serious-discussion

[young scroll]

6, cuz engineer

[shadow glacier]

e + π

[wispy pike]

hey

What does the r = 1- sin stand for?

If I square it, it looks like a circle

[toxic gale]

I believe it is called a cardioid and it looks like a heart.

,w graph r = 1 - sin theta

[fathom swallow]

Results provided by WolframAlpha

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

Requested by PhenomPlasma#3806

[wispy pike]

wow

haha

the author is educated

[fair mural]

not really lol

[charred mortar]

Fat heart

[old fox]

something's wrong I can feel it

occupied help channels are still under ✅MATH HELP (AVAILABLE)

[fair mural]

@old fox #❓how-to-get-help

possibly notice how the help channel has changed names

[long matrix]

nooooooo

my ping count is stuck at 67

[old fox]

they just changed it

[toxic schooner]

u can unread pings btw

so u go unread 2 pings

[long matrix]

no thats cheating

[fair mural]

shuri what channel do you want me to ping you in

[long matrix]

no, baka

i am counting my natural @ helper pings

[fair mural]

https://tenor.com/view/sumire-heanna-love-live-superstar-love-live-liella-sumire-gif-22570668

[old fox]

why do helpers look like mods and why do people with foundations role look invisible

[fair mural]

foundations role has always been invisible

[hidden violet]

What is the Bayes Nash equilibrium?

[modern geyser]

quantum what is this

[sick burrow]

Oh wait foundations role makes you invisible?

Oh lmfao

[toxic schooner]

i think thats only for darkmode

in light mode u will be visible

[long matrix]

https://tenor.com/view/discord-lightmode-gif-18450013

[sick burrow]

The question is am I deserving of foundations role

[toxic schooner]

i am definitely not

and i dont think i ever will be

[sick burrow]

I have a semester of mathematical logic a semester of set theory and I'm currently taking a semester of model theory

Ultra or nG or Tropo am I worthy

I feel like I'm not

[surreal sapphire]

do the topic roles even do anything

[sick burrow]

No

[toxic schooner]

they supposedly ping u

[sick burrow]

I feel like the more just signify areas of knowledge/interest

[surreal sapphire]

i dont think they are pingable?

[sick burrow]

Yeah they aren't

[bright hill]

wait really

[vivid halo]

you'll probably be fine lol

might just take more work than you think but you'll be fine

[toxic schooner]

oh yeah, i thought they pinged for some reason

[sick burrow]

I think topic specific helpers was the intention but I've never seen them pinged nor can I ping them

[toxic schooner]

Interest as well huh?

[sick burrow]

hm?

[surreal sapphire]

i am interested in everything

[sick burrow]

Well I mean like

[toxic schooner]

im not into everything

[sick burrow]

The big brain people here don't have every role

[toxic schooner]

but into quite a few things

[vivid halo]

oh sorry I think I misunderstood what you were asking

yeah if you're interested in that stuff give yourself the role lol

[sick burrow]

Like nG has only alggeo and foundations

[vivid halo]

I don't even have foundations

[toxic schooner]

like out of this, im interested in 1,2,4,5(maybe, not really), 8 and 9

[vivid halo]

just AG/NT

[sick burrow]

Oh right

[long matrix]

7️⃣

[ancient flame]

we need a category theory role

[sick burrow]

I mean NT is just the theory of PA right

[ancient flame]

oh we have if

it

nvm

I'm dumb

illiterate

[sick burrow]

nG why sully

[ancient flame]

NT is NOT part of pennsylvania

[sick burrow]

Number theory is the study of positive integers aka Peano Arithmetic

Peano Arithmetic can do set theory

QED Number Theory is just Foundations

[ancient flame]

I taught my friend some basic set theory and he taught me about black holes

trading knowledge

[sick burrow]

Wait what is the term

For a theory powerful enough to do arithmetic.

Like the condition in Incompleteness that isn't recursive enumerability

[ancient flame]

yes

[sick burrow]

I love zpordle

[neat lintel]

Out of these I'm only interested in 2, or maybe 1 too, idk

[toxic schooner]

i feel like im interested in intersection of fields

so naturally, many fields will interest me

[leaden skiff]

field the algebraic object or fields of science

[sick burrow]

skips combinatorics and foundations

[toxic schooner]

i dont happen to be interested in foundations

i just dont like it

like at all

doesnt seem fun to me

[sick burrow]

Combinatorics though

[toxic schooner]

rn

combi isnt interesting rn

but i might go into it

we shall see

[toxic schooner]

[bright hill]

blitz is active now?

[toxic schooner]

yeah

lol

[near fox]

if you are interested in any flavors of "discrete" abstract algebra, then there will be lots of connections with combinatorics

[neat lintel]

Cool looking complex equation

[dense belfry]

There's only one strategy for zpordle

Up to random choice

[long matrix]

hi

im not enjoying #discussion

[fair mural]

hi

[long matrix]

nor #chill

fml

[fair mural]

shuri do you want a cat picture

[long matrix]

meow meow

[neat frost]

SHURI

[bright hill]

[neat frost]

Omg just the person I need!

[long matrix]

aw hi kitty kat

yes slurp?

[bright hill]

#discussion is giving me some severe existential dread atm

[long matrix]

its just giving me the beginnings of a headache

i dont wanna think

[neat frost]

Idk I was bored

[long matrix]

u needed me

[neat frost]

So I said that

[long matrix]

cus u were bored

[neat frost]

Yes

[long matrix]

right, ima afk

[neat frost]

Well no

I was bored

So I said that

[long matrix]

very cute of u

[neat frost]

Thanks 👉 👈 🥺

[long matrix]

oi the fuck

[neat frost]

Lmfaoo

Which page is this?

[long matrix]

https://en.m.wikipedia.org/wiki/Wreath_product

is that me or the page

[neat frost]

The page

Happened to me too

[long matrix]

uhuh

go fix it slurp

im sure its some latex issue

[neat frost]

I don’t think so

$\displaystyle (a_{\omega})_{\omega \in \Omega} \in A^{\Omega}$

[neat frost]

See latex is fine

Their backend must be bitching

[long matrix]

uhhhhismssmkss

[grim mason]

hey guuys can u do my survey its for marketing class 🙂

id appreciate it

[old fox]

it's not April 1st anymore

[grim mason]

when it says "j addison" pretend its ur school btw

[old fox]

yo $4+4=8$

[grim mason]

huh

[fathom swallow]

hyperlix26

[old fox]

hmm apparently it still is

[delicate knoll]

why?

[shadow glacier]

eat ass$!$
whats with this new font?

[fathom swallow]

ryаn

[toxic schooner]

its comic sans

one of the most hated fonts

[frail kindle]

$WHAT IS THIS FONT$ WHAT IS THIS FONT

[fathom swallow]

sunflame

[frail kindle]

is this a joke$?$

[fathom swallow]

sunflame

[deep mango]

(\textrm{does this look like})(a , joke , to , you)?

[fathom swallow]

ryc

[eager yarrow]

(\textrm{pee})(pee)$

(\textrm{pee})(pee)

sus$!$

[fathom swallow]

dq

[eager yarrow]

(\textrm{pee})(pee)$

[deep mango]

Use backslashes before the parentheses.

[eager yarrow]

What

(\textrm{pee})(pee)$

[deep mango]

\( \)

[eager yarrow]

(\textrm{pee})(pee)$

i did

the backslash dissapears

[deep mango]

Yeah

[eager yarrow]

(\textrm{pee})(pee)

it's not working

(\textrm{does this look like})(a , joke , to , you)?

[deep mango]

Are you using them on all the parentheses

[eager yarrow]

(\textrm{does this look like})(a , joke , to , you)?

What

(\textrm{does this look like})(a , joke , to , you)?

(\textrm{pee})\

(\textrm{pee})

I dislike this bot

[deep mango]

Its discords fault

For using backslashes as escape characters

[eager yarrow]

What do i do

I'm lost in life

(\textrm{pee})

I can't

do this

[deep mango]

(\textrm{pee})

[fathom swallow]

ryc

[deep mango]

[eager yarrow]

How

Teach me your ways

[deep mango]

\(\textrm{pee}\)

[eager yarrow]

(\textrm{pee})

[deep mango]

Copy and paste that

[fathom swallow]

dq

[deep mango]

There

[eager yarrow]

Oh my god

[deep mango]

See?

[eager yarrow]

Oh my lord

Oh my god

Thank you

[deep mango]

Backslashes before the parens

[eager yarrow]

Oh my

[deep mango]

Now experiment in #latex-testing instead of here

[eager yarrow]

Oh my

Thank you

[toxic schooner]

now wait

is this a permanent change?

or just for april fools

and whats the actual command to do it

[old fox]

\( and \)

[shadow glacier]

\(\begin{tikzcd}
    && {\mathcal{x}} \\
    {\mathcal{P}^{E\circ F}} &&&& {\mathcal{C}} \\
    \\
    \\
    && {\mathcal{A}}
    \arrow["{\text{sugg}}"', from=1-3, to=5-3]
    \arrow["{\text{deez}}"', from=2-1, to=5-3]
    \arrow["{\text{nuts}}"', from=1-3, to=2-1]
    \arrow["{\text{lol}}", from=1-3, to=2-5]
\end{tikzcd}
\begin{pmatrix}6&-1\\ 2&\begin{pmatrix}1&\int _0^1\sqrt[3]{1+7x}dx\\ 4&\begin{pmatrix}\sqrt{12\sqrt{23\sqrt{34\sqrt{5}}}}&\left(f\:\circ \left(f\circ \left(f\circ g\right)\right)\right)&\frac{2}{1\div 3}\\ ASD^{ASD^{ASD}}&EEEE\infty \infty &\frac{\partial }{\partial x}\left(123\right)\\ \infty &\frac{d}{dx}\left(123\right)&\log _{222}\left(333\right)\end{pmatrix}\end{pmatrix}\end{pmatrix} \)

[toxic schooner]

oh thats the usual command?

its not an april fools thing?

[shadow glacier]

idk i just wanted to try something a bit bigger

[fathom swallow]

ryаn

[shadow glacier]

ok thats fun

[ancient flame]

LOL

pain

(painnnn)

[fathom swallow]

guh mode

[stark birch]

god this reminds me of that Zach Galifianakis meme just looking at it

[waxen lily]

(\textrm{the sun is a deadly laser})

[fathom swallow]

DETOX (143 🍓)

[old fox]

we can make a religion out of this

[neat lintel]

I will be entering uni next year(CS major), I don't have any previous experience with competition math, I want to prepapre for the PUTNAM, I just want to have a fun time solving challenging math problems nothing more, any advice on how i should get started?

[shadow glacier]

uni math is completely and exactly like competition math

you basically go in and have to solve questions really quickly for exams

if you don't know the few dozen tricks, you'll be dead instantly

also make sure you get a powerful calculator, since people with the best calculators always do better at uni maths

[neat lintel]

resource's wise where do u think I should start? ik only HS lvl math no fancy number theory or real analysis

[shadow glacier]

u really dont need to, considering ur CS, unless ur doing some theoretical CS, your not gonna do much maths. Some number theory might help, so you can go give some number theory courses on khan academy or aops, but its not really necessary.

most CS grads are never going to use real analysis

[neat lintel]

I dont really care if I use the thing I prepare for the exam in my major, I just love math and dont mind studying topics I wont explicitly need

[shadow glacier]

then do a math minor or something

and study whichever math you find fun or enjoyable

u can go find some introductory books on: calculus, linalg, geometry, number theory, group theory, set theory, mathematical logic, graph theory, combinatorics, statistics, etc
read the first few chapters, see which one is most interesting

[toxic schooner]

no, dont

[stark birch]

[young scroll]

Cuz pi is 3 and e is 3

[neat lintel]

well said

[torn willow]

Um what

Calculators are useless except for exams tho now that python is a thing

[alpine kindle]

@neat lintel don't listen to ryan lol

[torn willow]

I bet you can't find one thing calculators are better at compared to computers

Because computers are quite literally the next stage of evolution of calculators

[bright hill]

good morning

[dire mulch]

Good morning DarQ.

I am grumpy today, for some reason my body decided to wake up at 5:30 am instead of my usual time 6:30.

[waxen lily]

when does daylight savings start

[dire mulch]

It happened already.

[old fox]

huh so #serious-discussion is #discussion now

clever

they changed the order

[waxen lily]

wild

[dire mulch]

How did you not know?

[bright hill]

maybe they switched the name

[toxic schooner]

what the hell is going on here

[bright hill]

#discussion is #serious-discussion now

[dire mulch]

It's not even April fool's day anymore.

[waxen lily]

its still april, fool

[alpine kindle]

morning

[flat harbor]

NOOOOO

(\mathcal{L} = \bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi)

[fathom swallow]

blo

[toxic schooner]

[flat harbor]

why am i being discriminatated

[waxen lily]

,w discriminatated

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by DETOX#0236

[toxic schooner]

(\mathcal{L} = \bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi)

[fathom swallow]

Shyshu of the Golden Flower✓

[toxic schooner]

wtf

[flat harbor]

the bot hates physics

[toxic schooner]

(is it working )

bad bot

[fathom swallow]

Shyshu of the Golden Flower✓

[toxic schooner]

oh it just isnt working now

😭

[flat harbor]

they turned it off

bastards

americans woke up and decided april fools over

[gentle bay]

.

[toxic schooner]

i need access to #vent

[gentle bay]

Hey!

.

[gentle bay]

Physics Server.

[toxic schooner]

oh then nvm

[toxic schooner]

ok wth is going on here

what is this

its getting worse

[alpine kindle]

laplace transform?

[toxic schooner]

no thats the lagrangian i think

[neat lintel]

Hi I want to know quantum, what operator is that in the middle of those states?

[leaden torrent]

subtraction

🐗

[neat lintel]

Lol

[toxic schooner]

genius nami

wouldnt have guessed that

[neat lintel]

$\ket{\psi}$

[fathom swallow]

Lysh

[neat lintel]

Ask me about not knowing anything about infinite dimensional state spaces

[toxic schooner]

[neat lintel]

Anyway I need to keep reviewing elementary calculus

Otherwise I'm gonna be stupid forever

[flat harbor]

it is legranjian for the funny electron

[toxic schooner]

i am starting to recognize lagrangians

i will be a genius physicist

[inner finch]

amongus

amongus physics

[flat harbor]

its just partial derivative

[deep mango]

Argh im on mobile and cant fix channel order

This is so annoying

[toxic schooner]

😭

someone do it please

it hurts my eyes

[flat harbor]

caught red handed trying to put feet discussion at top

[toxic schooner]

fuck this april fools shit

go back to order

[thorny rapids]

im sorry but i have no idea what anything here means

[flat harbor]

its hilarious tho

[toxic schooner]

same

[flat harbor]

i wouldnt post in discussion 2 otherwise

[neat lintel]

Blo

[deep mango]

WHERE IS DISCUSSION

[old fox]

gone

on top

[toxic schooner]

waot

[flat harbor]

give me mod perms

ill fix it all

[old fox]

look up

[toxic schooner]

where the fuck is discussion

give me mod

[deep mango]

😭

[toxic schooner]

i will fix it better

[flat harbor]

below events

lmao

[toxic schooner]

what the fuck

who the hell is doing this

i will find u

and i will rip u

[old fox]

#discussion here's discussion

[deep mango]

I can't move it, it keeps rising...

Oh it's back

Phew!

[toxic schooner]

good

[leaden torrent]

im told to move it down, i do, people complain

[toxic schooner]

it better stay this way

jeez

[leaden torrent]

im told to move it up, i do, people complain

[toxic schooner]

no nami let it be, its perfect this way

[old fox]

b&

[neat lintel]

yea i thought most exams dont even allow calculators, also most questions are proof based so tf u gon do with a calculator

[old fox]

wtf

the server pfp was an April fool's joke?

[long matrix]

i see no difference

[ripe wasp]

the physics server april fools joke was better

[old fox]

oh was that a topology joke?

genus 1 shit whatever that is

huh didn't realize it was a coffee cup, there was a stream that blocked the 1st quadrant of the pfp so I only saw the thing you use to hold the cup

[alpine kindle]

Zpordle 4/2/2022 6/10
🟥🟨🟩🟩🟩
☑
https://mabotkin.github.io/zpordle

got the same

[static loom]

same

my sequence was: ||0, 1, 5, 37, 101, 613||

[alpine kindle]

exactly the same

as me

[static loom]

nice

I'm guessing your strategy is the same as mine or nearly the same

[alpine kindle]

yep

[static loom]

I only ever increment by creating the mixed radix basis

[alpine kindle]

i just add the denominator to my guess

[static loom]

so like 6+n*8 is how I think of my guess when going for p=3 and that led to 6+8(0+27+81)

yeah that's how I describe it too, adding the denominator

[toxic schooner]

what was the joke

[ancient flame]

existing

[toxic schooner]

[ripe wasp]

they literally transformed into a music server

[toxic schooner]

oh so thats an actual headphone i see?

oh its phi as a headphone

[ripe wasp]

yeah a psi with headphones

no but like not just that they renamed everything

i don’t remember exactly but it had stuff like classical mechanics -> classical music

and

e&m -> edm

[toxic schooner]

icic

[ancient flame]

ede > edm

[dapper pivot]

is philosophy like an opinion????

[distant karma]

a philosophy contains opinion

where most are based on reasoning

[dapper pivot]

oh it’s like an educated interpretation then

or educated opinion on what’s presented

[alpine kindle]

if anyone's on r/place
does anyone want to remove the orange triangle from the pcm part

[toxic schooner]

which part?

wtf

[alpine kindle]

on the left

[toxic schooner]

damn it i accidently used mine

left huh

gimme a sec

wait a sec what do you mean by pcm

[alpine kindle]

370,630 coords

[alpine kindle]

politicalcompassmemes

[toxic schooner]

Ohh

[alpine kindle]

ie nazis

[toxic schooner]

i was thinking physics chem maths

ofc the indian flag is there

[sand smelt]

r/math is making a hilbert curve around (1640, 290)

[torn willow]

What's this thing again

[toxic schooner]

its a reddit thing

[torn willow]

r/place?

[toxic schooner]

people have the choice to make a tile any color they want

yes

and collectively peole can make a ton of things

its very cool ngl

[toxic schooner]

Oo

[sand smelt]

the plans are here https://old.reddit.com/r/math/comments/tui3co/new_hilbert_curve_in_rplace/

[alpine kindle]

unite and grief pcm (nazi subreddit)

(390,630)

[toxic schooner]

omg its going pretty well

[alpine kindle]

yes

it's very good

[bright hill]

do you have any idea how many people we'll be up against?

[limber thunder]

tons, apparently

there's a whole sub behind that triangle thing lol

I filled a square red and it got filled back in less than a min

[neat lintel]

apparently

[modern geyser]

What is this

[fervent pebble]

looks like a hilbert curve

3b1b made a vid on 'em

something like

"is infinite math really useful?"

wait i found the link

https://www.youtube.com/watch?v=3s7h2MHQtxc

it's a good vid 👍

obviously

[toxic schooner]

hilbert curve

[modern geyser]

Valley

You need to escape chill and go to #❓how-to-get-help that’s how you farm enough cheese to get very active

(The highest achievable rank on this server)

[fervent pebble]

hmmmmmmmmmm

the issue is that helping people in this server is usually pain and suffering

[limber thunder]

I avoid the help channels like the plague

to be fair I have zero interest in ranks either

I'm already emeritus

[modern geyser]

Well you had very active already so it would make sense

We should have a new sticker on this server

Be like Shuri. Get 10000 chat points per day by helping people 24/7.

[limber thunder]

idk I was here before these were implemented

[modern geyser]

Oh jeez

[limber thunder]

I don't think I ever had the active role

[modern geyser]

Wait how did u get emeritus then,

[limber thunder]

idk I've had it since the roles were implemented as far as I can recall

maybe I met the criteria at some point before the roles existed

[bright hill]

fake emeritus

[modern geyser]

True lmso

[leaden torrent]

Hilbert's Curve: Is infinite math useful?

what is with this clickbait ass title

this is like some weird inversion of betteridge's law of headlines

where the answer is "obviously yes but your example is perhaps the worst possible case for it"

[river linden]

yes ^

[bronze pelican]

He talks about teaching deaf people to hear visually using this somehow

I may be misremembering

Or see with your ears

[odd narwhal]

That was just a silly example

For the sake of the video

[neat lintel]

Hey, so since we definitely live in a simulation that God has us trapped in, and we're essentially creating our own simulacra to toil endlessly to our will, how do we best serve our tiny, mostly theoretical, army of minions?

and how do we scream at God, "WE WANT TO LIIIIIVE"

I fear the ghosts of neural networks wiped from memory could collapse our society if they were a bit more organized.

[prime oyster]

sin(x) = sin(x+π/9)

solve for x:

i know it i just want to see if you know 🤓

[leaden torrent]

[swift sinew]

We don’t. Teach us

[prime oyster]

ok so basically sin(x) = sin(y) when x and y are an equal distance from pi/2

so like sin((pi/2)-n)= sin((pi/2)+n)

[prime oyster]

so in this case the distance from x to pi/2 and (x+pi/9) to pi/2 have to be equal

so x is pi/2 minus half of pi/9

x= (pi/2) - (pi/18) = 4pi/9

$\left|\frac{\pi}{2}-x\right|=\left|\frac{\pi}{2}-\left(x+\frac{\pi}{9}\right)\right|$

[fathom swallow]

fredreck_willickers0913

[prime oyster]

this is what this equation is saying

you can drop the absolute value signs and multiply one side by -1 and then solve for x to get 4pi/9

[hollow jackal]

mod check
can one of yall get rid of my helper role

[deep mango]

Sure

[hollow jackal]

thanks ryc

[deep mango]

No problem danny devito

[ancient flame]

ryc best mod

[deep mango]

In the future if you want a guaranteed response dm modmail

Or ping mods I suppose

For role adds/removals

[ancient flame]

PING MODS!!!!

@MODS

[deep mango]

[fading hull]

@polar panther

[sterile hare]

u busy?

[fading hull]

Yes

Why

[sterile hare]

nvm was stuck on a problem finally cracked it

[prime oyster]

The willicker theorem:

$\sin\left(x\right)=\sin\left(x+n\right)$

$x=\frac{\pi-n}{2}+ℤ\pi$

[fathom swallow]

fredreck_willickers0913

[prime oyster]

the willicker theorem

[prime oyster]

why are you "people" ignoring the willicker theorem

[jolly thicket]

your theorem

[jolly thicket]

not sure

[toxic schooner]

2 things, firstly, $\mathbb{Z} \pi$ doesnt mean anything

[fathom swallow]

Shyshu of the Golden Flower✓

[toxic schooner]

u probably meant to say, k*pi, where k is an integer

secondly, wheres the proof?

iamjon whats the problem

and thirdly, what even is n? is it a natural number? an integer? a rational? a real?

probably should write down a statement

@nimble shuttle explain ur sullies

[prime oyster]

my source is i made it the fuck up

[modern geyser]

Zpi = pi^Z

[toxic schooner]

?

what

what in the world is pi^Z

[prime oyster]

a real

[toxic schooner]

ok good

now the proof

[prime oyster]

alr so type this in desmos
sin(x) = sin(x+n)
x = (pi-n)/n + zpi

[toxic schooner]

[prime oyster]

z= [-100...100]

[toxic schooner]

what

thats ur proof?

[prime oyster]

thats the proof

[toxic schooner]

...

[prime oyster]

u type it in desmo

[toxic schooner]

thats not a proof

wtf

[prime oyster]

i dont know how to make a proof 😢

[toxic schooner]

u have to show from the condition u have, for example here, that sin(x)=sin(x+n) will be true only if n is of a certain kind

[toxic schooner]

specifically this kind

[muted dagger]

Hey, I was just wondering, does anyone know how to approach equalities like this? The task is to solve for Δθ https://media.discordapp.net/attachments/488104216678760469/960069185994653696/166579831138418688.png

[prime oyster]

petition to make "proof by desmos" a valid way of proving things

[toxic schooner]

petition overruled

[prime oyster]

alr so here is the proof

[torn willow]

I don't know isn't that obvious?

Just use the half angle formulae

[neat lintel]

Huh

[fathom swallow]

Blitz

[neat lintel]

But I'd write it as

[fathom swallow]

Blitz

[neat lintel]

Actually no, this is bad notation

[fathom swallow]

Blitz

[neat lintel]

It works if we treat R as additive group, but what if someone interprets it as a ring

[prime oyster]

ok so this isnt a real proof but whatever

If the distance from pi/2 is the same for both arguments of sin, the output is the same.

For $\sin\left(a\right)=\sin\left(b\right)$

$\left|\frac{\pi}{2}-a\right|=\left|\frac{\pi}{2}-b\right|$

where a and b are any real number

So if we want to solve for x in: $\sin\left(x\right)=\sin\left(x+n\right)$

plug x and (x+n) in for a and b

$\left|\frac{\pi}{2}-x\right|=\left|\frac{\pi}{2}-\left(x+n\right)\right|$

with equations like these there are two cases. One where you just drop the absolute values and solve for x, the other where you drop the absolute values, multiply one side by -1, then solve for x.

Case 1: $\frac{\pi}{2}-x=\frac{\pi}{2}-\left(x+n\right)$

Case 2: $-\left(\frac{\pi}{2}-x\right)=\frac{\pi}{2}-\left(x+n\right)$

There is never a solution for x in case 1. Therefore we can just take case 2, solve for x and that simplifies to:

$x=\frac{\pi-n}{2}$

that is one solution for x

[fathom swallow]

fredreck_willickers0913

[neat lintel]

Respect for typing out an essay

[toxic schooner]

oh so its like cosets?

[toxic schooner]

[toxic schooner]

yeah thats better

nice

[neat lintel]

Yeah. In a vector space this is pretty standard notation imo

[toxic schooner]

i see

i have only seen this used in what little of cosets i have seen

[neat lintel]

For example, look at wikipedia definition of absorbing sets

[prime oyster]

i forgot to mention that this is for non-zero n

if n is zero the solution for x is over the reals 🤓

[neat lintel]

Not absorbing sorry, I always mix those up. Balanced set

[toxic schooner]

yeah

[toxic schooner]

wait i dont find anything related to this on that page

[toxic schooner]

oh lol

[prime oyster]

What if instead of proving things we just said “well you can’t disprove it”

I think that would be good

[wraith aurora]

but then u have to prove the fact that u can't disprove sth?

[prime oyster]

Just say some shit like pi^pi^pi^pi = 3.946 x 10^38 and if you can’t disprove it it must be true

[wraith aurora]

no

[devout nacelle]

These are equivalent claims. A disproof would be a proof of a statements negation.

[neat lintel]

Something is proven when it's convincing enough

[prime oyster]

What I’m saying is even if you can’t prove something, as long as you can’t disprove it, it’s true

But.I don’t actually think that

[devout nacelle]

This is an acceptable point of view in real life situations (and how theories in physics, etc. are set up), but the essence of mathematics lies in concrete reasoning. Of course, you can assume something to be true in a framework and explore its consequences.

[wraith aurora]

i think there are some true statements that godel or someone proved
they go like "u cant prove X from given axioms"
and "u cant disprove X from given axioms".

correct me if im wrong.

[devout nacelle]

Worst case scenario the statement you assumed to be true turns out to be false and you have to re-examine the validity of all results that were apparently leaning on it.

[neat lintel]

Something something there exist things which you can't prove nor disprove

[prime oyster]

Unicorns are real because u can’t prove that they’re not real

Case closed

[devout nacelle]

[wraith aurora]

nice one.

[devout nacelle]

I claim that there exist no unicorns. Can you prove me wrong? Does that make my claim true?

[wraith aurora]

yea i think fredreck realised he was wrong and was giving an example to his own claim.

[neat lintel]

Do rhinos with one horn count as unicorns

[devout nacelle]

Oh, alright then.

[neat lintel]

Or horses with icecream on their head

[wraith aurora]

u gotta ask the government of scotland for the definition of unicorn

[prime oyster]

Lol I was trying to do this from the very start

Because I’ve heard ppl irl say similar things

[torn willow]

What exactly are we arguing over

[wraith aurora]

yes, its easy to confuse those concepts. ive argued the same for proof by contraditions with many ppl

[neat lintel]

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

Real unicorns

[dense sorrel]

i know this isn't the best question to ask on this server

but is knk's c programming a modern approach good book for beginner

[neat lintel]

that's the book im using

it's really good

are you a total beginner to programming or to c ?

[dense sorrel]

total beginenr to programming

[neat lintel]

i already knew 3 languages before starting the book so it was a breeze for me, i still recommend the book, it goes through the content slowly and makes sure to tell you what everything does, and if it's complicated it the author tells you when it will be covered( don't jump directly to that chapter though), makes sure to understand everything and do the exercises, and best of luck

[dense sorrel]

thanks

[cyan goblet]

what exactly is inverse time?

taylor mentions this a lot - something having dimensions of time^-1 or time^-2

[prisma swallow]

Unit per time unit?

[cyan goblet]

oh that makes sense lol

[prisma swallow]

lol

I thought my answer was completely off

Hz(hertz) is time^(-1)

Refresh rate

[bronze pelican]

I hate this language of "obvious" and "easy" that mathematics use

I tend to find myself using that language too, but I have to correct myself

Its not necessarily obvious

[fair mural]

same

[median zinc]

Clearly, [statement, ...]
One way is to use the exact reason you are using when writing it as obvious.
Clearly, [statement on result but not reasoning]
vs.
Clearly, [statement, ..., because (...)]

[bronze pelican]

Just don't try to downplay the effort needed to understand things

And something you understand immediately may not be so obvious to someone who doesn't understand it right now

So try to take that into consideration

[ancient flame]

just like I hate the word trivial

[surreal sapphire]

my pov is if its really that obvious, you can write it down or at least mention the technique used

its also important when teaching

i dont mind when students tell me that stuff is easy but they should tell me why its easy and what they did to solve it

[dense belfry]

[surreal sapphire]

so i know they arent bullshitting me

[dense belfry]

Saying "it's obvious" serves a purpose in communication

It has its place

[surreal sapphire]

not in a paper imo

[dense belfry]

Honestly idk

[bronze pelican]

I understand that you can't elaborate on every single detail. But you don't have to say phrases like "its obvious " that demean effort

[dense belfry]

That's not why people say it

[surreal sapphire]

just write the proof is done by applying standard techniques (of ...)

[bronze pelican]

But that is the effect that it has

[limber thunder]

something akin to "this follows directly from ..." is more effective

[dense belfry]

I mean if you're trying to maintain flow

When talking about math

This sort of thing helps

[neat lintel]

I don't mind it, but I try to not write things like that in my proofs as it doesn't add anything to discussion

[bronze pelican]

You don't have to use these phrases, is my point

[dense belfry]

To just say "okay that's obvious" and move on

[long matrix]

explicit example?

[surreal sapphire]

maybe its fine in certain situations but its often misused

[dense belfry]

Well I do this when I'm doing work by myself

[surreal sapphire]

i use it in notes for myself

[dense belfry]

And talking to myself

[surreal sapphire]

but in writing for others i dislike it a lot

[dense belfry]

Also when I talk to my advisor

[surreal sapphire]

in verbal communication its also fine

[dense belfry]

I mean I think there has to be understanding about what obvious means

[surreal sapphire]

i can always stop you and say that its not obvious to me

[bronze pelican]

In verbal communication is where it's problematic

[dense belfry]

For me obvious means if you think about this for a short amount of time you'll likely figure it out

Assuming you have some set of pre knowledge

Something like that

[bronze pelican]

Why do you have to qualify the ammount of time someone spends thinking about something?

[surreal sapphire]

it depends on the people you are talking with right?
i wouldnt use this when teaching but with people i know well i am sure that nobody is afraid to speak up

[dense belfry]

[neat lintel]

It's not really about calling things obvious, it's about hiding the facts from me

[dense belfry]

That's not what I'm saying

I'm saying that I'm giving an estimate for how long I think it will take

There isn't any judgement

[bronze pelican]

Something you may need only a short ammount of time, may indeed take others a very long ammount of time

[long matrix]

you might be explaining something, and to justify skipping a detail, you might say 'its clear that' or something

[surreal sapphire]

thats just filler then and can be omitted?

if something is clear to me i dont feel the need to state that

[neat lintel]

People call hard things obvious too, it's more about experience. I wouldn't look hard into this

[dense belfry]

I don't agree with you at all about this pt

[long matrix]

imo it can help put you on the same page. If they don't find it clear, then you backtrack

[bronze pelican]

What don't you agree with

[long matrix]

Maybe i would phrase as a question rather than state.

"So it's clear that...?"

[bronze pelican]

Do you disagree with this excerpt

[dense belfry]

I think that it depends on your relationship with the person you're talking too

No I don't necessarily

When talking to a student it's different

But I think that "it's obvious" does serve a purpose in communication

[blazing pawn]

I think that words and phrases like this can be pedagogically useful

[dense belfry]

When you are trying to get across the fact that it's obvious

[blazing pawn]

They prime students to think a certain way about certain facts and parts of a proof

[bronze pelican]

The point I'm making is that its not necessarily obvious

[dense belfry]

Yeah that's a good point

[neat lintel]

Most often people are just lazy writing the facts

[dense belfry]

Pt if it's not the other person should say so

If you have a good relationship with them

But what you're saying is a vast oversimplification

Imo

[bronze pelican]

Instead of saying "its obvious" you could say "with a little bit of work we can see..."

[dense belfry]

No

I will not

[blazing pawn]

I think in books they can also be a signal to students about what their background should be going in

And what kinds of things should be familiar to them

[surreal sapphire]

why not state this more explicitly

[bronze pelican]

Like acknowledge that it takes work, don't downplay any effort thats needed even if its small

[surreal sapphire]

"if you have trouble with this argument, you need to go back and revise"

[bronze pelican]

Because what you think is little may be a lot to others

[long matrix]

i dont know about writing that in a book

often.

[surreal sapphire]

at some point it should be clear, but

i dont see how calling something obvious helps

[dense belfry]

I mean I cater what I think is obvious based on who I'm talking to

[surreal sapphire]

if a step is obvious, you can skip it

without stating this as a fact

[bronze pelican]

I think we can all agree that phrases like "its obvious" has no place in the classroom, and even in talks we shouldn't say it, cause it can alienate the audience

[blazing pawn]

I mean I think it has a priming effect and can make an argument flow more easily for a student

[dense belfry]

Oh I don't agree pt

[long matrix]

I think 'its clear' is less harsh than 'its obvious' but... synonym hmm

[bronze pelican]

Yes

Or "We can see"

[dense belfry]

Sometimes you need someone to tell you it's obvious

[bronze pelican]

I just don't like this language that hides effort

[surreal sapphire]

"We can see" makes no judgement

[blazing pawn]

I feel like there r instances when calling something easy is useful

[bronze pelican]

There are

[dense belfry]

Don't overthink this

Is a good one

I say that a lot

I just don't like these weird pedagogy generalizations

[neat lintel]

I think it's obvious that books should not use it's obvious etc.

[dense belfry]

I disagree

[neat lintel]

Why

[dense belfry]

I like the energy

Of it's obvious

[neat lintel]

It creates errors and confusion

[bronze pelican]

Its not necessarily obvious is my point

[dense belfry]

So

[neat lintel]

It's nothing but bad practice

[bronze pelican]

And this can alienate people who do not immediately grasp the logic you used

[long matrix]

If we could have an explicit example that would help discuss 🤔
Maybe some of us think it should be used in there, or maybe not

[dense belfry]

I think people should just have a better sense of what "it's obvious" means

Because that's not how I interpret it at all

Lol

I'm going full contrarian

[swift sinew]

“Immediately follows” is nice too

Although Used in slightly different contexts

[bronze pelican]

Just get rid of the immediately

You don't have to qualify how long it takes you to get somewhere

[swift sinew]

tru tru

[surreal sapphire]

did you always interpret it like that though emma

i wonder if this has an actual effect on beginning students

[dense belfry]

No, but interpreting it like this makes me feel good

[bronze pelican]

Because what I'm saying is: it takes different people different ammout of time to get to the same place

[surreal sapphire]

time to go ask my pedagogy research friends

[bronze pelican]

Just because it takes you this "short" ammout of time doesn't mean it will take others the same "short" ammount of time

Or even tha your sense of "short" accurate at all

[dense belfry]

Obvious isn't about length of time

Well it's not only about it

[bronze pelican]

Obvious mean immediate

[dense belfry]

It's also about knowledge you need to understand the argument

No it doesn't

[bronze pelican]

It mean"you should understand this"

[dense belfry]

Obvious doesn't mean immediate

[bronze pelican]

What does it mean?

[dense belfry]

It means it doesn't take a lot of thought

To get there

[long matrix]

These words all have slightly different meanings/connotations 🤔
'immediate', 'obvious', 'trivial', 'clear'

[dense belfry]

There is a short path

To this knowledge

[neat lintel]

Well, it doesn't mean that

It can be interpreted like that

[surreal sapphire]

trivial is the worst of those for me

[bronze pelican]

This is the whole thing

[dense belfry]

Yeah this is all interpretation

[bronze pelican]

I'm talking about all these phrases at once

[dense belfry]

Which is why this bothers me

That you're saying this

[bronze pelican]

The whole language of downplaying effort in mathematics

[dense belfry]

That's not what the language does

On an interpersonal level

I don't really use these sort of words when teaching

[long matrix]

hmmm, I think some of these really do have justified usage - and aren't as 'bad' as you make them out to be

If only we had an explicit example to discuss

[dense belfry]

But when I'm talking to people it's useful

Okay here's an example

Let's say I'm working on a theorem with my advisor

And there are a lot of small details

That I want to ignore

But I know how to resolve them

I'll say "these are obvious"

So we can move past them

[neat lintel]

I think this is bad

[dense belfry]

And proceed to look at the important parts

[bronze pelican]

You can say "I know how to resolve these issues but let's talk about this other thing right now"

[dense belfry]

I mean

When you're doing math

[swift sinew]

You could also trade the “obvious” or “clear” remark with a 2-3 word explanation on how it implies. Like “Since R is complete” - even if it isn’t a full explanation, it helps the reader understand better without undermining the knowledge of the reader

[dense belfry]

I'm the moment

[neat lintel]

Because you should pay attention to every detail

[dense belfry]

It's easier to just use less words

Lol no

Blitz that's dumb

[bronze pelican]

Thats more clear and less prone to being interpreted "ur stupid for not being as fast lol"

[neat lintel]

You can do that at home

[dense belfry]

There are time's to pay attention to detail

Yes

I agree

And I do

[neat lintel]

Yeah. Good

[dense belfry]

But anyway less words is better

[bronze pelican]

I understand that you cannot give eveyr detail when communicating and you have to choose what to explain for say of keeping it cohesive

[dense belfry]

When you're trying to figure things out on the spot

[neat lintel]

I wouldn't use "it's obvious" anyway because it's not my style

[dense belfry]

And you don't want to be distracted by forming coherent thoughts

[bronze pelican]

But using language like "obvious" is harmful

[neat lintel]

Sounds like you're bragging and I don't like to brag

[bronze pelican]

You can move on to the next thing you want to say without using such language

[dense belfry]

If I'm talking to my advisor

I'm sure he can take it

[bronze pelican]

I'm just saying its not necessarily obvious, even to your advisor

[dense belfry]

I agree

[neat lintel]

I would just say, let's not focus on those

[dense belfry]

But it's up to them to believe me or not

Often my advisor doesn't believe me

And he'll press me on it

Which is good

So it really depends on the dynamics of your relationship

[bronze pelican]

Who decides what is obvious?

[dense belfry]

But saying any words at all is hard

When I'm doing math

So saying "it's obvious" is helpful

In communicating

[dense belfry]

Who cares

[bronze pelican]

I care

[dense belfry]

About my private conversations with my advisor?

[neat lintel]

Well, it's the same with everything in language

The speaker decides

[dense belfry]

Do I say it's obvious to you a lot pt

[bronze pelican]

I'm taking about the language we use in mathematics

[dense belfry]

Sure

[bronze pelican]

As a community, that can be alienating , especially to beginners

[dense belfry]

And I'm saying what you're saying is valid, but a big oversimplification

When trying to apply it uniformly

I agree that there are audiences I wouldn't want to say that too

But there are times when you are allowed to ask for a certain amount of knowledge

[bronze pelican]

You could even say "one can check..." instead of "its obvious "

[dense belfry]

And there are uses of that word that are helpful for other reasons

[bronze pelican]

Like you can achieve the same utility of this language without the harmful aspects

[dense belfry]

I don't agree it's uniformly harmful

Like you seem to think it is

I just alter how I talk to people on a case by case basis

But I am not going to monitor my speech if there isn't a compelling reason too

Also how do you know you can achieve the same utility with different words

[bronze pelican]

I'm just saying whats obvious to you may not be obvious to others and we should be mindful of that fact when communicating mathematics. From that perspective, we should minimize our use of phrases like "its obvious".

[dense belfry]

And I'm saying that applying that thinking uniformly doesn't make any sense

[burnt juniper]

as long as you're friends or close to the person

isok tbh

jus like

know the vibes

[swift sinew]

Additionally, reducing how much we use “obvious” forces us to better understand exactly what’s going on behind the scenes

[dense belfry]

Yeah being overly formal kills the vibes

[burnt juniper]

yea

[dense belfry]

Saying things like "this is obvious" maintains flow

And let's you move on

Especially if they agree

[burnt juniper]

it's like how once you're close enuf you can just ask the person why they look homeless today

[dense belfry]

And if they don't they should be able to tell you

Without judgement

[burnt juniper]

yee

[ancient flame]

guys it literally just depends on the person, some people may get offended and upset if you call something obvious while some others may not

simple

[burnt juniper]

im probably mildly infamous already for overusing "it's immediate that blah"

[bronze pelican]

You can maintain flow without using these phrases

[dense belfry]

[burnt juniper]

it's the vibessss

vibesssssss

[dense belfry]

If you're flowing

You aren't thinking about your words

At least I'm not

I'm too in there

[ancient flame]

but you can eliminate phrases

[dense belfry]

So you develop phrases as shorthand

To communicate

[burnt juniper]

ye

everyone has their own style

[bronze pelican]

Also this is besides the point. I dont care toomuch about what language you use when communicating with people close to you. I'm talking about the language the math community uses as a whole

[dense belfry]

Okay good

In that case I still think you are oversimplifying

But whatever

[burnt juniper]

if you're doing like functional analysis using "it's obvious that lim_nf_n converges" when f_n are uniformly bounded + whatever should be clear that like

if you have never seen this

[ancient flame]

just avoid saying something is 'obvious' as much as possible unless you know the exact education level of your audience ezpz

[burnt juniper]

you should like

[bronze pelican]

What am I oversimplifying

[burnt juniper]

look back a bit

[dense belfry]

Yes, if some ideas are staples of a field you can say they are obvious

[burnt juniper]

it's kinda like a sign that

if it isnt obvious

please

go back

[dense belfry]

Yeah that's a good point

[ancient flame]

why wouldn't you just explain it then and there

if it's so obvious

[dense belfry]

Because of time

And flow

[ancient flame]

...

[bronze pelican]

You dont have time amd space to explain everything detail

[ancient flame]

but if someone doesn't understand a detail you should help them understand...

[bronze pelican]

I understand this, my point is that you can acknowledge that while using less harsh language

[burnt juniper]

funniest way of saying "clearly" as far as i know lel

[burnt juniper]

um

do you really need to explain

[dense belfry]

It depends on eg who the talk is aimed at

[burnt juniper]

like

it's probably better

to say it is obvious

than to explain every small thing when the person clearly has not enuf prereq

uk

[dense belfry]

If a talk is aimed at experts in a field

[ancient flame]

and then the person will be lost for the rest of whatever you're talking about

[dense belfry]

They will be talked to as if they are experts in a field

[ancient flame]

that's why I say it depends on the education level of your audience

[dense belfry]

Sure

Of your target audience

[ancient flame]

yes

[burnt juniper]

people reading textbooks arent kids anymore tbh like

[dense belfry]

Not of your audience

[burnt juniper]

youll meet a lot worse irl

soz

[bronze pelican]

So what?

[bronze pelican]

Are you saying that makes it okay?

[burnt juniper]

using phrases like it's clear it's obvious implies that

if you dont know

you should really not be reading this

[dense belfry]

I mean it's not inherently not okay

[fair mural]

lol

[dense belfry]

This is a stylistic choice

[fair mural]

i have no idea how someone could have that opinion

[bronze pelican]

Justifying demeaning language just because people will experience worse in other places in the math community is exactly the problem

[burnt juniper]

it isnt even demeaning...

[burnt juniper]

you have not seen how people talk in person or people outside of asia are too nice LOL

[swift sinew]

There have indeed been times where I've been helped out by phrases like "immediately" because then I realized that there's a quick way of proving it and was then able to figure it out

[dense belfry]

Yes

[burnt juniper]

this as well

[pale orchid]

in fairness, there is a difference between "immediately" and "immediately from..."

the former is useless

[dense belfry]

No

[burnt juniper]

not rlly

immediately kinda implies

it's literally immediate

you probably dont need to throw any strong things at it

[dense belfry]

Immediately tells you you should search close to home

[burnt juniper]

yea

just write down definitions
stare at it
tada

[swift sinew]

My argument isn't necessarily just about the word "immediately" but like how phrases like that can sometimes be a hint to just step away and see if there's a quick solution

[bronze pelican]

It also means you should be able to figure out where to look immediately. Which is not a trivial task. Even if the path traveled is short, finding the direction to move in is not that obvious necessarily

[dense belfry]

Sure

[swift sinew]

This is true, hence why i suggested earlier to just include a 2-3 word explanation, even if incomplete

[burnt juniper]

honestly

[dense belfry]

But what we are saying is it really isn't that clear cut

[burnt juniper]

we are also lazy

[dense belfry]

Yes

[burnt juniper]

you really

dont feel like typing

[dense belfry]

Anyone even writing a book is doing a service imo

[burnt juniper]

something that is simply simple algebraic manipulation or definition throwing

ya

[swift sinew]

that is just a poor excuse though

[dense belfry]

A person can choose to read or not

[burnt juniper]

if you pay more money

then sure

but

you dont rlly get money from writing books

just communicate the key ideas

the intermediate step can be worked out by anyone