serious-discussion

[late valley]

enough to keep me awake but not too much to distract me

[empty stratus]

Sibelius' 2nd Symphony gets the blood pumping.

[frozen merlin]

i recommend mos def, the roots, mobb deep

[late valley]

will listen

[alpine kindle]

4'33" on loop

[late valley]

my favorite phrase from 4'33" was when they

and then they

[alpine kindle]

my favourite phrase is when someone sneezes

[late valley]

idk i really liked those page flips

[alpine kindle]

i don't like music when I'm trying to focus

because then my attention is torn between the music and the thing i want to focus on

unless it's 4'33" in which case that's what I'm normally hearing anyway

[neat lintel]

what's 4 feet 33 inches?

is it like a very height-conscious rapper?

[rapid ginkgo]

I dont recommend this, just go with silence

If you like some piece of music, then it will just autoplay in your head

if its new music, it takes too much attention

if its not good, it annoys you or gets filtered

[modest rune]

I listen to music when i work 24/7

[alpine kindle]

4 minutes 33 seconds

[modest rune]

what a strange recommendation lol

[alpine kindle]

i agree with their recommendation

[modest rune]

Kind of odd rec but the ChessBrah Edm playlist is nice. It has a lot of music with strong consistent baselines/tempos that help me focus

If someone is asking for music recs, recommending silence is not very helpful lol

I am sure they thought of silence.

[modest rune]

I can guarantee that it will at least not make you sleepy.

[open aspen]

im just perpetually damn sleepy when i do homework at home, so its either auditory stimulation or cocaine

idk if silence would do it for me

anyone else have this problem

[modest rune]

I use it to help with adhd

Music is just the right amount of distraction

[rapid ginkgo]

the best help for adhd is to just have no inputs besides the thing you wanna do

[modest rune]

That is such a silly thing to say lol

If you have adhd, you should know by now that almost everyone has different coping and medical strategies that do/don't work for them. If you don't have adhd, you shouldn't say anything lol

[rapid ginkgo]

and stimulants

[modest rune]

But tons of people with ADHD take advantage of using outside stimulus to help them focus, whether that is studying is busy places like coffee shops or music or whatever.

[rapid ginkgo]

There is never enough coffee and nicotine to be ingested

NEVER

[modest rune]

Cool.

[neat lintel]

thnx

[rapid ginkgo]

Its not really good.

ypu are just pumping noradrenaline and dopamine with extra steps

cut out the steps and just sit alone in a quiet room with a lot of tobacco, coffee, paper and needed books

[modest rune]

You should be much less confident in prescribing solutions to other people.

Not to mention the encouragement of nicotine lol

[rapid ginkgo]

Its far more sustainable than taking dextroamphetamine every day lol.

[alpine kindle]

just let them listen to music goddamn

[rapid ginkgo]

or methylphenidate

[alpine kindle]

advocating for drug usage over music is a bad idea

[open aspen]

yeah this is insane

[modest rune]

lmfao

[light needle]

you see there is this thing called lung cancer...

[open aspen]

what an off the wall take

[rapid ginkgo]

Dont smoke?

Smoking is optional

[modest rune]

But music is not

[blazing pawn]

Crazy idea, maybe dont offer unsolicited medical advice telling them to start doing tobacco

[modest rune]

Music is a hard no

now

chewing tobacco

[blazing pawn]

Instead of listening to music

[modest rune]

thats up to you

[alpine kindle]

michael why are you dying on this hill

[blazing pawn]

While making overgeneralized and dubious statements about existing ADHD medication

[modest rune]

You are very quickly making a fool of yourself lol

[rapid ginkgo]

I do it, but I am a degenerate

[modest rune]

That we agree on.

[meager sonnet]

nicotine is less safe than Adderall LOL

and not really good for ADHD?

[rapid ginkgo]

in what ways? people just use shitty ROAs or dont care like me

[rapid ginkgo]

its good for everything

[modest rune]

...

[rapid ginkgo]

There isnt anything its bad for

[modest rune]

Lifespan?

[blazing pawn]

[modest rune]

inb4 lifespan is bad for adhd

[blazing pawn]

Gonna put a stop to this

[modest rune]

the longer you live the more adhd you have

[alpine kindle]

michael stop dying on this hill

[fair mural]

can there exist an $m\times n$ matrix $A$ and an $n\times m$ matrix $B$ (with $m\neq n$) such that $AB = I_m$ and $BA = I_n$?

[fathom swallow]

quantum

[teal lion]

Sure, just take m=n.

[fair mural]

you’re hilarious you know that right

[long matrix]

certainly

try invent examples

[fair mural]

i’ll just do the 1x2 and 2x1 case because anything after that takes way too much work

[long matrix]

could just play around in a matrix calculator

[deep mango]

so for the 1x2 / 2x1 case, there is an issue

[long matrix]

Maybe I lied I can't come up with one

but i swear i seen em before

[deep mango]

the product of a 2x1 vector with a 1x2 vector is a 2x2 matrix. but it will always turn out to have rank 1

why? the second column is a multiple of the first (try to see why by writing down a general product of two vectors like this)

so you can never have the identity formed from the product of a 2x1 and 1x2

[long matrix]

does what you said not generalise?

ohhhh

[deep mango]

this turns out to be true for mxn times nxm whenever m > n. the rank of the first matrix is at most n, and the rank of the second matrix is at most n. well, a product of matrices cannot have a bigger rank than either of the factors (you can prove this using the fact that the rank is the dimension of the image).

[long matrix]

@fair mural i may or may not have scammed

[fair mural]

grrrr

[deep mango]

so you can't get I_m from a product of an mxn and an nxm.

but you can get I_n!

from nxm times mxn

[long matrix]

i think u can also get an almost-identity matrix (some diagonal entries are 0)

[deep mango]

(a good option here is to just take the identity matrix and to add some rows/columns of 0's)

yes you can

[fair mural]

i’m not this good at linear algebra

[deep mango]

you can get something which is the nxn identity and then m-n extra zeros on the diagonal

[long matrix]

You haven't seen linear transformations yet have u

[fair mural]

i have

[long matrix]

$$T_A : \bR^m\to \bR^n$$

[long matrix]

A is an (n x m) matrix

[fair mural]

i know

[deep mango]

yeah so i think of this stuff primarily in terms of the dimensions of the image and the nullspace/kernel

[long matrix]

You think about dimensions for why ryc said the above is impossible yh

rank-nullity thm

So the problem is if m > n

[deep mango]

the identity needs to be surjective: it needs to hit the whole image. an nxm matrix sends R^m to R^n, so if m > n, it's going to squish some stuff down to fit in R^n. and then the mxn matrix sends R^n to R^m, so since m > n it can't fill everything in. there's too much space.

then doing nxm first and mxn after (since we apply right to left this would be mxn times nxm times vector) we 1. need to squish some stuff down together and 2. cannot hit everything at the end.

meanwhile, if you do mxn first and nxm after, you put R^n into R^m where you don't need to squish anything down, and from R^m back to R^n you do need to squish stuff down - but the stuff you squish together could be outside of the stuff you put in R^m from R^n. so it doesn't prevent you from having a bijection.

[limber thunder]

I mean that's about 2/3 or 1/2 the typical course load in a semester (it's as if you enrolled in CS50 and some honors calculus), definitely doable if you have the time

[glad grove]

Next year, I'm looking at applying to colleges for math. What are some good mathematics colleges to look at (and maybe some that aren't always highlighted?) I'm looking for a major where I can take some graduate courses in my undergrad and also to explore a wide variety of topics.

[neat lintel]

Florida State University

Iowa University

top schools in country of USA

[vivid halo]

lol

[glad grove]

ah 😭 😭

oooo alright

I'm looking at UC berkeley UIUC and UMichigan

so that's cool

[neat lintel]

Why?

Also I want UT austin very bad

[vivid halo]

among the state schools those are some of the best probably

[raven plank]

hello

[neat lintel]

But im sad that my grades and my self as a student are highly underwhelming

I have a 3.5 atm and it can maybe go to 3.7 by last semester

[charred mortar]

#❓how-to-get-help

[neat lintel]

im also not smart so i dont know what would boost application so that i have sure fire way of getting in

[charred mortar]

You’ll have better luck asking in the right channel

[neat lintel]

im hoping i get lucky or have an advisor that knows a guy

[raven plank]

hello guys!!! who is good at probability and statistic

????

need help

yeah

[weak sand]

is there a name for this subtype of perverse incentive
if it's -25 °C outside, the students get to stay inside in the warm comfort 20°C, but if it's one degree less cold, i.e. -24 °C outside, then they must go in the cold
this makes the students wish for extremely cold weather, so they would not have to face the extremely cold weather

I couldn't find a proper name for it, so I decided to call it "radical threshold"

[charred mortar]

sounds more like "terrible criteria" tbh

or "terrible policy"

like that sort of policy makes no sense anyways

maybe there's a better example of what you're describing out there

[inner finch]

lol

Not sure about how accurate this is to real life. But i think this describes what u have in mind, suppose you have a badly designed welfare system where you get money below a certain threshold of income (aside from the welfare ofc), so you actively work against raises in wages so you can keep the welfare

[median zinc]

I'd use game theory words but climate temperature is not something that is 'decided' by n-players

At least, not directly

[inner finch]

All of the players are god(s) 🙏

[weak sand]

yes, the weather thing is exactly like a welfare trap

[weak sand]

too broad, need more exact names

i have come up with "benefit cliff" and "no sliding scale"

[ancient flame]

wow really fsu is a good math school?

interesting

[neat lintel]

Probably

[ancient flame]

icic

alright

[waxen lily]

hey its the con||cat||e||nation|| guy

con||cat||e||nation

[toxic schooner]

[weak cradle]

Hey I have a question

Is it possible to do math research privately?

I spent years studying maths and physics at Uni but never graduated and don't intend to in the nearby future

[vast surge]

What I recommend doing is, when you get a proof of a big, famous open problem like the Riemann Hypothesis, make sure to send all-caps emails to a bunch of professors who don't know you telling them about your work.

[ancient flame]

hi

[weak cradle]

Ah yes. Way to get sued...

[vast surge]

Nah, just laughed off as a crank

[weak cradle]

That too

[vast surge]

Outside of academia, especially if you don't have a higher degree, it's hard to gain the credibility required for people to take you seriously

[weak cradle]

Fair enough

[vast surge]

If you're independently wealthy and have the right contacts it might be possible, but even then it's iffy as to whether it's doable

[long matrix]

to me the worst thing about trying it privately is doing something someones already done

Someone might have pointed that out to you at the start and saved you a lot of time

[hybrid quest]

That's were I'm at with a bunch of questions I have. Someone's likely found the answer.

My degrees aren't in math either, so I'm good with doing things for recreation for now

[alpine kindle]

iffy as in "similar to equivalence"? /s

[hybrid quest]

This for sure, the problem I was talking about yesterday. Someones got to have done it

[sick burrow]

I mean if a random nobody proved something important then would they not be taken seriously?

Isn't the issue more than you need to be immersed in the mathematical community to prove anything important in the first place and you're not getting that without formal schooling

[brisk wolf]

i would say it also depends a lot on the actual field of research

[surreal sapphire]

you first have to get people to read your things

[hybrid quest]

Well dang, I should go back to school then

[outer vector]

so i know its just serving a purpose butt

WHY IS THERE A LIGHT GLARE AT THE TOP RIGHT

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[static loom]

snapshot of nuked north america

[chilly hull]

my 20 yottawatt flashlight

is too powerful

[outer vector]

lol

[waxen lily]

looks like a mistake

[outer vector]

depresso

[hushed turret]

is that a question

[alpine kindle]

so we have

forall a F.g(a) = F(a) + 1

therefore

[neat lintel]

welcome back @alpine kindle : )

[fair mural]

why are you denoting function composition like that

[alpine kindle]

F.g = (+1).F

[neat lintel]

what

[alpine kindle]

haskell

[neat lintel]

what's (+1).F ??

oh

wow that's just weird

[alpine kindle]

F composed with g is equal to the function that adds 1 composed with F

[fair mural]

using what’s most convenient > using what you like

[neat lintel]

and what then? any ideas, Alison ?

[alpine kindle]

I'm not gonna put circ in writing every time i want to compose functions

[alpine kindle]

give me a g

[neat lintel]

well I ruled out g(a)=a^2+1

so let's go a^3+1

[alpine kindle]

ok

so

F(x³+1) = F(x)+1

let's check some points

F(1) = F(0) + 1

actually

we can rewrite this

F(x) = F(cbrt(x-1)) + 1

[neat lintel]

ok

interdasting

[alpine kindle]

so F(0) = F(-1) + 1

[neat lintel]

is there a fixed point tho

[alpine kindle]

no idea

[lament pebble]

Is there a chat in this bih where I can pay for people to do my math

[alpine kindle]

there is almost certainly more than one solution

[alpine kindle]

nope go to another server

[lament pebble]

😭

[fair mural]

not sure why you need to pay

#❓how-to-get-help

[neat lintel]

x^3-x+1=0

[alpine kindle]

uh

you're forgetting the F

[neat lintel]

there is a real fixed point

I mean a not x

sorry

[alpine kindle]

it doesn't matter

[alpine kindle]

gonna do some implicit differentiation

[lament pebble]

Ight well peace you fucking idiots

[neat lintel]

for this a, we get a back

[slate wolf]

@lament pebble

need help

[alpine kindle]

3x²f(x³+1) = f(x)

this is our original function that we actually need

[neat lintel]

which means we get a contradiction

allyc it doesn't work

[alpine kindle]

flr what are you talking about

[slate wolf]

i can help with whatever you need buddy, (talking to @lament pebble )

[fair mural]

they left

[alpine kindle]

where is the contradiction

[neat lintel]

integral from t to t is 0

[fair mural]

lol

[slate wolf]

well nvm then

[neat lintel]

right?

[slate wolf]

impatience will get those nowhere sadly 🙁

[alpine kindle]

the integral can be 0 for some values of a

[neat lintel]

so if I find
a such that a^3+1 = a, the function does not work

[alpine kindle]

it does

[neat lintel]

my idea is that it's 1 for ALL values of a

at once

[alpine kindle]

oh

[neat lintel]

that's the fun

[alpine kindle]

wait

flr

[neat lintel]

but it's difficult to find a good g

[alpine kindle]

yeah

wait

what about ln x

[alpine kindle]

if you use ln x you get
F(ln x) = F(x) + 1

[neat lintel]

0 is a bish

And any negative value

[alpine kindle]

just say it's only defined on (0, +infty)

[neat lintel]

Ok..

[alpine kindle]

well

actually

nvm that's annoying

[neat lintel]

XD

[alpine kindle]

what about cosh x

no fixed points

wait why didn't x²+1 work

[neat lintel]

I had a discussion about this in calc

But essentially

int -a to 0 is 0

[alpine kindle]

uh

is that a general rule

[neat lintel]

As long as g(a) is an even function, I think

[alpine kindle]

hold on

[neat lintel]

The way you get that result is by considering -a

[alpine kindle]

this seems wrong

I'm gonna try and solve x²+1

[neat lintel]

Int from - a to a^2+1

int from a to a^2+1

=1-1=0

But also

= int from - a to 0

[alpine kindle]

ohh

[neat lintel]

And that wouldn't be a problem until we consider that int 0 to 1 is 1

[alpine kindle]

it's from -a to a

[neat lintel]

No

[alpine kindle]

it is

int from -a to a over an even function is 0

[neat lintel]

Oh yes

[alpine kindle]

wait

hold on

[neat lintel]

Over an even function?

No

[alpine kindle]

we don't know f is even

[neat lintel]

when g is even

g

Not f

[frozen merlin]

this is an odd function thing

[alpine kindle]

wrong

[alpine kindle]

nvm yeah

g is just defining how the limits are set up lol

it's not actually being integrated

[neat lintel]

I know

[alpine kindle]

then integral from -a to 0 doesn't involve g

anywhere

[neat lintel]

It makes it equal 0

[alpine kindle]

why

g isn't in the expression

it shouldn't affect it

[neat lintel]

Because

int -a to g(-a) - int a to g(a) = int -a to g(a) - int a to g(a) = int - a to a

=0

[alpine kindle]

f isn't necessarily odd

and that's what we're integrating over

[neat lintel]

f is not even mentioned

[alpine kindle]

it is

[neat lintel]

It can be anything

[tender tulip]

If ordered pairs are actually {a,{a,b}} does that mean ordered pairs are actually classes

[neat lintel]

Literally any function

[alpine kindle]

integral from -a to a isn't necessarily 0

[neat lintel]

I used the properties of integrals only

I proved why it is

When the equation holds

[alpine kindle]

oh

wait

[neat lintel]

Waiting :3

But might fall asleep

[alpine kindle]

sorry

[neat lintel]

So goodnight if that happens

[alpine kindle]

so

g cannot be even

[neat lintel]

and cannot have fixed points

[alpine kindle]

easy
(x+1)²

[neat lintel]

Hm

Let's try

Good idea @alpine kindle

[alpine kindle]

F(x²+2x+1) = F(x) + 1
f(x) = (2x+2)f(x²+2x+1)

aaaa

this looks like pain

[neat lintel]

:))))

[alpine kindle]

what about x² + x + 1

[neat lintel]

Wait

[alpine kindle]

f(x) = (2x+1) f(x²+x+1)

[neat lintel]

Factor the 2

[alpine kindle]

just do it in your head

[neat lintel]

You get x+1

[alpine kindle]

yes

[neat lintel]

??

[alpine kindle]

i thought you were telling me to write it out

[neat lintel]

I was suggesting that maybe it's not pain :)

[alpine kindle]

f(0) = f(1)

[alpine kindle]

actually you're right that one is better

[neat lintel]

:)

[alpine kindle]

f(x) = 2(x+1) f((x+1)²)

ok

we know a root

f(-1) = 0

f((x+1)²) = 2 (x²+2x+2) f((x²+2x+2)²)

this looks very much like it diverges everywhere

[neat lintel]

Why

Both arguments grow

Not one

[alpine kindle]

nono

[neat lintel]

?

[alpine kindle]

as you unravel it more and more it gets bigger and bigger

[neat lintel]

?

Why?

I mean why does this imply divergence?

@alpine kindle ?

...

[alpine kindle]

sorry got distracted

[alpine kindle]

the value of f(x) diverges to infinity if x isn't -1

[brave gulch]

whats the main problem tho?

[alpine kindle]

idk really

[ancient flame]

what's an embedding

[torn willow]

So if A is a subset of B

The map f:A->B f(x)=x

Is called embedding

It's just switching sets

[ancient flame]

oh okay

ty

[torn willow]

Embedding is broader than that actually(it's a map f:X->Y preserving certain properties that allows you to identify X as a substructure of Y)

But that's the meaning in this Context

[ancient flame]

alright ty

[modest rune]

They just mean injective group hom

bad name

[ancient flame]

oh ok ty

[strong light]

guys im an idiot but

i was just wondering if this proof of there being infinite primes is valid or not

if there is finite primes, then we can multiply every prime before the last prime * the last prime, and then add 1, and we will get a new prime number?

[forest jackal]

it's close but not quite valid, the resulting number need not be a new prime number itself, but it must have a prime factor that is new. @strong light

[strong light]

but if we multiplied every single prime before the last finite prime then what would that prime factor be other than itself?

wait but

how is there another prime factor srsly

im confused

[strong light]

i also see the whole, like if it was this easy to find large primes it wouldnt make sense but yeah, and we also end up getting an algorithm for huge twin primes, all too easy to be true

[forest jackal]

well that's the contradiction, which completes the proof the way you wrote it.
you assume there is a finite list of prime numbers.
you multiply them all together and add 1.
this is a number N that is not divisible by any prime in your list.
any number can be factorised into primes, let p be a prime factor of N.
as mentioned before, p cannot be in your list of all primes, which is a contradiction.
=> your assumption that there is a finite list of prime numbers is absurd

[strong light]

but i dont understadn where its invalid thats why i asked

[strong light]

uh did you read my post

i asked if it was a valid proof by contradiction

of infinite priems

i never said that there was finite priems

[forest jackal]

yes, I have read everything you wrote.

[strong light]

so this does atleast prove that there are infinite primes right

[forest jackal]

I know you didn't, but you started the proof by setting up a contradiction: "if there is finite primes"

[strong light]

well thats the same way people proved root2 was irrational, If root2 is rational we have a contradiction etc etc

[forest jackal]

like I said at first, it is close, but the problem is that you cannot deduce that the product of numbers in your finite list + 1 is a new prime, you can only deduce that it has a new prime factor. that is all that was wrong in your original post, and it is a relatively minor point.

[strong light]

OH like

the finite prime could just be higher

is what ur saying

?

well then it would go on to infinity right, it would never stop

sorry im a nimrod xD

[forest jackal]

Eg/ 2x3x5x7x11x13+1=30031 is NOT prime, but it is divisible by 59, which is a prime number not in the set {2,3,5,7,11,13}

[strong light]

OHHHH

and we cant physically multiply the primes until 59

since the product might include a new prime

hm

well

the problem lies in taking every prime before our entire product is what youre saying?

it gets larger and larger and we cant account for the new primes that might be there every time or something?

[strong light]

so ok i understood we cant physically take every prime below a number because as we multiply primes and add 1 we arent accounting for primes outside the set and if we do account for said primes it would just create a larger unknown set, is this the reason its invalid?

just checking if i understood since i dont want to walk away with a misconception

[neat lintel]

Would love an argument

[weary garnet]

hi, I'm wondering whether I should pursue a degree in pure math, physics or computer science

I'm interested in computing stuff (software development/machine learning) as a career but I'm not sure if i'll be able to get into a computer science course in university

what kind of math would a degree in physics involve?

I've enjoyed the linalg, calculus and group theory that I've been self studying so far

[tender tulip]

I’m a dumbass but because N is infinite, and P generates it through the action of multiplication, wouldn’t P also have to be infinite in order to generate every element of an infinite set (the commutative monoid’s set)

[forest jackal]

Nope. The set of powers of 2 is infinite, but has a finite set of generators. (Namely {2} ).

[tender tulip]

That’s only a subset of N

but fair

[forest jackal]

I know, I was just providing a counterexample to your claim that an infinite commutative monoid cannot have a finite generating set.

[tender tulip]

Yeah, good point

Could we use Z/nZ’s set, and say that N is just an infinite Union of Z/nZ with 0 removed

And because the Union of finite sets is always finite unless it’s limited, it must be an infinite Union, but I don’t think that’s very “formal”

But Z/nZ isn’t a field in this case,

But just it’s SET

We could use a recursive definition

[forest jackal]

Yeah that's not formal at all, you need to be much more precise.

[tender tulip]

hm, let K = N x N

Nvm

Let N* = N{1}, an infinite Semigroup. Now, let K = N* x N* or the Cartesian product of N and itself. Define subset of K denoted V which is all (x,y) such that there doesn’t exist a z member of N* that divides both, then somehow say there exists an infinite amount of x such that {x} x N* and N* x {x} are subsets of V. But then we get back to were we started

saying that there is an infinite amount is a pain

[tender tulip]

Would using the fact that each natural number as a prime decomposition be formal

or could we somehow prove there is a bijective mapping of N/{1} to P

[tender tulip]

n and n+1 are coprime, so we know V is infinite because (n,n+1) and (n+1,n) must be elements of V for all n elements of N*

w a i t

n is coprime to n +1, and for all n of N there exists an n+1.

Implying there are finite primes, there must be a natural number k that is the product of all elements of k, but that must be coprime to k+1

which due to the fact that all n can be represented as composed multiplications of primes with repetition implies contradiction

Because there must be a minimum natural number that divides k+1 but ISN’T prime and also isn’t 1, but k+1 is coprime to k, which every prime divides, at least 1 prime divides every natural number, thus there is a contradiction

Proof complete (completely ignoring how I didn’t prove n and n+1 are coprime)

[strong python]

can someone plz help me with the question:

[tender tulip]

Let me find a way to prove n and n+1 are coprime

Without using additive or multiplicative inverses which aren’t guaranteed with (N{0},+) and (N,*) Monoids

[torn willow]

Just use bezout?

[tender tulip]

What

Assume they are, n = ma, n+1 = mb, 2n + 1 = m(a + b), m(a + b) must be congruent to 1 mod 2

[torn willow]

nvm no additive inverses

What I meant was if there exist integers a and b such that ax+by=1 then x and y are coprime

[tender tulip]

Idk where to go from here

[hushed turret]

what?

go by contradiction assume some prime divides n and divides n+1

[tender tulip]

That’s literally what I’m trying to avoid

[hushed turret]

why

[tender tulip]

this

I want to try to ignore primes for the contradiction

[hushed turret]

i mean it doesn't need to be a prime

[tender tulip]

Also because why the fuck not, I want to ignore primes

[hushed turret]

you could equally assume some arbitrary integer (not equal to one) divides both and derive contradiction from that

[tender tulip]

wouldn’t that need the idea of multiplicative and additive inverses

[hushed turret]

apply euclid's algorithm to n and n+1

[tender tulip]

let me just do a funny and N\{1}

[hushed turret]

i mean you're working with N why does that bother you

wait it doesn't need either of those things idt

well it needs additive i guess

[hushed turret]

how are you doing n+1 without 1

[tender tulip]

bruh

n = ma, n + 1 = mb, m not equal to 1
1 = mb - ma = m * (b - a)
but no n * m = 1 where n and m are natural numbers that aren’t 1 by preserving order and 1 being the minimum of the set

[tender tulip]

Fair

But b - a isn’t guaranteed to exist

Nah wait we assume it does

b > a, multiplication preserves order

[heady hemlock]

hey

i made an equation myself

this is a undefined thing I made

and I like it

[tender tulip]

Basically the whole thing,
Proof by “idfk there’s always a bigger prime”

(All variables are natural numbers from this point forward)

Lemma: there does not exist an m ≠1 that divides n and n+1
Proof:

1. n = ma, n + 1 = mb
2. if ma + 1 is mb, then m must divide 1, which simply is impossible because addition and multiplication preserve order, and thus the only number lesser than or equal to 1 that preserves this is 1, which m isn’t equal to. Contradiction.

Whole proof:
Let P be the first h-th primes,
Let k be the product of the first h-th primes
There is no natural number greater than 1 that divides both k and k+1, and because the first h-th primes divide k, then k+1 must be divided by a different number (possibly prime itself), thus there is always another prime that divides k+1

[surreal sapphire]

2*3*5*7*11*13 + 1 is not prime

[tender tulip]

oh shit

Let me fix my proof rq

@surreal sapphire (sorry for the ping) is there a name for a proof of infinitude by there always being a greater element?

infinite ascent?

[surreal sapphire]

🤷

[tender tulip]

Calling it that I guess

[pale orchid]

i don't think it has a special name

[tender tulip]

Is that a correct proof?

Like I know jack shit from number theory I kinda just pulled that out of my ass at 3 in the morning after 2 hours of sleep

[surreal sapphire]

order has nothing to do with your lemma

[tender tulip]

alright, I’ll fix that when I have the patience. I’ll just say there exists no divisors of 1 except for 1 itself

[surreal sapphire]

every other statement looks correct now

[pale orchid]

i think you could've done something a lot easier

like say there is a number m that divides both n+1 and n

[tender tulip]

Fair

[pale orchid]

so m must divide n+1-n

ending up with m | 1

[surreal sapphire]

in general this is a lot of words for saying "every kth number is divisible by k"

[tender tulip]

Fair

[surreal sapphire]

i guess that uses order then though

[tender tulip]

Once again I’m barely thinking about it and went from n and n+1 being coprime and the product of the first n primes to that

[neat lintel]

We're reaching a level of heresy previously unheard of

[normal sparrow]

Yo check this out

https://youtu.be/VYfWfrk5P7w

A proper non euclidean game

Holy shit

Like w spherical and hyperbolic geometries

[robust osprey]

Ok

Good

[frozen merlin]

i think hyperbolica is better when viewed as a proof of concept than as an actual game

but i'm excited to see this kind of stuff in more complete games in the future

[robust osprey]

Bruh

[limber thunder]

I remember seeing the hyperbolica dev videos

on that same channel

[solemn sequoia]

Does anyone have any insight to how Hungary's education system approaches mathematics? Do they follow the Soviet / Russian model? I was looking into the history of the Int'l Mathematical Olympiads and it was the first time I realized how well Hungary did in those competitions.

[lapis dune]

Hungarians get a natural +3 bonus to their Mathematics stat

[median zinc]

Physics too

[robust osprey]

This chat is dead

💀

[long matrix]

What can you do with curves on Wolfram? (I can't find anything on it atm)

Eg. square(cat curve) and root(cat curve) can be done, but I can't figure out any other operations or ways curves can be combined

[median zinc]

I saw you were trying to add them, not sure why they don't try Minkowski addition or similar...

[azure matrix]

I don't know why, but something about the 'reality'/'meaningfulness' of number 0 began to not sit well in me. I'm not even sure how to express it, but I think it has to do with counting, which is, historically, the very basics of math, so I'm not getting into, at least, the modern formalism. Let me try this way. If there is something, it makes sense to count it. But if there is nothing, it's not meaningful to give it a numerical value. We just can say we don't own it and that's it. I can imagine that adding no apples to one apple gives one apple. At the same time, it seems a bit bizarre to me that we are assigning a value to an absence of something. Someone says, "Zero is not nothing. Zero apples is nothing. But zero itself is not nothing." Maybe, that fixes my problem? Or what?

[modest rune]

Zero is not meaningless if thats what you mean

It's a number just like any other

[neat lintel]

are assistant prof normally want tenure so they would push their postgraduate students hard? Do they care about undergradaute students also?

[vivid halo]

This is literally what kept up mathematicians at night like 1000 years ago

[long matrix]

Mom: having nightmares again, son?
Son: none

[mortal igloo]

Zero is the equivalence class of the empty set when considering sets modulo bijection

[surreal sapphire]

you can try thinking about it with respect to money

[azure matrix]

It wouldn't be surprising. The standalone number appeared only in the islamic golden age.

[surreal sapphire]

you can have no money and that makes sense and is meaningful, right?

so having a 0 is pretty useful

[long matrix]

'whats greater than everything and worse than everything?'
'nothing'

Confusion can come from thinking about it like this

[torn willow]

Abadou moment?

[azure matrix]

But we can say we don't have money and that's all. We don't have to say 0 (zero). But if we have money it may be important to know its quantity.

[torn willow]

Ok, it's not abadou

[long matrix]

could you expand on this a bit, interested

[vivid halo]

presumably the linguistic confusion is that for counting numbers, the common procedure is to start with an observation that there is something common between "3 birds" and "3 rocks" and "3 seeds"

from that you abstract away and define the number as the abstract quantity that is common between these situations

[mortal igloo]

Hmmm you could look up cardinality on Wikipedia but I wasn’t saying anything too profound

[vivid halo]

but in the case of "0 birds" and "0 rocks" and "0 seeds" you have to be a little more careful linguistically

since there is seemingly no concrete particulars that you are abstracting away from to begin with

[surreal sapphire]

i think its useful to have everything "on common grounds", so having no money should be expressible with a number somehow

[vivid halo]

one linguistic solution is to pin this as "an absence of birds" and "an absence of rocks" and "an absence of seeds"

then there are concrete particulars with a common quality you can abstract

[long matrix]

'sets modulo bijection'

what sets, specifically

Just any old set or?

[mortal igloo]

It’s actually pretty hard to put yourself in the mind of people 1000 years ago when thinking about zero

[mortal igloo]

All sets

Take all sets in the universe and arrange them by size

Each pair of sets of the same size (there is a bijection between them)

Shall be considered equivalent

The equivalence classes you can start naming them by 0, 1, etc

[long matrix]

In which case the equivalence classes correspond with the cardinals?

ok sure.

[mortal igloo]

Yes

[long matrix]

Is this the standard way of defining the cardinals?

I havent taken set theory =...=

[vivid halo]

yeah

[long matrix]

I have only seen 0 := {}, 1 := {0}, ...

[azure matrix]

In any case, it gotta be important to create 0. Maybe, in arithmetic? At least, in algebra, I think. But how? And is this the same problem as with negative/complex numbers?

[vivid halo]

sets up to bijection = cardinals
well-ordered sets up to ordered bijection = ordinals

[vivid halo]

probably Stanford Encyclopedia of Philosophy has a very detailed explanation for this

the linguistic/philosophical issues about this have LONG since been resolved

https://plato.stanford.edu/entries/nothingness/

obviously it's like

useful to have for pragmatic reasons and the deeper philosophical issues have long since been resolved

there are similar linguistic and philosophical pitfalls related to talking about a negative number of objects and so on

[vast surge]

So, I have a question, if it won't hijack any ongoing conversation

[fervent pebble]

you should read the Book of Proof 👍

[vast surge]

Oh yeah this is a solid book

[long matrix]

thank you

i have so much math to catch-up on

[fervent pebble]

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

[fervent pebble]

it's online and free

like officially

so check it out

calc prereq

[long matrix]

big ty 💙

[brave hollow]

I am not sponsored but I hear some loch guy has a book on proofs as well

Shuri you should try that

[vast surge]

I was wondering, are there manifolds that are not (homeomorphic to) varieties? I know that there are varieties that are not manifolds (for instance, V(xy) is just the coordinate axes), but I was wondering about the other direction

[long matrix]

#proofs-and-logic intro to proofs?

[azure matrix]

Maybe, I should just know/recognize real world applications of negative numbers and that will clear my doubts about 0?

[long matrix]

yh im 4th yr uni, but i have a good number of gaps in knowledge - courses i shouldve taken

[brave hollow]

yeah I guess that, although I thought you were being sarcastic

[vivid halo]

debt

[vast surge]

Negative numbers appear all the time. Owing money to someone means you have negative money. If you have a string and you count the number of clockwise loops, a counterclockwise loop is a negative number. Etc.

[long matrix]

nah, the last sections of book of proof i need to brush up on

[azure matrix]

Yeah, I know about owing money.

[vast surge]

Then what's your problem with negative numbers?

[azure matrix]

I think I don't have a problem with them, though knowing more applications might be useful.

[neat lintel]

they give sense of direction

they are as useful as any number is

even in counting

[azure matrix]

Perhaps, my concern doesn't go that deep, and it's about grouping and seeing a common thing. If we insert 0 as a number, then it shares with (other) natural numbers the quality of being number. But, in terms of their real world manifestations, I'm treating 0 as nothing and others as something, and there is no commonality between nothing and something. That's why there is a confusion, I think. Do you see?

[vivid halo]

right, this is the confusion that (very smart) people were stuck on for hundreds of years

it requires some kind of reconciliation between "quantity" and "absence" so as to treat these on equal footing

I think the Stanford article explains a lot of different aspects of this

[azure matrix]

I'm afraid it's a bit much for me. There gotta be a way of just accepting)

[fervent pebble]

just trust in the smart ppl

then

just accept what they say

[vivid halo]

I dunno just accept it?

that or read Stanford or something similar where people actually explain things in a precise way

[blazing pawn]

From a less formal philosophical view this kind of depends on how you think about numbers

As cognitions

By less formal I mean escewing standard mathematical constructions of the naturals

[azure matrix]

Could you elaborate?

[azure matrix]

Maybe, using the concept of reference point in space or time?

[vivid halo]

nah it's easier than that lol

again I suggest you read through Stanford carefully, it's not supposed to be easy but you have to just deal with it if you want a proper explanation

otherwise you just have to accept it and move on

the point is you need to go to some other source like this if you want something that actually grapples with linguistic and philosophical issues in a way that's deeper than what we've already said

[blazing pawn]

Actually referencing space and time is not like totally inapplicable here lol

The example I was thinking of is for example kants critical philosophy of mathematics

[azure matrix]

But it seems there are a lot irrelevant things in the article and it doesn't talk about 0 very much. Can you refer to specific sections/paragraphs? Or I can read only parts that surround words "0" or "zero"?)

[blazing pawn]

I dont want to get into too many details but kant has a notion of mathematics and numbers that are basically like

[vivid halo]

it depends on what answers you're trying to get answered and I can't really point you to anything specific since I'm confused on what your actual objections are

I assume you're not objecting to the mathematical definition of 0 since that's a nonissue

just how this links to linguistic and philosophical issues of nothingness

[blazing pawn]

Okay in the interest of not confusing you im just going to say that kant basically thinks of numbers and mathematics as being like, a thing you can reason about by abstracting from real/empirical objects, but whose actual objects are "pure" and not actually dependent on any concrete thing

We talked briefly earlier about the idea that numbers come from abstracting away from objects (like we look at 3 pens, 3 books, 3 balls and abstract away from the concrete objects)

Here the direction is reversed: the abstraction is what allows us to use math to reason about empirical objects

[vivid halo]

well moreover the abstraction for 3 and so on is the same for 0, so long as you set up the linguistics of this properly

as I explained

[azure matrix]

yeah, it's not about the formalism

[blazing pawn]

Fudging things a lot I guess for kant numbers dont come from counting objects in space (the abstracting away i talked about before just lets us use numbers to talk about that) but from successive moments in time

[azure matrix]

it's about connection to the real world

[vivid halo]

yes this is easily explained through "absence"

or through some other instantiation of "nothingness"

[blazing pawn]

My point is that if thinking about absence of things existing in space is a problem for you kants view of arithmetic is not reliant on space but on time

And here zero doesnt have to have anything to do with the nonexistence of a given object but with the relationship between two moments in time (e.g being the same, so a single snapshot instead of an interval)

[vivid halo]

right this is yet another way around things

[blazing pawn]

Kinda hate myself for saying that because kants actual view was more complicated but that is roughly okay

[hushed turret]

that sounds interesting

[blazing pawn]

This isnt actually that unreasonable if you want to think about numbers from any sort of non psychological perspective because if "abstracting away" refers to like, physical things in the world and not just representations of them in our mind then you have to deal with contiguity anyway

That should have been a reply to the "arithmetic is reliant on time" bit

[neat lintel]

I never got why people needed to base their understanding of numbers in the physical world.
Yet, if we do do that, why not take voltage?

just anchor our understanding of the real number in terms of voltages

why use things like time, space..?

[vivid halo]

I mean you don't, there are "synthetic" ways you can do this by pure thought alone

though it's good to know that what you're talking about has some grounding in reality, otherwise it loses some amount of usefulness

[neat lintel]

My personal view of math is it's a hallucination inspired by reality that distils patterns in a consistent enough manner to be recombined and be useful

So I concur.

[hollow gorge]

anyone know how many different ways 8 people could be arranged in a circle? permutation I think since order matters

i'm pretty sure the answer isnt just 8 factorial

[azure matrix]

So, 0 is a moment in time like "right now"?

[hollow gorge]

i put the photo of the problem in #math-discussion

[blazing pawn]

Technically speaking these numbers would correspond to relations between points in time so it would be something like "the distance between a point in time to itself"

I think thats a fairly valid physical meaning

This is kind of fudged anyway

[azure matrix]

Why not in space as well?

[blazing pawn]

I think getting into the reasons Kant believed this would probably not be very productive

And require a decent amount of background in his philosophy

But my point was more that, like, there are many ways in which you can make sense of 0, philosophically, since there are already many different philosophical conceptions of what numbers actually are

And this is one of many examples

[azure matrix]

ok, i'll keep in mind

[azure matrix]

@blazing pawn But how are, practically, all people comfortable with the idea that there is a number that corresponds to nothingness? How does it seem/feel natural, even though it became independent not long ago in the grand scheme?

[azure matrix]

Do they just accept?

[vivid halo]

it feels completely natural, because it is

I don't think it's a matter of accepting, there's some really simple justifications of how this follows from natural language (which I have already given) that most people find to be sufficient explanations

[azure matrix]

Only this one?

[austere dragon]

How does 0 not make sense naturally? Do you mean objectively?

[ripe wasp]

i’m thinking of taking a group theory course this summer

and it says the prerequisites are modular arithmetic and some basic combinatorics

anyone know any good concise sources to learn this?

i’m familiar but not too comfortable with proofs, which is kinda why i’m taking this course

it’s the aops group theory course

[jovial ember]

Hmmm

[vivid halo]

yes, this is pretty much the standard explanation

idk what about it you don't get

[jovial ember]

Books on discrete math

Should include both modular arithmetic and stuff for counting

[jovial ember]

Post this again in #book-recommendations

I think you’ll get better responses there because more people check that regularly who might know a good recommendation

[ripe wasp]

ah right thanks

[vivid halo]

like if you grant the argument that is going on in the "3 birds" and "3 stones" argument

literally the same argument works for 0

unless you have some philosophical confusion about what "nothing" or "absence" means

in which case read Stanford

but I get the feeling you know what "nothing" means unless you're being intentionally extremely pedantic about it

[azure matrix]

No, actually, it seems to help. Maybe, I'll check out that article, but now I'm a bit relieved.

[vivid halo]

yeah I mean it's a natural confusion to be had, a lot of people have had this confusion historically

I think a lot of the historical resistance to this idea is that if you're taking an extremely physical interpretation of the world then it's kinda hard to see why these two examples are the same, or at least analogous

since it's very easy to say "well in the case of 0 things, what things are you referring to?"

so it does take some kind of a philosophical leap to get out of this kind of rut, some of this requires making precise what "nothing" is

there's a section in Stanford on the subtractive argument that gives one kinda primitive answer to this.

To paraphrase, think of a world with finitely many objects (I suppose this is not too absurd, it's probably harder to imagine infinitely many things!)

if you can imagine that world you can imagine that world with one of those objects removed from it

[fading fjord]

if i make .3 cents in 13 minutes how much a day

[vivid halo]

if you follow this to its logical conclusion you arrive at some world with no objects in it

(this at least is some attempt to answer some of the pre-objections along the lines of "oh well you can't imagine nothing")

[azure matrix]

against those who denied the existence of void?

[vivid halo]

right yeah

another instantiation of this, if you can imagine or conceive of some finite set of objects, and those objects have some properties that you can describe, then if you pick some properties you can describe a subset of objects that satisfy these properties

if you choose two mutually exclusive properties, well then you have the empty set

certainly the empty set is one way to make "nothing" precise, so long as you grant that you can group things into collections

there are extremely pedantic arguments against stuff like this but at that point you get into analytic philosophy stuff where people are honestly just trying to be as pedantic as possible all the time

there's definitely a very exhaustive treatment of these arguments and counterarguments on the Stanford page

hope this helps

[azure matrix]

But I am/was not denying the 'existence' of nothingness. I was just confused about representing nothingness by a number.

[bronze pelican]

https://youtu.be/L0B548ZUOEk

[vivid halo]

this is lovely

"HOW OFTEN SHOULD YOU BEAT YOUR KIDS??"

hahahah the modular forms chorus

[bronze pelican]

Yes!

[vivid halo]

have read a lot of Zagier and Gangl papers so it's always funny to see like

personal lore like this

[neat lintel]

😂

edgy

[cobalt star]

i guess you can think about it like

Between the positive numbers and negative numbers

Like you can have $1

and you can have -$1, ie. owe $1

and having $0 is like in between the two

like if you didn't have the number 0, there would be a gap going from -$1 to $1

You would have to earn 2 dollars to get from -1 to the next integer

which is weird

[azure matrix]

How can't you have $1 right after -$1? Could you describe a real-world situation/process?

[fathom swallow]

Narynbek

[cobalt star]

ok maybe i put it this way

Say you write out all of the integers in a line, evenly spaced

if you didn't have 0 then -1 would be next to 1

so on this line, you can see that usually when you go from one integer to the next(moving towards the right), all you do is add 1

so if you had -3 dollars, to get to the next one (-2), you just earn 1 dollar

but going from -1 to 1, this doesn't work

because if you earn 1 dollar, you go from -1 dollars to no dollars since your debt just cancels out

yeah this doesn't necessarily justify that zero has to be a number, but if it wasn't there we would have a gap in the number line

which is annoying

crap i suck at explaining things

[azure matrix]

But you always have no dollars in the case of debt, because as soon as you earn a dollar you automatically lose it since it's not your money.

[leaden torrent]

do you have anything better to do

[azure matrix]

Oh, but I can have the state of no money and no debt. I guess I can see it now.

[pale orchid]

0 never existed

it's all a hoax

[static loom]

there is no nothing 😌

[leaden torrent]

all numbers are hoaxes

who needs more nuance than "a few", "some", "lots"

[pale orchid]

furthermore, 101 = 11

[toxic schooner]

and 10000=500

[fair mural]

yes remove the trailing 0s

in fact just remove the 0s

[waxen lily]

im sick of writing the $ sign before the number

its better at the end

[static loom]

can you write me a check for 9 dollars, I'll give you 20 dollars if you do

[gray loom]

I wish I was born as one of the autistic kids on TV like Sheldon or the Good Doctor instead of just me lol

[median zinc]

You mean being a main character and being 'smart'?

[gray loom]

Maybe not a main character

Elon Musk bad

But

I wish his brain chip was actually capable of fixing my brain

[deep mango]

While I understand the sentiment, these caricatures of "autistic kids" are pretty screwed up and harmful and it's not cool to reduce people with ASD to these caricatures. Please don't do that.

[gray loom]

Yeah I'm aware they're super fake

Just wish that was something actually possible instead of just being me

[median zinc]

Are you unhappy with your capabilities?

[lament edge]

isnt everyone

[deep mango]

Not me

[gray loom]

It sucks not understanding stuff everyone just immediately clicks with

Sometimes it's just practice

But when someone explains something in a certain way it might as well be hieroglyphics

[median zinc]

I'm not sure if I relate because I'm doing hard stuff and everyone is drowning except the professor

[deep mango]

I think it's easy to convince yourself that everyone immediately clicks with these things, but usually that's definitely not true

People will do anything to look like they know what's going on

[inner finch]

Hey come on, it all gets better with practice

I never was good at school and was always behind

[deep mango]

Yeah

[inner finch]

Don't beat urself up about it

A time will come with enough effort you'll be better

[gray loom]

Most of my other subjects are fine rn

[inner finch]

see thats good

[gray loom]

Stats, specifically this probability stuff is just alien

I can't really wrap my head around it

[inner finch]

ahahaha that's actually common believe it or not

Are you doing those counting problems rn? Permutation combination type stuff

[gray loom]

I think my next unit is about sampling estimates/distributions

So hopefully that's easier to keep track of

[inner finch]

I see i see. Hopefully it will

If it helps i was never good at stats

but i still managed to get an A on my exam

So i think you will be fine too

[gray loom]

Depends how the next exam and the final goes

There's a bunch of other little assignments to hopefully make the grade up

Very much bombed this one. Not sure what the average is gonna look like

[inner finch]

Ooof

Also grades aren't the end of the world. I'm sure you know this and just want to do well, but it's an important thing to remind oneself. I hope you'll do well, if ur having trouble understanding stuff u can have a look at the #probability-statistics channel

[gray loom]

"C's earn degrees" they say

But I wouldn't mind a B or solid A-

I don't know if I can make deans list for a minor but that'd be a real treat if possible

[sonic sentinel]

autism is when you like something

[sonic sentinel]

||yes i understand this is tangentially related and isnt the main personality trait of the main characters in the shows||

[sleek wing]

what the fuck

[reef geode]

Is there a specific time SAT scores come out or do they release at midnight

[toxic gale]

I know I'm several hours late, but I don't think a single person in my class was good at this topic. We all memed about it, so if that's what you couldn't understand, you are most definitely not alone.

[charred mortar]

Permutations are hard stuff

Combinatorics in general too

[toxic gale]

Yeah. Especially since I think it requires a lot of thinking and understanding compared to the rest of the standard stats curriculum, where you just memorise a bunch of tests.

[ancient flame]

for a function, we need this information:
$$f(x)=y \text{ such that } f:X \to Y$$ where $X$ is the domain and $Y$ is the codomain. what is the $y$ part called, where $y$ could be something like $x^2$ or $\exp(x)$ or smth?

[fathom swallow]

guh mode

[tall badge]

"f(x)=.." is commonly called the rule of f

[ancient flame]

oh okay ty

[leaden torrent]

you'll also here the term 'graph'

[empty stratus]

Horribly so.

But such is life.

[charred kayak]

how would you determine if you're on the right level on math

a lot of people say you should master algebra, geo and trigo before starting with calculus

how can you tell ur good at math already anyway

[warped carbon]

If you can answer the question without paper.

[charred kayak]

if i get

90 percent

on any random algebra questions on the internet??

[warped carbon]

Changed my mind.

[charred kayak]

why did u edit that btw 💀

[warped carbon]

I was wrong with the first one.

[charred kayak]

ah yea

answering without the paper is different now

yea thats a better

something

ty

[warped carbon]

Probably should have crossed it out and reposted instead of editing it, my bad.

Like.

[charred kayak]

its good

[warped carbon]

I know I can do Algebra II because if you point me at a random Algebra II problem, I can about nine times out of ten tell you what the answer is in well less than a minute.

Likewise for Trigonometry.

[charred kayak]

why are there roman numerals with

algebra

what's in algebra II that's not in just algebra

[warped carbon]

American education goes Algebra I->Geometry->Algebra 2.

Don't know for sure why.

[charred kayak]

we have geometry for 1st grade until 12th i think

but 1st grade geometrys are just basic shapes

[warped carbon]

In my experience, Algebra 1 was like really basic "This is how you can move variables around in an equation", and closed on finding the roots of quadratic equations by factoring.

Algebra 2 covered the rest.

Which is.

What.

Polynomial division, completing the square, transformations of graphs….

[charred kayak]

screenshotting to google and youtube these words later

[warped carbon]

Where're you right now?

[charred kayak]

wdymm

[warped carbon]

In your maths education.

[charred kayak]

im pretty sure im stuck in fractions 😭

my math level is like 4th grade

[warped carbon]

Calculus is a long way off, man.

[charred kayak]

right 😭 💔

[warped carbon]

I wouldn't be worrying about stuff like that yet.

You'll get there when you get there.

I learnt most of my maths at community college.

Placement test was great.

Took like.

Two years to get me from Algebra II through single-variable Calculus.

So that's like three or four years from you, if you went at breakneck pace.

[charred kayak]

haaaaahhh

[warped carbon]

You'll get there.

Well.

If you try to.

[charred kayak]

yea i will

i actually already been trying since last year

and i keep finding out what im missing

so i asked about the levels to know my place so far

[warped carbon]

If there's a two-year university near you I'll bet they have a placement test you can take.

Or you might be able to find one online.

I don't know of any though; I should.

[charred kayak]

can definitely do online

ive never heard of placement tests in my country

[warped carbon]

They actually just got banned in the state I live in.

Oh.

[charred kayak]

huh, why

[warped carbon]

They're called matriculation tests.

Sometimes.

[warped carbon]

Something-something racism.

Allegedly.

I really can find no justification for it myself.

[charred kayak]

weird

[warped carbon]

Fucking right?

[toxic gale]

A lot of people like using Khan Academy for algebra. If you haven't tried it, might as well give it a go.

[charred kayak]

ahh yea

[toxic gale]

Pretty sure they have a placement test you can do to tell where to start.

[charred kayak]

but some people said you would try books instead

[toxic gale]

It depends on your learning style, honestly.

[warped carbon]

If you can solve the problems it doesn't really matter how you learned to solve the problems.

[toxic gale]

I like books because I like going at my own pace. I find Khan Academy quite slow.

[charred kayak]

yea thats what they said

[warped carbon]

You could probably teach yourself the entirety of secondary school maths with Kuta Software and an Algebra calculator.

[charred kayak]

they said their 2 months of learning was actually in a book that took only a short time

[warped carbon]

Given the right attitude.

[charred kayak]

ill check, gotta screenshot

[warped carbon]

Let me get a book for you.

Hang on.

[charred kayak]

😳 alr

[toxic gale]

Then again, it's still better than nothing. Some people can't stick to books and prefer video lectures.

[charred kayak]

yep

[toxic gale]

At the end of the day, the different routes will get you to the same place. It may be slightly slower or faster, but it's ultimately not too different.

[warped carbon]

Holy shit why is it so hard to find what Algebra I textbook my college uses?

Jesus.

[charred kayak]

[toxic gale]

Maybe because a lot of high school textbooks are basically the same.

[warped carbon]

No, like.

There's a fucking "Books" button.

But it just redirects to the bookstore.

[toxic gale]

That's irritating.

[warped carbon]

Which has it down as the fucking MyMathLab certificate.

Not the actual name of the book.

Presumably because the certificate is, I suppose, technically all you need to take the course.

[toxic gale]

That sounds painful. Never really had to deal with this online book shenanigans thankfully.

[warped carbon]

Okay.

https://files.catbox.moe/rcqzvv.pdf

I THINK this is it.

[warped carbon]

Admittedly this would never be a problem to anyone taking the course, since it'd just be in the syllabus for them.

Probably why it's broken.

[warped carbon]

It it's not, doesn't really matter anyway.

Since.

One book will be as good as another.

More or less.

[warped carbon]

@charred kayak.

[charred kayak]

hey

[warped carbon]

Really though, you're probably less limited to online learning resources than you think you are.

I'm sure there's a brick-and-mortar institution somewhere within transportation distance of you that could provide better service.

If you're determined to do it yourself using the internet, though, then this would be a fine enough textbook to start with.

Unless it's too advanced.

If it is, let me know and I'll dig up the book for the course prior this one.

[charred kayak]

sure 😳

is working btw

[warped carbon]

Cool.

If you want my advice for learning math, it's this.

Always try and do the problem without paper first.

Like, in your head.

Talking out loud or using your fingers or props is fine.

That's why I say "Without paper" rather than "In your head", slight difference.

Then right down the answer.

Then try and solve it on paper, and if they match, check with a calculator or the answer sheet.

Too many people become fucking paper-operators instead of ever actually learning maths because they never try and do it without paper.

If you don't know how to solve a problem, you can usually plug it into Symbolab and it'll show you how to solve it step by step.

If you're using a calculator to learn understand why the moves it is making are legal.

Don't just memorize the steps.

Memorizing steps isn't learning math.

It's okay not to understand exactly why things work when you're just beginning on new material, but you should try and get to understanding the why as quickly as you can.

[wild lantern]

There's nothing wrong with using paper lol

[warped carbon]

Good luck.

[warped carbon]

Fight me.

[wild lantern]

Good luck doing anything nontrivial without some paper.

[charred kayak]

when u said ur first reply i immediately thought of this bahaha

[warped carbon]

Point me to an Algebra 2 student who can explain why the fuck synthetic division works.

Or a Calculus student, even.

[wild lantern]

How is that at all relevant to using paper vs not?

[leaden skiff]

hard disagree

[wild lantern]

Seems like writing out some stuff might actually help people explain things?

[leaden skiff]

like the best thing to do is to go get a piece of paper and write down everything given in the problem statement

[wild lantern]

I tend to draft and doodle out proof ideas as I work on problems.

[leaden skiff]

trying to do it in your head will just make it harder for no reason

[wild lantern]

Not saying doing a bit of thinking without paper is a bad idea fwiw.

[leaden skiff]

i think avoiding paper is a bad idea

but thinking without paper is not

[wild lantern]

Sometimes going for a walk or staring at a wall can be kinda helpful too lol

[toxic gale]

Yeah, for me, even seemingly easy problems I have trouble doing without paper. It's easy to mix up things when you don't write down.

[leaden skiff]

yeah, don't intentionally handicap yourself

don't try to avoid any one technique

[warped carbon]

I would argue that's because you don't have enough practice doing things without paper, though.

Rather than an intrinsic and irreconcilable problem.

[leaden skiff]

why do you need practice doing things without paper?

[toxic gale]

Fair, but I can't say I tried nor wanted to try practising it. 😂

[warped carbon]

I only know so much.

[wild lantern]

I guess oral exams exist

[warped carbon]

I got good at maths by doing things without paper.

It seems to have worked for people I've suggested it to.

[leaden skiff]

i mean, yes oral exams exist, but they test your ability to explain

[warped carbon]

I could, and do sometimes, try and come up with justifications why but the actual core of my reasoning is empirical.

[leaden skiff]

they don't ask something like "find the taylor series of e^(ix) and prove it's equal to cos x + isin x" in an oral exam do they?

[wild lantern]

This was like quite a few semesters ago but the one I did for number theory was mostly explaining definitions, ideas and etc but that included key ideas from proofs and junk.