serious-discussion

[timid bronze]

This too

[viral yew]

if I hear smth funny my friend said I just remember it bc bro said it irl

[timid bronze]

Bro I’ve TALKED to my friends through my status

We talked to each other through statuses

[viral yew]

this crazy bro

[mystic raft]

I’m not surprised this happened

Much worse was done to talk

[timid bronze]

Discord flopped withh this one 🥀

[mystic raft]

I’ve used a base 64 encoder to talk to my friend on a server

[timid bronze]

Do yk Trello

[mystic raft]

They will never know

[mystic raft]

Nope

[timid bronze]

It’s like an organization site I used for a server and

One time my friend got grounded

And they couldn’t use Discord or anything

So they talked to me through there

😭

[mystic raft]

This is just so funny and dumb at the same time

I would probably use slack since people consider it “work”

[viral yew]

yes

[viral yew]

what tha hail

[timid bronze]

He’d talk to me by commenting under a card

😂

[timid bronze]

Omg ew not Slack

I don’t like thinking about it 💔 Reminds me about having a j*b..

[viral yew]

hey can we sync about <topic> rq
<link to zoom>

[mystic raft]

Employment is beautiful

It’s fundamental, I should say

[viral yew]

I'm working on <JIRA ticket>, are you using the test env rn? I want to deploy to it

[timid bronze]

My TAs pissed me off this semester because finding theirzoom link for office hours was a scavenger hunt 🥀

[viral yew]

lol

[viral yew]

do you live on west coast

[timid bronze]

My dream is to not work

[timid bronze]

I’m in the CST time zone

[viral yew]

I want to work on my dream

[timid bronze]

That’s the most I’ll say

[viral yew]

explains a lot

I sleep now I'm on east coast

[timid bronze]

EST

CST is better

It’s the Correct Standard Time

[fresh comet]

[viral yew]

ok vro

[timid bronze]

Hi my favorite mathcordian

Your reminder for today

[fresh comet]

I shall go to sleep slightly earlier today

[timid bronze]

Me too but at the same time I don’t want to

[fresh comet]

how're you holding up?

[timid bronze]

Nothing crazy

Wbu

[fresh comet]

that's not an answer

are you doing okay?

[fresh comet]

I'm a little tired, a little anxious, a little sad, but I'd still say that it's going okay :>

[viral oracle]

[mystic raft]

If only I was the community notes guy

[timid bronze]

Yes I meant like

Nothing crazy is going on in my life rn that’s of concern

[timid bronze]

I’m sorry, I hope you feel better

I’m always here for you

[fresh comet]

I know I know, but that didn't tell me how you're feeling this very moment

[fresh comet]

'ppreciate it, but don't forget that it goes both ways c:

[viral oracle]

I will give you both if accepted

[timid bronze]

I feel hungry because ig I didn’t eat enough at 5 PM xD

But I can’t go grab smth light rn

[mystic raft]

I’m back again… is there something wrong rn?

[timid bronze]

My mom gets pissed any time she sees me up in the kitchen late

For “religious” reasons

[timid bronze]

No

[timid bronze]

Yes pwease

[viral oracle]

[fresh comet]

ah, I see

[fresh comet]

[viral oracle]

https://tenor.com/view/cat-fenec-fox-lick-cat-fenec-fox-lick-gif-12624062

[fresh comet]

https://tenor.com/view/cat-rabbit-cat-rabbit-cat-and-rabbit-cat-sleep-gif-5780726925060253864

[timid bronze]

Cat and bunny hug is crazy cute

I love seeing diff animals be besties with each other

😭

If only humans could learn from this shit and not be bigoted towards people who are different from them .. 🥀

[viral oracle]

https://tenor.com/view/cat-kiss-dog-lick-kiss-cat-dog-gif-13534897395749114474

[turbid sedge]

I guess bro

[turbid sedge]

Oil and water imulsion

[viral oracle]

https://tenor.com/view/cat-hello-cat-peek-cat-door-cat-peek-door-gif-17361470248875227911

[turbid sedge]

??? @moderatoes I find this extremely disrespectful and unsuitable for a fiscussy 2 user. Please take nessesary actions

https://tenor.com/view/watch-yo-tone-meme-anger-mad-thragg-gif-6417141235193562233

[rose ridge]

Get out of here

https://tenor.com/view/thragg-supercut-hard-thragg-he-has-me-invincible-gif-14238247084429664073

[turbid sedge]

NO

LOWWWWWWWWWWWWWWW

TAPERRRRRRRR

FADEEEEEEEEEEE

Ts aint eren

[old oak]

I suppose it's some kind of quality-conservation principle, when #discussion becomes interesting, #serious-discussion becomes a cesspit

[turbid sedge]

blame lockie cuh

this one's done by them

[lusty terrace]

hello everyone

[rocky shuttle]

happy birthday

[silent junco]

not sure whose birthday it is but happy birthday

[foggy meadow]

happy birthday

[old oak]

BIHRATPHPDAYY

FORG

[rocky shuttle]

equinaurx (see bio) and it's also metal's birthday

[silent junco]

ah

happy birthday equinaurx and metal

[turbid sedge]

Happy birthday insider

@lusty terracehbd

[rose ridge]

Happy birthday

[lusty terrace]

thank you everyone !! sorry i was drawing LOL

[mellow flame]

hello i have a fr question

extra #fr because its 2 am

are/were u broke broke in grad school

[rocky shuttle]

no

fr

[mellow flame]

is that normal

like

when i was first looking into programs, the stipends were around 35-40k so i assumed that was the standard 😭

im rechecking some (i applied to) and theyre like half that!!

[sharp mulch]

Yeah it can vary quite a bit

[rocky shuttle]

idk it depends a lot on the location, too, my grad school's in germany

[mellow geyser]

let's talk here? @hollow gale and Manifold guy?

i dunno how to ping your name

[hollow gale]

i dont think he wants to talk

[mellow geyser]

oh ok

[fresh oriole]

this manifold guy does

[hollow gale]

the fake one

[mellow geyser]

Nice: )

[raw cedar]

why are so many people called manifold

,av @fresh oriole

[fathom swallow]

manifoldcuriosity's Avatar

Click here to view the image.

[fresh oriole]

like a fake R^4

[mellow geyser]

i think you last said what it formally was? I cannot find the comment

[hollow gale]

like a fake S^3 you mean

[mellow geyser]

let's decompose that statement

[raw cedar]

S^5 lives in R6

[rocky shuttle]

fake glome

[fresh oriole]

here’s the definition given in Pugh:

A cut in Q is a pair of subsets A, B of Q such that:
(a) A U B = Q, and A and B are disjoint and nonempty (i.e. A and B are a partition of Q)
(b) If a in A and b in B, then a < b
(c) A contains no largest element

[raw cedar]

jargon

[fresh oriole]

the definition HChan gave is essentially that of A (the other set B is determined from A, so it’s not strictly needed to be mentioned)

[hollow gale]

im trying to avoid talking about sup and inf lol

[mellow geyser]

from (a), can we say that A and B are right next to eachother?

if it is, it would make sense why it's called a "cut"

[fresh oriole]

I’d say it’s from (a) and (b)

[hollow gale]

yes, you are quite literally cutting the rationals down some point

and defining a real number as the bottom half of that cut

that's why it is called a cut

[mellow geyser]

ok. i like that you included (b), because it's making me think. Is (b) necessary?

[hollow gale]

it is necessary to remove duplicates

[viral oracle]

if a in A and b in Q? shouldn't it be b in B?

[fresh oriole]

so for example there’s A = {p/q | p/q <= 0 or (p/q > 0 and (p/q)^2 < 2)} and B = {p/q | p/q > 0 and (p/q)^2 > 2}

[fresh oriole]

yes, my bad

[viral oracle]

npnp

I had just come across an exercise in analysis asking for a proof of this (or something similar? I'm not sure if it is identical because:) for the reals but not the rationals

[mellow geyser]

actually i thought those 2 statements were equivalent, not?

[fresh oriole]

property (b) is meant to encode that A is completely to the left of B

[viral oracle]

if a in A and b in Q, then you can pick some b in Q that is less than a

[mellow geyser]

fair

[mellow geyser]

i see. I just thought the fact that saying they're disjoint from (a) was enough for that

[viral oracle]

I think maybe it would be easier to describe the cut property as two nonempty, disjoint subsets A and B, with A U B = Q (or R), and a < b for all a in A and b in B

[mellow geyser]

nevermind, i take it back. I see what you mean

[fresh oriole]

yeah because otherwise they could be disjoint but all mixed up alternating back and forth

[fresh oriole]

I don’t think we can say A U B = R, because we’re looking to construct R from Q

[mellow geyser]

how did we get (or R)? Is this what someone was talking about when they gave the sqrt2 example?

[hollow gale]

ignore the R

just think about it as Q

[viral oracle]

oh then I'm mistaking what this is about

ignore me then

[fresh oriole]

this pair of sets essentially uniquely specifies sqrt(2) using only rational numbers

[mellow geyser]

by having the cut exactly at rt2?

[viral oracle]

the definition I stated is a property of the reals, so since you're specifically talking about Q and constructing R from it, then yeah that would not work as well

[fresh oriole]

yup. It’s larger than everything in A, but smaller than everything in B

[mellow geyser]

Ok, this get's us one irrational number, but how does it guarantee that we can do it for all irrationals? Because I notice that it wouldn't work for something like pi

[hollow gale]

why wouldn't it work for pi?

[mellow geyser]

because pi isn't the root of a rational number

not just square root, any rational root

[hollow gale]

well, that just means that you cannot explicitly describe what the cut looks like

but it is in there somewhere

[raw cedar]

except you can in this specific example.

[hollow gale]

just like how you can't actually describe most real numbers but there are still there somewhere

[fresh oriole]

it’s less obvious how to express pi in this way, because we aren’t allowed to just use the pi symbol to make the cuts

[raw cedar]

there are multiple monotone series for pi.

[fresh oriole]

unless we’ve defined pi elsewhere already somehow

[hollow gale]

yeah, most conventional definitions for pi employ the use of sine and cosine

which need the real numbers to work

any series definition would be somewhat unconventional

[raw cedar]

...........

[hollow gale]

it works but this goes against the sprit of the question

[raw cedar]

indeedddddd

[mellow geyser]

i'm a bit confused on how it works

[hollow gale]

can you tell me what you understand a dedekind cut to be?

[mellow geyser]

from what I understand: of a set Q, a dedekind cut is the element of Q \ A \ B, where A and B follow the properties we discussed

[serene vault]

just seeing this, thank you!

[hollow gale]

can you spell them out for me?

[mellow geyser]

A and B don't share any elements. Every element in A is less than every element in B

am i missing anything? this is how i understand it

[fresh oriole]

almost, except Q \ A \ B is empty

[mellow geyser]

wow. This one is interesting

[fresh oriole]

the cut is the pair A and B itself

[mellow geyser]

it sounds like root 2 shouldn't exist then

[hollow gale]

I don't know what Manifold is saying

the cut is specifically A

[raw cedar]

it did not exist before the construction.

[raw cedar]

does not matter

[fresh oriole]

I’m following Pugh where he takes it to be both, but from what I understand we could equally well take either one by itself, since the other is uniquely determined from it

[hollow gale]

I'm trying to make it easier to understand

[mellow geyser]

if we derive rt2 with the property that it shouldn't exist, i'm not understanding how it exists after the construction

[hollow gale]

but since you're confident that you can do it then i will take my leave, enjoy

[mellow geyser]

rt2 isn't in either set, and Q \ A \ B is empty, right?

[fresh oriole]

well, next you need to learn how to do arithmetic with these cuts

and once that’s done, you can prove the square of this cut equals 2

[mellow geyser]

why? Multiple brains produce better results

[raw cedar]

money does not actually have value. it is just a piece of paper, and yet we can do reasoning and calculation about it. why is that?

[hollow gale]

it is annoying me that people are responding to my comments with um actuallys

so ill leave for a cleaner chat

i hope you all have a good day

[raw cedar]

who did tha

[hollow gale]

.

[mellow geyser]

i don't think he did it with that intention

[hollow gale]

it's fine, I'm done with this

as I said have a nice day, feel free to ping me any other time

[raw cedar]

cool

[fresh oriole]

peace 🕊️

[raw cedar]

uhm

BACK TO TOPIC

we need more people for discussion

ill go recruit some from math discussy

[mellow geyser]

how do we do arithmetic?

[fresh oriole]

so, the definition of a cut is quite elegant, but this is where things get messy

[placid shadow]

What are the rational numbers? Just any number that’s not irrational nor complex?

[fresh oriole]

eh, maybe it’s not so bad

[idle steppe]

A number is rational if it is equal to a/b where a and b are integers and b≠0

[raw cedar]

yes! so like 2/3 or 5/6

[idle steppe]

So, a ratio of two integers

[serene vault]

(that's why they are called rational)

[raw cedar]

no wai

[placid shadow]

Omg

[idle steppe]

A number is irrational if it cannot be represented as a ratio of two integers

One example is √2

[mellow geyser]

where the integers are coprime

[fresh oriole]

if x = A|B (this is Pugh’s notation of the cut A and B), and y = C|D, then:

x + y = E|F where

E = {r in Q | for some a in A and c in C, r = a + c}
F = the rest of Q

that’s the definition of a sum of cuts

[serene vault]

coprimality is sometimes optional, which is why the proof of sqrt(2) being irrational usually has it as a separate assumption

[mellow geyser]

i think you're right, but it almost has no harm in assuming it in everycase, it would get rid of multiple representations of the same number

[serene vault]

oh I'm not saying it's harmful in any way

[mellow geyser]

but then again, in the spirit of making as least assumptions as possible, maybe not having it is better

[serene vault]

it's just that usually it's not specified

unless coprimality is important in a context involving Q

[idle steppe]

Heres this funny proof of cube root of 2 being irrational. Suppose the cube root of two is rational. So 2^(1/3)=a/b where a and b are integers. And b≠0. Cubing both sides we get 2=a³/b³
So a³=2b³
a³=b³+b³. Do you see the contradiction?

[mellow geyser]

never seen the proof here, but isn't this fermat's last conjecture?

theorem, i guess.

[idle steppe]

Yeah, this contradicts fermat's last theorem

[fresh oriole]

using a hydrogen bomb to take out a mosquito

I wonder if there’s any hidden circularity in that

I really hope not

[idle steppe]

I would have no chance of finding that

[mellow geyser]

sorry for diverging from the arithmetic. My attention is back to the definition

[idle steppe]

Im NOT gonna look at the proof of fermat's last theorem

[fresh oriole]

haha yeah, no

there’s a very nice short proof that the nth root of m is irrational whenever m is not a perfect nth power of an integer

it relies on the fundamental theorem of arithmetic

you consider a rational number p/q and express the numerator and denominator uniquely factored into primes

and cancel any common factors

then consider raising it to the nth power

this just copies your primes, and no new cancellations are possible

[mellow geyser]

so this is very much intuitive. Just as you take the sum of any number (assuming you have already constructed the reals)

[fresh oriole]

so it can’t be an integer since there’s stuff in the bottom that doesnt cancel

[fresh oriole]

yeah, take all possible sums from A and C. It makes sense

multiplication is a bit worse because you have to worry about signs

[mellow geyser]

Doesn't this mean that the new cut E|F doesn't preserve the property that E and F have: every e in E is less than every f in F?

[fresh oriole]

it should still

E should take the form (-infty, r) intersect Q

and then F is (r, infty) intersect Q

[mellow geyser]

and x + y is r

[fresh oriole]

where r = x+y

yup

[mellow geyser]

dedekind was gauss' student, right?

[fresh oriole]

good question, not sure

[mellow geyser]

I remember reading that on wikipedia

[fresh oriole]

apparently he was Gauss’ last student

[mellow geyser]

wow. Last was a blast

[fresh oriole]

no cap

[mellow geyser]

i will ask about the pi thing at the math village thing I will go to though. It still bothers me a little

i'm guessing we will discuss dedekind cuts since the name of the workshop is "real numbers"

or "Reel sayılar" in turkish

I think this is all my time (and maybe yours too) permits me to talk. I really enjoyed your company. I hope the conversation benefitted you, which it should. Of course it also benefitted me

[fresh oriole]

yeah, it was fun!

[mellow geyser]

I hope to see you around. I may come back later today or even another day

[fresh oriole]

I know what you mean about pi

[mellow geyser]

: )

[fresh oriole]

I chat here a lot so I’m sure you’ll see me around

[slender echo]

This man is the manifold madman

[fresh oriole]

haha, wassup Tiny

what were we talking about last night…

oh, groups

that was good

[slender echo]

Yeah

I hope to learn abstract algebra eventually so that I can truly know groups

[fresh oriole]

you can do it! though I must say, having studied it a fair amount, I can’t say I truly know them

there’s a ridiculous amount of depth hidden in those axioms

but the more you learn the more interesting it gets

[slender echo]

That sounds cool

I’ll get there one day

[fresh oriole]

have you studied any set theory? just basics like unions, intersections, and how to notate them

[slender echo]

Yes,”How to prove it” studies some set theory along the way,and I’ve been studying that book

So far it’s gone up to families of sets and their operations,aswell as power sets

One of the chapters close to the end are about cardinality and ordinality,and/or counting if I remember correctly

[fresh oriole]

nice

you’re probably ready to start contemplating the definition of a group, then

[slender echo]

I look it up every now and then just to take a gander at higher mathematics

[neat lintel]

Helloo girls

[tight sequoia]

ladies under my message

[obtuse grail]

Hi lemon

[safe drift]

!help

[quasi jetty]

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

[safe drift]

!da2a

[unkempt moat]

Meow

[foggy meadow]

@torpid bay Do you want to help me make thing thingy into an integral?

[placid shadow]

meow

[timid bronze]

Me studying for a physics final

[placid shadow]

🤭 it's definitely like that for some exams

[tight sequoia]

Hello ladies

[jagged forge]

what r u, the guy from old spice

[grand wraith]

im using khan academy to prem myself for trig within 4 weeks, should i use something else or am i taking the right path?

[hollow mist]

Aight, ima ask something. I'm self studying linear algebra, and it's TOUGH. Everytime I feel like I understand something and feel like the concepts are getting easier and I can coast a little, the following concepts get harder and harder.

It constantly checks my progress speed, and every time I think I can speed up now that I get concept X, the textbook keeps giving new topics that stall me. It's hard to keep up with any reasonable completion schedule when this happens, and it's really demotivating.

Anyone have thoughts and opinions on this? Whether this is normal/How to speed it up/how to not be demotivated?

reposting here since #discussion was busy

[rigid geyser]

It's impossible to get to a spot where you just coast because then you rapidly move to a spot where you struggle

And while you're coasting you're not learning so that's a good thing

[hollow mist]

I get it... but it's requiring all of my brain power from the absolute start. It's tiring, and I can't imagine that someone keeps doing this for 3-4 months for an entire course like this....

I guess I want to know if this is really that normal. I don't think I'm keeping ace with the recommended schedule of the course even because I'm having to explore so many practice problems to understand it completely lol

[rigid geyser]

What text are you using

Just curious

[hollow mist]

gilbert strang

intro to linear alg

4th ed

[rigid geyser]

strang is probably a little more numerical calculation focused

idk if that is what you want or not

are you used to not struggling like in highschool level topics?

[ocean harbor]

LMFAOOOO

i did the same thing before cuz bro was expect me to memorize stuff

[timid bronze]

LITERALLY 💔 cumulative finals are so ass fr

[ocean harbor]

frfr

[rigid geyser]

my preference would be a newer text by meckes/meckes designed for first course in LA for math majors (not eng). However that may or may not be better for you depending on whether a rigour focus helps you learn or not.

[hollow mist]

yeah, i never had problems in high school. single var diff and integral calc was easy, so was stats.

[rigid geyser]

possibly you are not used to not being throttled by the clss being slowed down for the pace to fit all students

you are probably also overestimatinhg how much the avg person who makes it thru a basic LA class understands all the material

but its immensely better for you to not be throttled

[hollow mist]

lmao that's... one way to say it.

[hollow mist]

I guess I'm doing it slightly as a preparation for machine learning studies for bioinformatics, but I am also going to have to know some rigor since a lot of machine learning methods in new fields (like bioinformatics) require intensive proofs. You can't get any new methodology published or accepted without a reasonable amount of mathematical analysis, interpretability, and proofs.

so having rigor and the application related background is kinda... both important?

[rigid geyser]

personally i just returned from a long time away from mathematics (in industry) and am trying to self learn some stuff after forgetting like 90% of what i knew and its not uncommon for me to be stuck on a page for a day

[hollow mist]

(i am a bioinformatician by training)

[hollow mist]

Alright... if that's how it is, that's how it is I guess. I just never imagined that students metaphorically climb a 45 degree incline for 3 months at a stretch every day.

Having the reference frame that this difficulty is normal gives me enough confidence to stick around for it.

[rigid geyser]

its especially true if youre trying to make sure you understand the material vs able to pass a test by memorizing some rules and blindly applying them the same way you did on the practice problems

[hollow mist]

If I have to continue my work in publishing ML proofs, I kinda have to understand the material lol.

[rigid geyser]

yep

[hollow mist]

AHHHHHHHHHHHHHHHHH

suks bolz

[rigid geyser]

a lot of these texts also have a ton of exercises with the assumption that the professor will choose which ones are good for the way theyu are teaching the material, which can suck if youre on your own

because its harder to choose yourself which ones should be done

[hollow mist]

Yeah... im doing all of them.

Ngl, doing all of them IS teaching me a LOT

[rigid geyser]

i looked at strang and there is like 70 per chapter

or something

[hollow mist]

but it's definintely slowing my pace down compared to what the avg uni student would do.

[rigid geyser]

thats also where a well varied amount of potentially more difficult exercises can be good (one of the reasons i recommend meckes/meckes over strang)

[hollow mist]

what did you mean by this?

[rigid geyser]

doing 5 deep exercises could be more enligthening than doing 20 small ones

but yeah. doing all of them good. youll be doing way more than a normal student does though

there are some books that interspere the exercises with the text instead of the standard "end of chapter" which is sooo nice

[hollow mist]

I actually made the mistake of starting with Hubbard and Hubbard

That shit was sooooo abstract that each page was taking me 3 days

I have a copy of it from honors linalg from when I was in college

Ill try meckes

[rigid geyser]

doesnt hurt to have a secondary text to read up on concepts you are confused on anyhow

[hollow mist]

I have realized this to be true more and more. Having 2-3 textbooks on a topic actually helps a bunch

thanks for the reassurance @rigid geyser

[tight sequoia]

hi

[pine glacier]

can someone further explain why gojos limitless applies zenos paradox?

it is something im interested in explaining to other people

if someone could answer this, that would be great.
-thank you.

[rocky shuttle]

https://tenor.com/view/gojo-satoru-gif-23751503

[pine glacier]

uh ok. doesnt really seem to answer my question

[rocky shuttle]

https://tenor.com/view/gojo-gojo-satoru-jujutsu-kaisen-jjk-hidden-inventory-gif-10879791057434111097

[pine glacier]

uhhh. doesnt seem to answer my question 🤔

[rocky shuttle]

https://tenor.com/view/gojo-satoru-jujutsu-kaisen-jujutsu-stamp-over-stamp-gif-21968636

[magic python]

Poor ants

[pine glacier]

can someone elaborate zenos paradox to gojos limitless technique??

i want to further my understanding and help explain it to other people

[rocky shuttle]

expand your domain

[pine glacier]

plss

someone answer

[true zinc]

No, because powerscaling random anime characters is utterly stupid

[rocky shuttle]

https://tenor.com/view/gojo-satoru-gif-949319236308169219

[sharp mulch]

What sort of explanation to do you want

[pine glacier]

this isnt an anime fight im trying to explain. just trying to get some people to help. hoping someone can answer my question tying in zenos paradox

[sharp mulch]

It's a piece of fiction

[pine glacier]

zenos paradox

is not fiction

[shrewd tree]

Does anyone like Sam and Colby? And reading? (React with '❣️' if yes)

[sharp mulch]

Yes but gojo's domain expansion is fiction

[pine glacier]

im not talking about the domain bro. im talking about "limitless"

im sort of confused how zenos paradox applies to this and want to further my understanding on it

[shrewd tree]

.

[sharp mulch]

Anyways

Based on some cursory searches online about gojo and whatever

So

Zeno's paradox is the idea that you can never reach a target because you can always subdivide the remaining distance into whatever right

It doesn't actually apply in reality because the shorter one of these remaining subsections is the shorter the time needed to traverse it

Blah blah blah convergent series

Jujutsu kaisen fandom site says ```Infinity (無限 Mugen?) is the base state of the Limitless and is essentially the power to stop.[4] The Limitless technique operates the same way convergent and divergent sequences do in mathematics. The Infinity is the convergence of an immeasurable series, anything that approaches the infinity slows down and never reaches the user.[5] This is because the technique takes the finite amount of space between the two subjects and divides it an infinite amount of times.[6]

In mathematics, no matter how many times someone divides a number it will never be reduced to zero. Instead, they will be left with fractional units so infinitesimal it would become immeasurable to their eye. The Limitless brings this concept into reality, so anything that attempts to penetrate this infinitely divided space will slow down to the point of appearing to stop completely.[7] ```

So if we want to say that this modifies reality so that zeno's paradox applies somehow

[pine glacier]

so you are saying that motion doesnt exist in that world which is why you said it is a piece of fiction

[sharp mulch]

One way to do it would be to have each remaining subsection of distance to be traversed take a fixed amount of time

[raw horizon]

Limitless technique, hollow purple

[sharp mulch]

So like

[pine glacier]

in that way, it appears the projectile is stopped

[sharp mulch]

Let's say you can move with speed 1

And want to travel a distance of 1

Zeno's paradox would break this up into a distance of 0.9 and a distance of 0.09 and a distance of 0.009 and so on

[pine glacier]

it would be graphed as an ASYMPTOTE

[sharp mulch]

And traversing these would take 0.9 time and 0.09 time and 0.009 time and so on

But if you say that each subsection takes 1 time

Then the amount of time needed to get somewhere will be infinite

[pine glacier]

then if you had unlimited time to reach gojo, gojo would be the limit

i assume right?

also thanks for the explanation

[lilac kite]

Hello

do you have any math recomendations

how do you learn maths by yourselves

[viral oracle]

watching vids, reading books, doing exercises, and occasionally asking here

[limber thunder]

this depends on what you know and what you want to learn, there's a ton

I'll repost smth I told another user

[cyan karma]

Zeno must have been smoking weed or something

[lilac kite]

tyyy All of this is practice, do any of you find ways to apply math before you learn it?

[viral oracle]

it can be helpful to understand where certain things apply I suppose, and there's usually a great job out there if you search "{topic} applications"

[limber thunder]

yeah I like reading about applications, though I kinda study in parallel to doing that

recently I was a TA for functional analysis and I also tried to focus in applications where possible

it appears in things like PDE, optimization

for more basic stuff like calc and ODE I also do try to relate that to concrete situations

books that aren't like, pure math oriented often have a ton of exercises inspired in application

[lilac kite]

how long have you been doing maths for do i have to have a lot of experience

[viral oracle]

a lot of experience to do what

[lilac kite]

master a topic of choice

[viral oracle]

depends on the topic and how fast you learn

[limber thunder]

everyone's at a different spot in learning, if you don't have a lot of "experience" you simply study the basics like calculus or maybe Book of Proof I linked above if you want to do proofs

personally I've been studying uni math for some years, currently first year PhD

[viral oracle]

I personally have decent experience with algebra and differential calculus, but only a few months into anything above calculus

[limber thunder]

what is your goal? why do you want to study math specifically, knowing that might help to give better recommendations

[lilac kite]

integral and multivariable calculus

[viral oracle]

like, what do you envision you using math for?

[lilac kite]

physics

[viral oracle]

engineering? sciences? pure math? applied math?

ah

[limber thunder]

cool

[lilac kite]

so how should i learn it

how have you learnt math

[viral oracle]

where are you in your learning journey?

[lilac kite]

i dont know

[viral oracle]

as in, what math have you learnt?

[limber thunder]

I take my own notes based on books or lectures, then spend some time doing exercises from books, that's like the basic loop for each chapter lol

studying in groups or explaining things to other people also helps a lot, if you can proficiently explain a topic to someone else then you've mastered it

and math can be a very social activity even if ppl don't often imagine it as such

[lilac kite]

What lectures do you do

[lilac kite]

Thanks so much 🙂

[limber thunder]

I meant my uni's lectures from when I was in undergrad, you can also find lectures in YouTube

[rocky shuttle]

there's a math for physics course in my uni where you essentially cover all the topics relevant for physics (which are usually covered in a full undergrad math study programme) but crammed into a single semester and only at the surface level

[limber thunder]

or in specific universities' pages like MIT Open CourseWare

[limber thunder]

also for this I would recommend Stewart's Calculus, and maybe Marsden-Tromba's Vector Calculus
ofc there's a lot of other books for these subjects specifically

[viral oracle]

I would say, Thomas over Stewart though

[limber thunder]

also covered fairly well in Paul's notes here

[lilac kite]

Woww tank yo so much i never knew about this

[viral oracle]

Thomas seems to provide a little more rigor from what I have seen so far (I do have both and work through both)

[timid bronze]

@deep mango Bruh

@velvet dagger Look at this shit

[viral oracle]

btw if Sofa is looking for an algebra book as well (since Idk where Sofa is in her learning journey), consider College Algebra and Trigonometry by Lial et al.

quite a lot of real-life motivated problems

[rocky shuttle]

(8 + \sqrt{3} i) (8 - \sqrt{3} i)

[velvet dagger]

Beautiful

[deep mango]

Dami play uno

Why dont you have a working computer?!?

[timid bronze]

How do you know that tf

Stalker

[ocean harbor]

bruh

[turbid sedge]

ironic

[ocean harbor]

hi

[viral oracle]

https://tenor.com/view/cat-hello-cat-peek-cat-door-cat-peek-door-gif-17361470248875227911

[turbid sedge]

sup my homie

[timid bronze]

ryc told me to send the pic

[ocean harbor]

have you seen this

its so silly

[turbid sedge]

least based ado frameworks

Ado fanbase never disappoints me

[ocean harbor]

real

[turbid sedge]

sure

[placid shadow]

Hewos hewos Hanako! 🩷

https://tenor.com/view/fox-cute-snow-gif-17016275113173743177

[viral oracle]

hihi

[turbid sedge]

hello hana

[viral oracle]

[timid bronze]

Syfm

[turbid sedge]

Unprofessional hate

[timid bronze]

I'm unemployed so it doesn't count!

[viral oracle]

uneducated hate

[latent edge]

https://tenor.com/view/fumo-fumofumo-reimu-reimu-fumo-marisa-gif-16432408177096756319

[latent edge]

it's so over

I regret doing this

[viral yew]

labubu?

[latent edge]

NO STOP

[timid bronze]

LMFAO

He sure likes them

[cyan karma]

2x is a good upper bound for X hope that helps

[timid bronze]

Look at the PFP

[viral yew]

I see

[latent edge]

yall for context she forced me to do this

[viral yew]

how

[latent edge]

too lazy to pull dms

[viral yew]

lol

no amount of blackmail would get me to change pfp

[latent edge]

i think it was a challenge

more than a blackmail

[vast wraith]

the labubus will follow you to the grave and there they will stay longer than any semblance of you because they are plastic while you’re decomposeable

[latent edge]

ally so evil

[timid bronze]

Time I get a job https://forms.gle/Jra35VkmnpXjmCH57

[viral yew]

f

[viral yew]

lol

[latent edge]

btw ally welcome back

I didn't say this before

wilted rose

https://cdn.discordapp.com/emojis/748173476468228167.webp?size=96&animated=true

[timid bronze]

Thank youu nD

[thin oyster]

Hi

[viral yew]

why is there only “yes” to being a weeb 😭

[turbid sedge]

https://tenor.com/ExMC.gif

[turbid sedge]

It's a nessasary quota

[timid bronze]

Please don't remind me of bad data collected in labs 💔

[timid bronze]

Hi

[latent edge]

for bad data collected in lab I'd just be like "yeah these are irrelevant" which ended up erasing 90% of the data

mamma mia

just to get that stupid line of best fit

[turbid sedge]

Biology majors when it comes to mess with the obtained data to get a straight line ( but the empirical equation represents y=kx²)

[timid bronze]

One time there was a group that I kid you not got perfectly precise results (0% error..it was literally the same) and the TA made them intentionally mess up their data so they could discuss experimental error 😭

[viral yew]

for a second I thought you were achooeus

[thin oyster]

You have 2 choice's save your 3 elder's or save 1 child what would u pick and why? Would u rather choose 3 lives over 1 or choose a child that has a beginning life story over 3 lives.

[viral yew]

3 elder woman so I can be introduced to their families and acquire a child to replace the one that died

[turbid sedge]

Mfs will claim they're sum johan liebert but they learnt dark physiology from booktok

[thin oyster]

What if that child was your brother almond?

[timid bronze]

I'm sorry but I dislike questions like these

[viral yew]

same strategy bc I am a sociopath

[latent edge]

your lab grade had a big factor on who is your TA

well the lab coordinator really

tfw my chem lab coordinator was the one person everyone hated in the department

[timid bronze]

No one likes any of the general chemistry professors here

[turbid sedge]

I'd rather do some combinatorics problem

[viral yew]

why did you react to your own comment bro

[timid bronze]

Only a couple of them are good

[timid bronze]

I just hate that we're forced to pick one

I'm not going to sit and decide who's life is worth more lol

Regardless of whether they are close to me or not, or whether they are younger or older

[viral yew]

health insurance company moment

[turbid sedge]

That one shonen mc:

[timid bronze]

Ok wait this one has me choking LMFAOO 😭 It's so sad though

[viral yew]

luigi we need your services again

[latent edge]

I wonder why

[timid bronze]

Your opinion was neither solicited nor required.

[latent edge]

I think making gen chem "interesting" is a skill

[turbid sedge]

WOAH

Canon bombing

[timid bronze]

I would say my gen chem prof 2 taught it well

He's one of the only good chem professors out here

[viral yew]

how do I obtain understanding of anime references without watching any anime

[turbid sedge]

It's expendable

Fuck you gonna do with refs 💔

Just lock in

🗣️

[timid bronze]

@turbid sedge

[turbid sedge]

Hi

[timid bronze]

Why was your main even suspended

[turbid sedge]

Uhm

That's..

I was

How do I put it

[viral yew]

i’m locked

[turbid sedge]

In a server which seemingly seemed right

But it had bad activites going underneath

[timid bronze]

I've been banned from a server before but my Discord account has never been in trouble ...

Bro is sus

[turbid sedge]

Only once?

I've been banned from

Countless servers

[viral yew]

real

[timid bronze]

What is bro doing

[turbid sedge]

And discord banned my 5 alts in the span 2020-24

Which I used .....

[viral yew]

i’ve never been babned before

who da hail was bro associating with

[turbid sedge]

No

It's like

I often get associated with frauds scam and exchange of illegal stuff

[timid bronze]

Bro.

That's cooked

[turbid sedge]

SWEAR I'M NOT A PART OF ANY OF THEN

Then

Them

[turbid sedge]

NO

Hear me out

[viral yew]

lol

[timid bronze]

I trolled in let's say a "mature" server when I was 14 😭

[turbid sedge]

I join in countless servers among which some gets banned from discord

[viral yew]

bruh

[turbid sedge]

That kind of servers

[viral yew]

I havent joined a server in months

[turbid sedge]

💔in 14 is crazy

[turbid sedge]

I do and get slimed

[quartz stump]

is mr. J. math in this server?

[timid bronze]

Who is that

[turbid sedge]

Who the fuh

[viral yew]

fr goofy ahh name

[quartz stump]

Mr. John Math

[viral yew]

lol

[timid bronze]

Is this a YT channel

[turbid sedge]

John pork!!?

[timid bronze]

Y'all stop they could just be asking a genuine question

[quartz stump]

this is a fan sub right? of John Math

[viral yew]

John Math

[timid bronze]

Noo, this is just a general mathematics server

[quartz stump]

oh interesting

[viral yew]

yes it is I know him personally

[quartz stump]

(im a postgrad btw) just joking

[turbid sedge]

Who could possibly be john math.....

[quartz stump]

oh really I heard he has a lot of enemies

[turbid sedge]

😭

OH THE GREAT FOUNDER

ONE WHO FOUNDED EVERYTHING

THE ONLY RADIANT ONE

MR JOHN MATH

PRAISE YOU

[timid bronze]

Idk it could be a YT channel, and they might think the YTer owns this server

[quartz stump]

John Math (~1200-1120 BC)

[viral yew]

the legend himself

[turbid sedge]

"Join my fan server:- .gg/math"

[turbid sedge]

[quartz stump]

I mean I can see that working

[timid bronze]

Still. Even tho it's a joke, responding like that can scare people from talking in dis 1 or dis 2

[turbid sedge]

You must be fun at parties

[viral yew]

no fun or parties here

john math said so

[turbid sedge]

MODS THIS IS DEMEANING

No fun 💔

No ally don't slime ne

[timid bronze]

This is lowk such a backhanded comment

[turbid sedge]

Got forbid a man ragebait

[timid bronze]

What's the attitude for

[turbid sedge]

No

[quartz stump]

beef

[turbid sedge]

I was just ragebaiting

[turbid sedge]

No thank you I prefer chicken

[quartz stump]

I suggest a math rap battle like that guy on youtube does sometimes

[turbid sedge]

Euler vs lagrange yo

[quartz stump]

fuck yeah

[turbid sedge]

I'm hungry

[quartz stump]

hungaryyyy

https://tenor.com/view/astolfo-femboy-hungary-kingdom-of-hungary-miklos-horthy-gif-9205644645611977898

I hope you people can't read

[turbid sedge]

Femboy....

[viral yew]

huh

[ocean harbor]

https://tenor.com/view/buddy-no-image-perms-gif-18006828907471357785

[slender echo]

I love this gif. Somebody told me to mic up and that they’d beat me up because they had an embed fail and I posted this very gif (Different server)

[ocean harbor]

https://tenor.com/view/food-snail-mmm-tasty-delicious-gif-21470000

[timid bronze]

People still mic up in this day and age? 🥀

Mic ups are all about who's the loudest fr

Dumb ahh cringe shit

[slender echo]

Apparently

Over an embed fail too

[turbid sedge]

This

[turbid sedge]

We left that shit in 2020

Except for the dream incident

[raw cedar]

[rose ridge]

https://tenor.com/view/morgan-jones-uzbek-gif-9108365450976190246

Holy unc

[turbid sedge]

no

[tropic pivot]

hi

[dire robin]

Helo second discussiers

[native badger]

Hello

[dim stirrup]

someone is an academic if they say insofar because who say that instead of as long as

[fickle lodge]

@tropic ember

[primal tinsel]

is P=NP or not

[turbid sedge]

https://tenor.com/view/thatguy-gif-8039501183055403907

[primal tinsel]

Did you know answer

[turbid sedge]

preuni math tb sum P?NP🥀

[raw cedar]

no

[primal tinsel]

ok

lets find answer together

[raw cedar]

no

[primal tinsel]

OK !

[clear adder]

Anyone interested in spamming DMs with GIFs whenever you’re bored or just feel like it? If so, send me a friend request/ DM.

[ocean harbor]

[ocean harbor]

you can do that in #chill

[tropic ember]

Yooo.

How are you?

[fickle lodge]

fine what are you doing in math land

luv you

consensualy

[tropic ember]

Awesome. I'm learning some Number theory here, i saw some good discussions.

[tropic ember]

No Gay. Same for you.

[fickle lodge]

nt slop

[tropic ember]

it's good.

You are an Algebraist.

[fickle lodge]

you should talk to yux he reccomended me a book which i forgot

[tropic ember]

Alright, i will remember it. Thanks Reed. Luv U (no Gay). 💖

[fickle lodge]

when will you come back to wh

[tropic ember]

I'm there now.

[old oak]

<@&268886789983436800> self-promotion

[silent junco]

this isnt the place to promote your youtube channel, thanks

[flint imp]

I need 500 views that’s it

Dude I can get reward for that

So please atleast watch it

[magic python]

And?

It's promotion?

[silent junco]

regardless, this isnt the place for it

[flint imp]

Well which channel does it

[silent junco]

none of them

[flint imp]

🤦

[silent junco]

sorry, youll have to look elsewhere

[flint imp]

500 views is not too much anyways

[silent junco]

thats the spirit

[old oak]

Then you should be able to get them without spamming random servers!

[flint imp]

See yah

[silent junco]

just watch it 500 times yourself

[flint imp]

If I have 500 accounts 😂

[silent junco]

fwiw there are people who do this (those who know )

[flint imp]

🤣🤣 I’m not that unemployed

[silent junco]

yeah good response

[flint imp]

K see ya

[unkempt moat]

@versed jungle

Is not this type of person

but he does have many alts

[turbid sedge]

I'm hungry

[hexed tangle]

https://tenor.com/view/hit-kitten-punch-cat-you-want-a-knuckle-sandwich-gif-16578466

[unkempt moat]

Eat fuuud

[turbid sedge]

Damn

[vocal vessel]

https://tenor.com/view/yup-yep-yes-excited-gif-24387991

[versed jungle]

i tried doing that for a friend's video

and gave up after about 5 accounts

[cedar trench]

Hey

[unkempt moat]

Meow

[cedar trench]

Why?

[unkempt moat]

Im a cat

[magic python]

Nya!

[cedar trench]

I don't understand

[old oak]

That's very commendable

[cedar trench]

Thank you.

[true zinc]

HELP

[sonic sentinel]

im convinced the former gifted kid stereotype "trying new things and quitting them when they don't come easily to you" is the result of former gifted kids trying new stuff at a higher rate and that mostly positive feedback at early stages in training is pretty much necessary and hard to find

First stage is for children which is an obvious difference but I don't think it changes much for adults. (also its talking about sport but i think the three stages apply to nonsport)

To understand my worldview better, I say if you're trying something new and have the choice between getting mostly positive feedback and getting real, harsh feedback, you would be better off getting mostly positive feedback until you have some level of competence where the "real" feedback is not too demotivating.

I'd love to hear other people's thoughts on this.

[unkempt moat]

I can attest that the stereotype is definitely real
I know somebody who would definitely be considered gifted who like isn't even willing to try basically anything new over a fear of being bad at it (like chess, certain games, etc) (being bad as in, not immediately very good without practice)

[sour glade]

behaviour reinforcement

[spark creek]

there are ways to get rid of the fear emotion gradually

I only know of one

[versed jungle]

[last rose]

meow

[magic python]

Nya!

[brittle vigil]

Heyy does anyone know why the graph of b²-4ac is true for predicting if the equation is always positive or negative

like does it have a proof or we infer from seeing the results when we tried it to see its sign

[agile fiber]

it comes directly from the quadratic formula

the number of solutions to ax^2 + bx + c = 0 is the number of times ax^2 + bx + c can switch signs

[obtuse grail]

Hi ola

[spark creek]

Sup

how's your day been?

[obtuse grail]

Nothing much u

[obtuse grail]

It's been great wbu

[spark creek]

it's alright here

wyd

[obtuse grail]

Ok great

[obtuse grail]

Btw where are you from

[spark creek]

what are you doing?

[obtuse grail]

Are you from Nigeria

[spark creek]

I wish I could tell you!

[obtuse grail]

I am watching film

[spark creek]

No actually, I don't wanna tell you

[obtuse grail]

Y Can't u tell me

[obtuse grail]

U want to tell me in Private

[rough basalt]

Only half seriously, after a certain point in progression all feedback is harmful

All external feedback maybe?

[spark creek]

you're the alt of a mod

why'd I tell you

[obtuse grail]

What I don't get

[obtuse grail]

Oh sry

[spark creek]

don't pretend to be unknowing of the scheme

[obtuse grail]

What?

[spark creek]

It's as visible as the june sun

[obtuse grail]

Ok

[silent junco]

please dont pressure people into revealing personal information

[obtuse grail]

I am not u are getting me weong

[willow pine]

is there a word for the class of complex numbers z s.t. |z|=1? the ones that can be written as e^ix?

[magic python]

Roots of unity

Or the unit circle

[agile fiber]

yeah it's the unit circle in the complex plane

[spark creek]

I think this person's an alt of the racist person

that was banned for a day recently

[magic python]

???

[agile fiber]

i would reserve roots of unity for the ones with a rational [multiple of pi] argument

[spark creek]

@obtuse grail this account

[agile fiber]

DM @polar panther with any evidence of this

[spark creek]

sorry, I wanna let the account some slack

[ocean harbor]

not sure what is going on but this user used to dm me randomly

im surprised they still talk here

[spark creek]

but, I just warned you in advance

[ocean harbor]

this kinda explains

[spark creek]

The account was made in the summer of this year

[ocean harbor]

ignore the account

they only dm active people or random ppl in here

[spark creek]

yea

[rough basalt]

campus being closed till after new years day is killing me

I need big boards to write on

[ocean harbor]

Isn’t that what winter break is meant to be?

[rough basalt]

winter break is my opportunity to catch up so I can seem smart lol

[ocean harbor]

that actually makes sense, good use of the break lol

[rough basalt]

well to be honest, I also do a lot better just reading and working up to things myself than going to classes

[ocean harbor]

thats a good skill to have

[rough basalt]

trying to find a good way to put it. Class moves both too slow and too quick for me lol

[ocean harbor]

true

[placid shadow]

Does anyone know what pre-requisites do I need to be able to understand what all of this is saying? I really want to be able to delve into this and I was under the assumption that you can read this without much knowledge but it seems really hard to me.

[silent junco]

youll be able to understand the statements (at face value) if you take any intro proofs or discrete math course. but to really appreciate set theory youll probably need a bit of mathematical maturity.

[placid shadow]

Tysm!

[sonic sentinel]

OK, but can you attest whether the stereotype is real for the reason I mentioned or for another reason? i.e. do other people try stuff at the same rate as them?

[unkempt moat]

I dont think thats the reason, but I'm not them so I can't say for sure

[pure sapphire]

We got irl presidential yaoi before gta 6 🥀

[unkempt moat]

❓

[pure sapphire]

Bubba?

Trump x Bill Clinton

I dont believe it at all though

[unkempt moat]

ohh

[pure sapphire]

I think it's cap

[worldly horizon]

what

[fervent hill]

#help-44｜stanley-🌲-v2-dans message
@short acorn regarding one-to-one for question 31,

,align
&\text{If }m_1+n_1 > m_2+n_2\text{, then:}\\
f(m_1,n_1) &> \frac{(m_1+n_1-2)(m_1+n_1-1)}{2}\
&\geq \frac{((m_2+n_2+1)-2)((m_2+n_2+1)-1)}{2}\
&= \frac{(m_2+n_2-2)(m_2+n_2-1)}{2} + m_2 + n_2 - 1\
&\geq f(m_2, n_2)\\\
&\text{Thus } f(m_1,n_1) = f(m_2,n_2) \implies m_1+n_1 = m_2+n_2

[fathom swallow]

Axe

[raw cedar]

oh i didnt see the "president"

ghost ping!

[short acorn]

ooo because they're positive integers

That's nice

Saved

[fervent hill]

yeah it uses the fact that m1, n2, m2 and n2 are positive integers in multiple places

for example, it's used to say that m1 + n1 >= m2 + n2 + 1
and this is used to make a substitution in one of the steps

[fervent hill]

@short acorn there is intuition for it:
f is going down each diagonal from left to right. first (1,1), then the diagonal along y=3-x, then y=4-x, and so on.
now m+n is different for each diagonal. so if m1+n1 > m2+n2, then they should be on different diagonals.
then we should have f(m1,n1) > the rightmost point on the previous diagonal, which should be greater or equal to the right most point on (m2,n2)'s diagonal, which should be greater or equal to f(m2,n2).
and indeed following this reasoning, the algebra went through successfully

[turbid sedge]

What are we tb

[wise bloom]

lmo

[tough yoke]

Create a help channel, and I'll have a look.

[tender idol]

Nah I’ll just reply here

[magic python]

!help

[quasi jetty]

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

[tender idol]

How did u do the bicen maths videos

[magic python]

You shouldn't take up a discussion channel when wanting help

[tough yoke]

I created a list of chapters I wanted to master for the week, and then watched all of them in his playlists. After studying a chapter from his channel, I would try to find past paper questions on PMT to complete. If I struggled on a question, I'd just study that certain topic, not the entire chapter.

[tender idol]

I’ve done the papers but every now and then I get stuck on these random questions

Like tn it’s mainly some 3D vectors/planes

[tough yoke]

You've probably not studied them properly in depth and practise, if you're forgetting how to answer certain questions from a topic from time to time then that shows you haven't fully mastered the chapter. I suggest you restudy the chapter from his channel, create notes, then attempt some PMT and past paper questions.

[tender idol]

Ok

Also one last question

do u have an alt in revision server

[tough yoke]

If you're still struggling, then you can send me some of the questions and I'll guide you through them.

[tender idol]

Thanks

[tough yoke]

No, I have already spoken about this.

[tender idol]

Nah it’s just there are some new things which make me believe u have an alt there

But anyways it doesn’t rlly matter

[tough yoke]

?

[mental rock]

@frank sequoia

[willow pine]

is there a reason why we write e^ix instead of e^xi?

[vocal adder]

For real numbers i say, to have more clarity

[rigid geyser]

I feel like the convention is literals then constants then variables within a single string of multiplied terms

[timid bronze]

@late mountain Edit: Accidental ping, sorry

<@&268886789983436800>

[magic solstice]

The kissing number of a polygonal concave shape that's symmetric along the x and y axis can reach higher than 6, right? If so, I can't find or think of an example 🙁

[winged pawn]

New pfp waw

[timid bronze]

Only for this server, I still have the other one as my universal pfp.. but I might switch back to having it in here

I'm indecisive

[viral yew]

can you edit server nick

[timid bronze]

Yes

[winged pawn]

Your main pfp is really cute, although I forgot where it's from

[viral yew]

cool

[timid bronze]

Thank you!!

I don't know where it's from

:p

[mint patio]

@bold citrus

[viral yew]

did you get off pinterest

[mint patio]

oh this is taken too

[timid bronze]

Yes

[bold citrus]

yo

[mint patio]

y’all mind if we hijack your channel to talk some maths?

[winged pawn]

Mood

[viral yew]

yes! i hate math!

[mint patio]

unfortunate

alright

[winged pawn]

You can just have two concurrent conversations

Nobody owns the channel

[mint patio]

if you’re ok with that!

[viral yew]

nah talk yo math son

[mint patio]

thank you :)

[old oak]

I thought your message in #math-discussion was telling the spammy kids to go to discussy 😅

[viral yew]

y everyone get pfp from pinterest

[mint patio]

@bold citrus okay so ‘solving’ a differential equation means finding the function(s) that satisfy the equation, that make it true

so for example let’s say some special system is modeled by the equation y’ = y

[winged pawn]

Picrew is where it's at

[timid bronze]

https://tenor.com/view/almond-milk-angry-birds-joy-gif-26076216

[mint patio]

‘solving’ that equation means finding the function y(t) such that its own derivative equals itself

can you think of a fnctn whose derivative is itself?

[viral yew]

😠 milk make my tummy hurt

[mint patio]

ping me when you see this ad

[viral yew]

ooh ooh I know

[mint patio]

go for it

[viral yew]

lol I learned diff eq already

e^x

[mint patio]

I figured

yes! good

but we can actually do better

[bold citrus]

i was catching up haha but yeah e^x

[viral yew]

laplace goes crazy

[mint patio]

we can do better than e^x

take y = Ce^x, where C is a constant real number

when I differentiate the constant is unaffected, so my solution can actually be any function of the form Ce^x

e^x, 2e^x, … all work

[bold citrus]

i see

[mint patio]

do you know about pdes? ;)

I got stuff to do I gotta go now lols

but I hope I could make that make sense to you

differential equations model systems

a lot of the time, each term in a differential equation will actually correspond to some physical behavior of the system

[bold citrus]

somewhat

[bold citrus]

oh ok

thank you for your helP!

[mint patio]

we can solve differential equations to find a function which models the behavior of the system we were describing with our differential equation

for example, that motion equation I gave you describes … well, motion

[bold citrus]

so the entirety of the system can be described with oen function>? or are we just finding a function that describes the specfic part of the diffeq we are targeting?

[mint patio]

so the solution describes how the system moves

in this case ‘system’ is a specific particle

[mint patio]

the latter!!

but you know the great part?

a lot of systems are essentially parameterized by just a few variables

you can come up with a system of differential equations by describing the behavior of each of those variables (coming up with a differential equation with each variable in it)

[vernal token]

Hi feather, long time no see again

[mint patio]

and so you can fully describe the system by solving that system and arriving at solutions for both

(or more)

[mint patio]

hi! I actually have to make my way out soon, but nice seeing you too!!!

[viral yew]

great microlecture, TA feather

[vernal token]

You in chat is a once-in-a-year occurence

[old oak]

<@&268886789983436800>

[stone ferry]

I would say "no advertisement" in french but I don't speak it

[quick beacon]

unlikely to be a human piloting ts anyway

[limber thunder]

ceci n'est pas un humain

[mellow flame]

guys why cant i change my per server nickname😞

personally i think hype moments and aura generating function is a really cool username

nicnname*

[agile fiber]

you can DM @polar panther to request a nickname change

[mellow flame]

omg fire

thank u

[ocean harbor]

https://tenor.com/view/retro-mario-goomba-bowser-pixel-gif-3184502427952960603

[cyan karma]

No matter what your gender is, it's time to man up and stick to your new years resolutions

[thick wind]

On average, how many people actually do that 💀

[cyan karma]

Probably like 1%

Source I made it up

[lunar ruin]

My new years resolution is to not change a thing.

[light escarp]

Well, they did a bunch of studies about this, what most concluded with was that you cannot expect to change your whole lifestyle in week lol. Hence why people start out slow losing weight by either drinking more water or eating healthier rather than just going straight to the gym and doing all the life hacks.

Often the resolution is too vague too.

[brave flare]

good rename

[viral yew]

i agree

[placid shadow]

https://tenor.com/view/happy-new-year2021-anime-gif-19775977

[ocean harbor]

I thought they created a new discussion for a second

[cinder zephyr]

Why are the other 2024 discussion channels hidden from me

[placid shadow]

And the negative 2024 channels as well

You can't forget about the negative ones

[thorn wren]

People are renaming discussion channels now

[dire sandal]

did you guys know that 2026 isnt prime

i hate leaving a year with a number that has cool math facts

[placid shadow]

Oooooo, but 2025 is because it can be divided by 5

[placid shadow]

How?

[dire sandal]

https://tenor.com/view/true-patrick-spongebob-truth-nuke-gif-15777863855591434629

[limber thunder]

https://tenor.com/view/hog-exploding-exploding-hog-funny-idiot-gif-13702011850125732811

[placid shadow]

https://tenor.com/view/stealinng-from-yn-steal-from-yn-patrick-steal-gif-3359143714421773067

[placid shadow]

Ah, 2026 isn't prime because dividing it by 2 gives 1013 which is only divisible by 1.

[vital niche]

happ new year!!

[rigid geyser]

it doesnt matter what u get when u divide by 2

[placid shadow]

Happy new year!

[vital niche]

20 mins late lmao

[rigid geyser]

obv even => not prime

[placid shadow]

why?

[rigid geyser]

being divisible by 2 alone is enough for it to be not prime

[placid shadow]

Interesting

How about 2030?

[rigid geyser]

i think we should re check - what is the definition of being prime?