to infinity

[mint canopy]

Buncho, are you ready to become the joker

[vocal roost]

ok

anyway

[deep mango]

I mean

Sure if N is being considered as an ordered index set

But it also has arithmetic

[vocal roost]

I don't even think i dare talk to people about the natural numbers anymore

because, this is tiring

[mint canopy]

yeah this is exactly what I'm saying

[pure sun]

Arithmetic…

It’s not even a ring

[mint canopy]

Yo, did you know in homological algebra, it's quite natural to start counting at -2 sometimes?

[deep mango]

I did not know that

[mint canopy]

It's really annoying lol

[vocal roost]

I should just completly end the conversation when i encounter that

[deep mango]

Is that just to make sure 0 has enough terms before it to do the five lemma on it

[arctic grove]

if physics calc counts

sure

[deep mango]

Thats like 50% a joke

My calculus started in grade 11

Or

We did derivatives in grade 10

[vocal roost]

there will be a day where i will see 10000 blocked messages in every chatroom

[deep mango]

But then we did applications of derivatives, integrals, and series / taylor stuff in grade 11.

[arctic grove]

then no

[deep mango]

Derivatives and integrals.

[arctic grove]

we do in maths in 12th grade

[vocal roost]

Finding the area under a curve
Finding the slope of the tangent line

two of the main points of calcalus

[tall badge]

whoa taylor in grade 11?

[vocal roost]

[mint canopy]

There's a bit more to it, but this is probably the stuff you'll find the most challenging, depending on your specific course

[arctic grove]

[deep mango]

Well we did everything in 11th

[arctic grove]

idk about others but here its like that

u dont learn integrals in maths class in 11th grade

[deep mango]

But there were different classes

[tall badge]

whoa series other than geometric ones in grade 11?

[deep mango]

Some people didnt do calculus at all

[vocal roost]

but this

ultimate gamer calcalus ^^

[tall badge]

ur hs calc curriculum is scary ryc

[mint canopy]

nesy, you were learning how to solve y' = y just an hour ago lmao

[vocal roost]

wat

[deep mango]

At the conference im at we use versions of generalized stokes like every 2 minutes

[vocal roost]

I was learning basic DE's

and now i know how to solve basic ones, almost

[deep mango]

It's so funny

[vocal roost]

idk im saying it is the ultimate gamer calcalus

[deep mango]

You need to know on every type of tensor in every damn dimension what exterior derivative is

[vocal roost]

simply because

i was told

that

[deep mango]

Or at least in a few dimensions and for 0, 1, 2, and n tensors

I mean sorta

Not like

The ones that michael penn does on his youtube or whatever

But we learned all of the common integration techniques

No I think you just never learn that stuff in a class

Since its very niche

And never comes up except in like

Physics

Oh well

You do learn about doing harder integrals in complex analysis

I forgot about that

People do that in like 3rd or 4th year of college usually or something

If they're a math major

[vocal roost]

I think

i understand this now

I've let it marianate in my brain for weeks

yes

of course

they are crucial for let's say, defining derivatives

[deep mango]

Sure

Yeah

They're like the first step

Calculus is all about understanding different important limits

Thats what makes it different from algebra or geometry

[vocal roost]

this f(x+h) thing implies how far away the second intersect of the secant line is from our first intersect right?

[deep mango]

Yeah everything besides the limits is more algebra and geometry lol

[mint canopy]

Yes! You need to be familiar with some standard algebraic manipulations.

[deep mango]

Yes

[arctic grove]

geometry maybe not

just be familiar with the basics

[leaden sage]

differential geometry though

[mint canopy]

Geometry can be a little bit helpful.

[arctic grove]

in defining integrals yeah

and also tangents

[vocal roost]

f(x) is what the limit is actually approaching, right?

[arctic grove]

but its uses run out after that

[arctic grove]

hmm?

[vocal roost]

this

[mint canopy]

No.

[vocal roost]

no?

i know it's equvilent of y1 in deltay/deltax

[mental parrot]

what does it mean if the critical points of a inequality is unreal.

[mint canopy]

Can you show us what you mean? Maybe also ask in a help channel: #❓how-to-get-help

[mental parrot]

okay

[arctic grove]

yup

[vocal roost]

Oh yeah, f(x) is just the position of our first intersect. the f(x+h) is the second intersect.

the difference between those, is delta-y, and then dividing with delta-x.

delta-x being h, right?

[deep mango]

Yeah

[worldly fulcrum]

Yep

[deep mango]

Delta y and delta x are both approaching 0

[vocal roost]

I guess I do understand the definition of derivatives on a acceptable level now.

[deep mango]

But when you divide two things which approach 0, the fraction could approach anything

[leaden sage]

its just a slope, a really small one, and you have to do some work around so mathematicians wont have to use hyperreals

[vocal roost]

Yeah

and the reason why you're "localising" the two intersects closer and closer

[deep mango]

Depending on which approaches 0 faster (and how much faster)

[vocal roost]

is to get an exact slope

[deep mango]

Yeah

[vocal roost]

and, the exact slope is like

the tangent line?

[leaden sage]

yes

[worldly fulcrum]

Yes

[vocal roost]

or the point of tangency

i mean

[deep mango]

You can use it to write down the tangent line, in point-slope form.

[leaden sage]

or the plane of tangency, or the...space of tangency?

[vocal roost]

This is how i think of it as

so, this red is our secant line i guess, the avarage rate of change.

And I said that, if we make the h approach 0, the intersect at f(x+h) gets closer and closer. Making our rate of change more accurate.

@deep mango (brah, this is a horrible drawing wtf) ^^^

[leaden sage]

thats the way its often taught, yeah

[deep mango]

That is correct

[vocal roost]

I wonder what's happening here

[worldly fulcrum]

my assumption is desmos froze

[vocal roost]

ye

much better

[vocal roost]

So basically, this is where our tangent line is?

Our m value can be used here:

(y1-y2) = m(x1-x2) right?

to find the equation of the tangent i guess?

[mental parrot]

The topmost mod of the maths disc has mc pfp

💀

[vocal roost]

now i no longer have to be trolled because i dont know what derivatives are

[woven whale]

mc ftw

[vocal roost]

haha! suk that trollers 💀

[mental parrot]

or the loss

[vocal roost]

drawing with a mouse

is becoming better

lol

[golden pendant]

animal cruelty is not okay

[bright hill]

[golden pendant]

dont use a mouse to draw

[vocal roost]

[storm sage]

some food for thought if you want: now that you know that definition of derivative, think about why this is also a 100 percent valid definition of the derivative:
$$f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c}$$

[vocal roost]

Hmmm

[fathom swallow]

Eric Tao (he/him)

[vocal roost]

säs

Well if we're tending towards c, with of course, f(c)

yeah

it definently seems valid

or, it is valid

actually

f(c) is the cordinate that is the first intersect.

f(x) is the second intersect.

And if x is tending to c, we're bringing these points closer.

making the difference, "more accurate, yet small."

[storm sage]

another fun thing: which of these are true, and which ones aren't?
$$f'(x) = \lim_{h\to 0}\frac{f(x+h) - f(x-h)}{2h}$$
$$f'(x) = \lim_{h\to 0}\frac{f(x) - f(x-h)}h$$
$$f'(x) = \lim_{h\to 0}\frac{f(x) - f(x+3h)}{3h}$$

[fathom swallow]

Eric Tao (he/him)

[storm sage]

yup exactly!

[vocal roost]

I think the first one

[storm sage]

how come

[vocal roost]

they cancel out

becoming 0

[storm sage]

what does

[vocal roost]

sorry

[storm sage]

oh

[vocal roost]

the numerator

[storm sage]

they're all 0/0

but two of these are valid and one isn't

:)

[vocal roost]

im suspecting the first one is

[storm sage]

fun puzzle

[vocal roost]

but i am not sure why

oh nevermind

they are conjugate

💀

so they dont cancel out

or do they?

[storm sage]

try drawing some graphs and secant lines :) may help

[vocal roost]

however, im suspecting this gives us a negative answer

but it could be valid though

[storm sage]

hehehehe

[vocal roost]

because we're approaching it from a different direction

so

this one is valid

Now one of these two are not valid

Hmmm

I'll try some values

[storm sage]

hey no using graphing calculator that's cheating :p

[vocal roost]

SÄS

[storm sage]

do it by hand

[vocal roost]

i dont even have pen and paper available

[storm sage]

rip

[vocal roost]

💀

[storm sage]

you'll figure the answer out too fast if you graph it by computer

xD

[vocal roost]

you little säs

[storm sage]

I want you to think about it

to make sure you really understand the derivative definition

[vocal roost]

The coefficents of h aren't matching here

[storm sage]

:)

let me know whenever you have a final answer and you want to check

[vocal roost]

ok

[vocal roost]

I've been experimenting with this

And i'm not sure

anymore

I don't think the function is valid, just by seeing that there is no correct "distance" between the intersects. @storm sage

hard without a graphing calculation though and a piece of paper

[finite tusk]

This works

[vocal roost]

its difficult without a graphing calculator

sadly

since, it makes it easier to visualize

[finite tusk]

Also you can do f'(x)= limit as h goes to 0 of f(x+nh)-f(x-nh)/2nh)

where n is greater than 1

And let's say n is a really really large numbers

[pure sun]

what do you mean "you can do"

[finite tusk]

As in the person has the ability

Please talk to me about mathematics not anything else that's not math

[sleek wing]

That sounds boring

[neat lintel]

many low quality inputs to the server recently

[pure sun]

what i'm saying is that that's not a valid definition of the derivative

so no, you can't do that

[vocal roost]

so buncho

this is invalid?

[pure sun]

oh sorry

you were supposed to figure that out

[vocal roost]

yeah

[pure sun]

but yes, it's invalid

[vocal roost]

i literally suspected it to be that

because well, it doesn't seem to be approaching the "cordinate" we want it to approach

[chilly coral]

Why's it invalid?

[vocal roost]

or maybe it's because i don't have a graphing calculator

[finite tusk]

Are you looking for a new way of finding the derivative?

[vocal roost]

no no

[finite tusk]

Okok

[vocal roost]

eric wanted to challange me

and i failed

[pure sun]

try to apply that definition to f(x) = |x| at x = 0

[finite tusk]

Idk

[chilly coral]

oh

[pure sun]

what is true

is that if f is differentiable

then that limit exists and is equal to theusual derivative

but the converse is not true

[finite tusk]

Remmeber differentiability implies continuity

Take contrapositive of the statement I put and it's equivalent to saying not continuous implies not differentiable

Same thing

[pure sun]

i dont see how that's relevant

[finite tusk]

That's not my problem

Sounds more like a personal problem

[pure sun]

i was trying to be kind but i can rephrase

[neat lintel]

lol get fucked buncho

[pure sun]

that's not at all relevant

[finite tusk]

Differentiability implies continuity = not continuously implies not differentiable

Continuous* @vocal roost

[neat lintel]

would you please be willing to explain what this has to do with what buncho wrote? 🙂

[finite tusk]

I wasn't talking to buncho

I was talking to @vocal roost

[pure sun]

well nesy and I were talking about what's called the symmetric derivative

which doesn't have the same relationship with continuity that the regular derivative has

also i gotta go so i'm gonna tag team @neat lintel on this one

you're in

;P

[neat lintel]

nah this isn't worth my time lol

sorry buncho

i'm hanging out at my bf's parents' house

[pure sun]

hahaha

have a good time

[neat lintel]

[vocal roost]

Symmetric derivative?

ooo

[leaden sage]

would an ODE ever be written with operators other than the basic +,-(and *,/)

[neat lintel]

it can be

the most general form of an ODE of order n is f(t,y,y',...,y^(n)) = 0

[storm sage]

that's fair, I was assuming the function was differentiable lol

@vocal roost the answer, if you want to check, is ||1 is valid if f is differentiable, 2 is always valid, 3 is invalid (it is zero minus the derivative)||

[vocal roost]

oof

[storm sage]

it does approach the coordinate: x+h→x, and x-h→x

[vocal roost]

hard to do it without a graphing cord or a piece of paper

säs

[storm sage]

try not to rely on graphing calculators :) they can often be misleading if you don't have the underlying intuition

[ancient flame]

wtf is this

[storm sage]

I gave him a challenge

[vocal roost]

i failed

[storm sage]

three derivative equations, pick which one is invalid

(it was that one)

[ancient flame]

ohhhh

lmao

[icy python]

aaa

[storm sage]

now that you know the answer though, think about why the answer is true :)

and you will learn a lot

[ancient flame]

the first one is cool

symmetric derivative right

[storm sage]

yup

@vocal roost here's another fun one: what's the derivative of x^x?

hint: ||rewrite the bottom x as e^(ln x)||

[vocal roost]

isn't it like:

x^x+1 / x+1

[mint canopy]

bruh the hint's too muchhhhhhh

[wild lantern]

⛓📏

[vocal roost]

OH

[storm sage]

shush

[vocal roost]

wait

[storm sage]

I made it a spoiler

[vocal roost]

it's

x^x/ln(x)?

[storm sage]

it's okay

[storm sage]

no

[vocal roost]

shit

OH

it's anti-derivative

[wild lantern]

No lol

[vocal roost]

i didnt take the derivative

[storm sage]

no wait

[vocal roost]

[ancient flame]

no wtf

[storm sage]

it's a derivative

[ancient flame]

lmao

[storm sage]

I'm confused

[storm sage]

lol

[wild lantern]

Start with erics hint x^x=e^???

[storm sage]

if you can take the antiderivative of x^x, I'll be impressed.. I forget how that works

[ancient flame]

your font is strange

[ancient flame]

iirc you can't

[vocal roost]

uh holdup

[storm sage]

Lol

[ancient flame]

,w int x^x

[fathom swallow]

Results provided by WolframAlpha

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

Requested by gmod#1227

[storm sage]

ahh

[ancient flame]

yup

[vocal roost]

Yeah I dont know how to take derivatives

of exponentials yet

then

[wild lantern]

D(e^x)=e^x

[ancient flame]

what's the derivative of e^x

oh

bruh

[storm sage]

Lol

[wild lantern]

Now you do

[storm sage]

do you know the derivative of ln x @vocal roost

[vocal roost]

[ancient flame]

what's the derivative of 5^x?

[vocal roost]

yeah it's 1/x

[storm sage]

yup

[bright locust]

Asking a question while it’s already answered

Hmmm

[storm sage]

that's all the info you need

[vocal roost]

uhhm

[storm sage]

have at it now

[vocal roost]

x^x = 1/x^-x?

[storm sage]

yeah but that doesn't help you

[wild lantern]

No

[storm sage]

well

I mean it's true

[wild lantern]

Oh wait lmao

Yes algebra lol

[storm sage]

start with the hint

[storm sage]

^

that should be enough for you to figure it out

given what you already know

:)

[vocal roost]

ln(x)^x?

[wild lantern]

Not exactly

[storm sage]

are you guessing

or did you actually do it

lol

[wild lantern]

Remember a=e^(lna) from algebra?

[vocal roost]

(e^ln(x))^x

i hate discord font

[wild lantern]

Yeah

Easier with xlnx in exp tho

[storm sage]

okay that's enough hints

:P

[vocal roost]

doesnt help me

[storm sage]

you do not have to graph it on desmos

lol

in fact that won't help at all

[vocal roost]

its ment to write on

[storm sage]

😭

[vocal roost]

not graph in this situation

[storm sage]

okay you might want to wait until you have paper

[wild lantern]

(This is a hint on what to do next)

[storm sage]

LOL

[ancient flame]

use latex

[storm sage]

took me the longest time to figure out what the ruler meant

[bright locust]

I like the way you use emojis as hints

[vocal roost]

im lost

[bright locust]

Maybe the ruler should be instead replaced by the discord rule book icon

[ancient flame]

lol

[storm sage]

it's okay

if you keep trying stuff, you'll figure it out

[vocal roost]

this hint isn't good enough

[storm sage]

(that is incorrect btw)

[storm sage]

you just gotta be patient

[ancient flame]

do you know chain rule @vocal roost

[storm sage]

math is all about perseverance

[vocal roost]

no

[storm sage]

F.

[ancient flame]

that sucks

[wild lantern]

Ah dang okay

[ancient flame]

uh

[storm sage]

okay I guess you have to learn that first

Lol

[vocal roost]

I literally said

[ancient flame]

yeah

[vocal roost]

i didn't know

[wild lantern]

So you need chain rule first

[ancient flame]

what rules do u know about derivatives

[storm sage]

and product rule

[vocal roost]

Power-rule for anti-derivatives

And reverse power rule for derivatives

[wild lantern]

Yeah you need more of the basic rules first

[storm sage]

okay you may want to follow the khan academy calculus tutorial

[ancient flame]

why were u doing calc 3 stuff yesterday and differential equations today then

[storm sage]

lol

nesy is just very eager

[vocal roost]

i didnt use the chain rule formula

[storm sage]

too eager..

[ancient flame]

you're literally not being productive at all when doing stuff like that

[bright locust]

@vocal roost want me to show you the chain rule formula

[vocal roost]

sure

[bright hill]

if you're tackling those stuff it's basically a given that you know what that is lol

[wild lantern]

Learning some breadth is fine ig

[ancient flame]

I mean yeah but still

[vocal roost]

I didn't do anything too crazy

[storm sage]

hahahahaha

[vocal roost]

I was tasting things

so

[wild lantern]

Everybody kinda pokes and flounders a little beyond their current understanding.

[bright locust]

@vocal roost

[storm sage]

nesy just watch it on khanacademy tbh

[vocal roost]

What version do you want me to use

[bright hill]

[ancient flame]

I guess but he's been posting and arguing with us about it

[bright hill]

tru tbh

[wild lantern]

Chain rule lets you evaluate derivatives of compositions

[wild lantern]

Yeah I don't mean to entirely advocating how nesy goes about it lol

[ancient flame]

when nesy sullies me

[wild lantern]

But I get being in calc and being curious about later calc shit lol

[bright hill]

anyhow

day #3 of telling nesy to pick up a book

[ancient flame]

yeah lol

[vocal roost]

Or find a book in the internet.

[ancient flame]

yes

[bright locust]

@vocal roost want a calculus book?

[ancient flame]

or even khan academy

[bright locust]

I have a teachers edition

[vocal roost]

I could take khan academy

over a book

if it has decent verbal instructions

[ancient flame]

then do it

[wild lantern]

Pauls online math notes+khan academy+prof leonard is p good

[bright hill]

oh, yeah

that's what I meant

[vocal roost]

Here is the issue, I've halted my calcalus learning because I've overextended

[bright hill]

you can check out the holy library or smth

[ancient flame]

that's not good

or the liberal generator

jk

[bright locust]

There’s the problem

[wild lantern]

Hitting ruts sucks but is normal lol

[bright locust]

You learned too much in x amount of days

That’s why you’re forgetting

[vocal roost]

I'm not

forgetting

[bright locust]

Which leads to confusion

[vocal roost]

anything

dude

[wild lantern]

Good to stay focused on something you can make progress on

[vocal roost]

I just don't Know

it's not the same thing as forgetting

[bright locust]

I know it’s not the same

But there’s a trend

[vocal roost]

Corrolation

is causation now?

No, it isn't

[ancient flame]

...

[wild lantern]

"Corrolation"

[ancient flame]

corrosion

[bright locust]

I didn’t say coorelation

[vocal roost]

In my case I have not

forgotten

anything

[bright locust]

I meant to say causation

[storm sage]

Lol

[bright locust]

Corruption

[vocal roost]

I have gaps in my knowledge

is not the same thing as forgetting

[storm sage]

nesy just watch the khanacademy calculus course

it's fairly easy to watch

and fairly comprehensive

[vocal roost]

Of chain rule?

[storm sage]

of like

all the topics, if you want to learn calculus

[wild lantern]

You won't really understand stuff too well if it's too far beyond where you are?

[vocal roost]

Yeah

Partial derivatives are not a hard concept to grasp, really.

[wild lantern]

It's good to get some glimpses but not to focus too heavily on the more advanced stuff yet

[vocal roost]

I've only done partial derivatives of the things I KNOW

how to

[chilly coral]

I remember trying to teach myself calculus before learning trig lol. Not a great idea

[vocal roost]

essensially

[wild lantern]

There are some subtleties. Like chain rule for partials is all janky, and you don't know chain rule for normal derivatives yet.

[bright hill]

it kind of is

[vocal roost]

It depends on what you're taking the partial derivatives to which extent

[bright hill]

but it always depends on how deep you wanna go

[vocal roost]

And here

I'm on the basic level

[wild lantern]

So, like, you know some things about partials, but there's more to it that you'd prolly need to understand normal derivatives better to understand.

[vocal roost]

I always learn the basics of things

I don't go furhter

If I dont have the necessery foundations

[bright hill]

[vocal roost]

And I do have the necessery foundations to solve some partial derivatives

it's literally not that hard

[wild lantern]

Sure sure

[vocal roost]

But for later things, then it will become, fucking incomphrehensible at my level

[wild lantern]

But like partials of composed functions IS basic

The chain rule for partials IS a basic fact about partials.

[vocal roost]

I just don't know how to utulize chain rule

[wild lantern]

Yah yah keep at it lol

Just takes time and practice

[bright locust]

Now’s the time to learn and practice for x hours

[vocal roost]

It's alright.

I practice for 20 minutes per day or 1 hour if i need it

[bright locust]

Good start

[vivid halo]

I mean the idea is that composition is one of these operations that lets you build more complicated functions from simpler functions, chain rule tells you how to differentiate a composition in terms of the derivatives of the original functions

[bright locust]

I have “fat finger syndrome” for typing for some odd reason

[vivid halo]

I guess some concrete ways you would use this is like

one consequence is derivatives for inverse functions, since you know a function and its inverse compose to the identity

but you know the derivative of the identity and the original function, so you can work out the derivative of the inverse

[vocal roost]

I know what inverse functions are at least

so that's like an ok start

[vivid halo]

this is usually how the derivative rules for inverse trig are derived for instance

[vocal roost]

You could call them: "Mirror functions"

as well

so long as you understand that the x,y switches places and etc.

[vivid halo]

yeah graphically that's one way to think about things

[vocal roost]

and also the two functions being "mirrored." in the graph

to the y=x line

which is like, yeah your mirror plate or whatever you call it

[bright locust]

The line of reflection

The line that makes the equations “1 to 1”

[vocal roost]

I watched a khan academy video of it

didnt show the formula

smh

so here we have it

[bright locust]

👍🏼

[wild lantern]

There's multiple formulas for it ig

[vocal roost]

and I still don't really understand it yet

This is taking the derivative of the outer function

leaving the inner intact