serious-discussion

[fresh comet]

convergence or divergence, it simply doesn't matter

[unkempt moat]

I get the Allusion!!!!!1!!

[fresh comet]

I should probably do my hmw

[unkempt moat]

I believe in you

https://tenor.com/view/motivational-gif-chibird-motivational-cartoon-greetings-good-fortune-cat-gif-16891294

Oh…

I forgot I lost nitro again

[fresh comet]

unfortunately algebra is hard and I am not good at it

[unkempt moat]

😿

hey we all start somewhere that’s what they say

[fresh comet]

https://tenor.com/view/ghost-hug-positivity-its-good-gif-14571097

[pure hollow]

Me with math but it's okie I'll be trying again and again and again...

[fresh comet]

that's the spirit

[unkempt moat]

Whether your skill converges or diverges it simply doesn’t matter

Was that a good one

😅

haha

[unkempt moat]

[pure hollow]

It's diverging from being good all I have to do is apply residue theorem

[fresh comet]

I like the residue theorem, but I'm terrible at doing the integrals

[pure hollow]

Residue theorem is messy when I have lots of poles with order n

[fresh comet]

[pure hollow]

I wish I could only deal with simple poles

Oh btw @fresh comet we are doing inner product spaces in lin alg rn it's fun

[pure hollow]

One day you'll do stats

[unkempt moat]

EEVEE EMOJI

I LOVE EEVEE

EEVEE CAT

[fresh comet]

https://tenor.com/view/sinay-yanis-gif-18864293

[true zinc]

Stats is awful

[pure hollow]

True but it's interesting too!

[unkempt moat]

This is me

how did you get this video of me

[fresh comet]

https://tenor.com/view/cute-eevee-gif-21737791

[pure hollow]

Don't question the means.

[unkempt moat]

ARE YOU STALKING MEE

or maybe you’re just a

Higher power

Haha

😅

was that a good one guys

[unborn meteor]

LOL

higher! powers...

[unkempt moat]

Hahahaha

[fresh comet]

https://tenor.com/view/cute-eevee-gif-25670637

[unkempt moat]

I know I’m just sooooo original and funny

😹

[unkempt moat]

THIS IS ME RIGJT MEOW

[unborn meteor]

you are!

[unborn meteor]

RIGHT MEOW

[silent junco]

jk it was pretty funny

[unkempt moat]

I also thought of this exact type of image

[fresh comet]

eh, weren't you leaving rays?

[fresh comet]

[unkempt moat]

In regards to when speedy said lol

[silent junco]

yeah but then i remembered im in two reading groups

[fresh comet]

oh

[silent junco]

ill just be less active

[fresh comet]

welcome back then

[silent junco]

thanks lol

[pure hollow]

Don't be fooled by @fresh comet outward appearance underneath it is wrath incarnate.

[fresh comet]

sounds good c:

[unkempt moat]

WHAT

It can’t be

[fresh comet]

[unborn meteor]

(not mine)

[unkempt moat]

AHHH

[fresh comet]

[unkempt moat]

NOO PLEASE DONT HIT ME

[pure hollow]

Nooooooooo babe don't go

[unkempt moat]

you don’t wanna see me when I’m mad

[silent junco]

I must.

[silent junco]

https://tenor.com/view/wolf-my-reaction-to-that-information-angry-reaction-wolf-reaction-gif-27080186

[pure hollow]

I hope it goes well nonetheless.

[fresh comet]

https://tenor.com/view/unspeakable-violence-unspeakable-violence-gif-25206571

[fresh comet]

you get hugs instead then

[pure hollow]

I'll be here waiting ~~ it's not because I'm unemployed and unproductive ~~

[pure hollow]

https://tenor.com/view/mumei-hug-vtuber-cry-hug-want-hug-gif-10581025261437264414

[unkempt moat]

HIP HIP HOOORAY

[fresh comet]

https://tenor.com/view/coupon-one-free-hug-nanashi-mumei-hug-rainbow-gif-5523438589016036862

[unkempt moat]

https://tenor.com/view/syno-i-love-you-syno-synowithazero-gif-2023483407273504018

[fresh comet]

[unkempt moat]

Oh…

I forgot this isn’t chill

[pure hollow]

https://tenor.com/view/zzz-zenless-zone-zero-belle-image-perms-gif-16211658476521656189

[unkempt moat]

😿 😿

[unborn meteor]

https://tenor.com/view/syno-i-love-you-syno-synowithazero-gif-2023483407273504018

[unkempt moat]

@versed jungle generously gifted me nitro

But then it ran out

So I got used to image perms

but now they ARE GONE

[versed jungle]

hi lexi

[unkempt moat]

but my muscle memory hasn’t adaptare

Adapted

[unkempt moat]

oh hi😇

[unkempt moat]

Yes!

[pure hollow]

Having no image perms implies that you are a lot less of a no lifer than someone with it.

[unkempt moat]

#bots message was this a good one

[unkempt moat]

💡

I’ll take it

[pure hollow]

Well taking it is a sign of coping from having no image perms
You see it's a damned if you do damned if you don't situation.

[unkempt moat]

😿

[quick burrow]

What's this?

[sage wolf]

evil discussion

[tropic pivot]

how many hugs per coupon?

[night wadi]

ONE

[tropic pivot]

okay, I'm good.

[near fox]

https://cdn.discordapp.com/emojis/679414194457673728.gif?v=1

Dancing cat embed failed

[ocean harbor]

https://tenor.com/view/cat-fall-epic-embed-fail-fail-funny-gif-21341768

[near fox]

Yes

copes

[night wadi]

@shut thunder you know anything about this cosmic microwave background radiation?

[proud olive]

https://tenor.com/view/syno-i-love-you-syno-synowithazero-gif-2023483407273504018

tf

https://tenor.com/view/cat-fall-epic-embed-fail-fail-funny-gif-21341768

[agile fiber]

you have image permissions in #chill

[proud olive]

you dont know me son

literally

[wraith magnet]

https://tenor.com/view/cat-fall-epic-embed-fail-fail-funny-gif-21341768

skill issue

[sharp mulch]

[rain lava]

https://tenor.com/view/epic-embed-fail-ryan-gosling-cereal-embed-failure-laugh-at-this-user-gif-20627924

[rain lava]

[lime vapor]

Can anyone give me 5 numbers from 1 to 50 and 2 numbers from 1 to 12?

[ocean harbor]

17, 42, 9, 28, 33

6, 11

[lime vapor]

Too late

[ocean harbor]

fair

at least i answered ur question rather than being ignored

[dusky fossil]

Anyone knows stuff about AI ?

[loud oxide]

Barely me. X E.

[true zinc]

<@&268886789983436800> user asked this in 2? 3? channels total

[radiant sparrow]

I only see them having asked this here and at #discussion message, seems non actionable to me

[true zinc]

[loud oxide]

Hi, anyone want math problems?

Also, how you been?

🐩 X E.

[loud oxide]

Why even in the Minecraft servers are there no moberators?

[coral crow]

https://tenor.com/view/sixseven-six-seven-six-seve-67-gif-14143337669032958349

[sharp mulch]

#chill

[woven tangle]

is there any hrk equivalent but for mathematics

[magic sleet]

Hrk full form?

[ocean harbor]

yes and it's garbage if ur wondering about math

[dusky fossil]

dm me

[ocean harbor]

for what

[warm lance]

!noai

[quasi jetty]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[true zinc]

What about it?

[shut thunder]

Theres a point in which light waves have so little energy that they basically dont exist for any practical purpose. The highest level of energy is gamma rays, the lesser ones are radio, microwave, etc...

So basically, the CMB is just a really old pic of the universe

they lose energy through space dilation

[shut thunder]

iirc its about ~300K years after the bigbang

[ocean harbor]

hi

how it goes

[warm lance]

good

[ocean harbor]

[warm lance]

[ocean harbor]

coming to lab and its so empty

many ppl dropped out

[warm lance]

,ti kensukeken

[fathom swallow]

The current time for kensukeken is 09:46, 21/11/2025.
usrcard is 13 hours ahead, at 22:46, 21/11/2025.

[warm lance]

makes sense

imagine coming to school at night

[ocean harbor]

that sucks i dont want it

[brave epoch]

Hello

[ocean harbor]

helo

[warm lance]

why does it feel good to me

i like the feeling of having dreams of going to school at night

[ocean harbor]

probably bc ur a night person

i remember having class at 6pm to 10pm and it was REALLY bad

[warm lance]

what class

[ocean harbor]

math

[warm lance]

a

[ocean harbor]

that was in hs tho

[warm lance]

oh, why that late

[ocean harbor]

long story

[brave epoch]

Yap yap

What in discussion 2 no time out

[ocean harbor]

i was taking precalc and calc at the same time

[brave epoch]

Why is there no timeout

[ocean harbor]

bc its quiet here

[brave epoch]

Oh so here lonely one's do we even talk abt maths nice to meet you

[ocean harbor]

we talk about randos stuff but typically not focused on math

[brave epoch]

Ohhh

[ocean harbor]

nice to meet you too however, im not looking for new friends

[brave epoch]

Ohhh ok thankx for letting me know wanna be friends

The obvious ans is no but jst asking

[ocean harbor]

[warm lance]

i sleep at 12am. is that a night person

i also wake up at 6 to 7

that's the average, i think

[ocean harbor]

ye

but do u have morning classes

at 8am

i usually get up at 5am and then catch my bus at 6:40am

i need 15 mins to walk on bus stop then it comes at 7am

[warm lance]

i don't go to uni anymore

bur yea, used to wake up early

[warm lance]

i see. so i am

damn

and i used to stay more late back then

[jolly vale]

2am

[warm lance]

not 12am?

[jolly vale]

which i have to force

if i leave it alone my schedule converges to ~04:30 (used to be 07:30)

yeah, 2am these days

12 sure as hell is not a morning schedule though

i'd say its an early night schedule

definitely will cause interference with the morning shift

[warm lance]

isee

[neat lintel]

Re
Eeeeeeeeeeeeeee

[echo pumice]

what is a good argument to back up ai being more harmful than beneficial

[night mason]

Hello I joined a math olympiad any tips?

[ocean harbor]

never been late before

[tropic pivot]

Hi there.

[tropic pivot]

It has knowledge power using it is good but depending on it is bad with using intelligence.

[night wadi]

but like, why do they have to stick around? easily, electrons can observe them right?
and even if you say something like "Well by the concept of electron radiating a photon, it would be just as the same energy as it got, so it'll get re emitted"
then how do we know the cmb picture? everything should just be scattered and displaced

[night wadi]

And, what prevents you from receiving the same photon that you emitted while you were observing that, twice or more.
Like a ball that a machine threw at you, and it went back to the machine (the machine is in a wall) and the wall got back the same ball to you

[night wadi]

And someone once said me, that virtual particles form and annhilate each other all the time.
Ever since I've been wondering a lot of things about what their characteristics would be;
if virtual particles can form, I don't believe they should be only in empty space where no atom is there for miles away.
what if, a pair of an electron and a positron form near a star bang or what u call those, ah super nova.
Wouldn't the electron that's formed move with a lot of energy that's kind of spread over? it wouldn't violate energy conservation laws because the star's concentration is reduced by the same amount.
So wouldn't THAT virtual electron which exists for a short time of world, emit such a energetic (very low to very high I'm not sure) photon that shouldn't really had existed?

[shut thunder]

Consider, the CBM is a 360 photo from our point of view as the center of the observable universe

if you measure that in light years squared as surface

thats about 27trillion light years squared of imaging

which has been reduced to about an image which is 10k pixels across

[night wadi]

oh

that's insane

but

shouldn't it be random and how are u able to reduce it even

I mean.. each picture, or say a rectangle of pixels, shouldn't align with any other at all

[shut thunder]

so, for each pixel, youre looking at about a 670 million light years across square

the CBM is already incredibly low res

Scatering doesnt account for how "bad" our equipment is

[night wadi]

hmm i see

well yeah true

[shut thunder]

If you recall, this phot

the blackhole is at 55million ly away

the CBM is at 46 billion ly.

[night wadi]

wait, I'm not really understanding this point of measuring it in light years squared.
Is it in light years as in time, or is it in light years as in area.
area shouldn't had been possible,
And how is it even possible for you to measure the time based on sheer recievances of photons? like how do u know this photon's made 600 light years away and so and so.

[shut thunder]

the machine detects a type of radiation that isnt visible to us

[shut thunder]

The image is a 360

so, in consequence, its a projection of a sphere

[night wadi]

hmm

so a 360 as in, all around a particle, like from any direction the photon can come in and should come in

[shut thunder]

if you take about the size of the photo in pixels, you know what percentage of the whole sphere is enclosed in each pixel

Now, whats the surface of the sphere?

4 pi * the radius of the observable universe^2

[night wadi]

wait hold on, I thought the universe was smaller then.
how does our observable universe currently relate to it?
I can think of it if you're taking into account of the expansion over all these light years by some weird equations,
that just seems impossible though.
so why are we using our universe's current radius

[shut thunder]

the CBM is basically the image of the edge of our observable universe

its the light thats reaching us from its length

[night wadi]

oh

well I mean yes but

[shut thunder]

if the radius of the observable universe is 46.5 billion ly

then the CBM is 46.5 billion years old

since its travel method is light.

anything closer would have reached us faster, so it isnt the oldest part of the universe we can detect

[night wadi]

why is it that the photons that we're observing, have to come from THERE exactly? I mean say this place right here is where it all began in a 5 cm ³ sphere (this place as in this earth's co ordinates)

then the photons, that emerged from the sphere's boundaries may as well have been getting deflected but stayed in similar areas right?

And that's not even the main point, say a few billion years ago, the edge was considerably smaller, why is it not that the photons we mapped were of the boundary at THAT time? and current situation of the boundary shouldnt matter to it.
Because by the light speed, we will receive the photons emitted by our boundary sphere in about a LOT of years later by then we'd be using new radiuses? how does that make sense

[shut thunder]

When you speak of light moving through space, time and length essentially becomes equal things

[night wadi]

hmm

i can see where you're coming from

[shut thunder]

The more it takes to reach you, the more distance it traveled

and viceversa

[night wadi]

yea

[shut thunder]

The CBM is basically our want to find the "oldest" pic of the universe

[night wadi]

hmm true

[shut thunder]

We use Microwave Radiation mostly because any other form of radiation is unpractical to detect with some acuracy

and even longer waves we cant detect inside earth since their period is larger than earth itself

[night wadi]

yea hmm, but what's microwave radiation anyways? it's all photons getting emitted right?
or do photons have different kinds of levels that they are emitted of?
say the electrons at the boundary of universe, why is it that they have to emit microwave radiation as well? why not emit something ONLY like a gamma high energy burst?

[night wadi]

hmmm but, here's another question

we don't believe earth is the centre of the universe right

[shut thunder]

Its the center of our observable universe

[night wadi]

so what about us getting unequal and different times of

[night wadi]

oh I see

[shut thunder]

We consider the universe to infinite so by extension there isnt precisely a center to it

But the observable universe is a sphere

And to be really precise, everyone has their own observable universe

But since a galaxy is compared to it, to it, we usually just call our galaxy, star system or planet, a single one.

[shut thunder]

Photons are emmited at, generally, all frequencies, only gamma survive the trip tho

[night wadi]

I mean... all of this seems like a declaration of things after you've made a scientific breakthrough of knowing the distances of our observable universe.

[night wadi]

oh I see

what do u mean "surviving" the trip?

[shut thunder]

The longer they travel, the lesser energy they have, since gamma is the most energetic frequence, that determines the longest travel possible.

[night wadi]

I mean all energies of photons should be able to, theoretically, travel infinitely without losing anything other than vaccum field right?

[night wadi]

oh right..

why is it that the longer photons travel they lose energy?

[shut thunder]

space dilation

[mild hazel]

Space does also have other stuff in it, even if its just dust. I belive thats called extinction?

All the dust can absorb light

[night wadi]

but even dust, it's all atoms and particles though right.
and in theoretical principle, they all should emit the same exact energies's worth of photons again
If they receive 2.5 mega watt photon, they emit 2.5 mw photon.
and, if gamma rays do not have a problem with getting deflected by these kinds of atoms, then the tiniest ones shouldnt too right?

[night wadi]

what's space dilation, is it something like a relativity concept

and, why does it affect purely zero mass particles like photons

[mild hazel]

Yep but they get scattered

[night wadi]

yea but even gamma rays have the same problem

no? maybe they also cause destruction such as moving the atoms they hit a bit too much away

but they'd get the same treatment just as much as cmb does right?

[mild hazel]

I'd imagine they are less effected. Gamma rays can penetrate materials quite well, which is why so much shielding is used when Gamma is involved

Probably works off the same principles

[night wadi]

I see

does it have to do anything with the amount of photons emitted here?

let me explain myself here;
since cmb is like low energy photons, the movement is VERY minimal and the amount of electrons received would be around 1-2 photons per electron, over a usual unit of time.

[night wadi]

But, gamma rays; they're like really high energy so high movement/disturbance may be involved.
And they in intuition, should emit way more than 1-2 photons per electron over the SAME usual unit of time

[night wadi]

so talking about this, if those 100 photons emitted by gamma rays, hit 80 electrons, they're not enough electrons to absorb everything at the same time, and they pass through maybe?

vice versa with 10 photons of CMB and 80 electrons of the chunk of matter,
Deflection is imminent here

is this agreeable upon? or is there another phenomenon here

[mild hazel]

So effectively you are asking if more gamma was emitted, and if that means more gets through?

[night wadi]

Yeah

[mild hazel]

Just through sheer numbers

[night wadi]

Yeah

I mean.. I don't know it I'm just a 14 year old, but that's the only logical explanation I can think of for why gammas last longer than cmb

[mild hazel]

It could be maybe... im not too sure on how much of specific frequencies was released

[night wadi]

hmm I see

[mild hazel]

No worries, it can be very confusing

I get confused very easily :p

[night wadi]

well yeah I'm just thinking over a lot of stuff over here

[mild hazel]

We do cosmology next semester so my knowledge is very surface level

[night wadi]

hmm I see

[mild hazel]

Good stuff, but dont be disheartened if you cant grasp something yet

[night wadi]

thanks for the advice. I just was sad mainly in the terms of the math pre requisites I needed to learn for equations, but guess life is life and I gradually progress

[mild hazel]

Yeah the maths is real important, you'll learn it slowly but always remember how important it is

[night wadi]

hmm well

by the way, do you know about vector fields and how particles who exert them behave with each other? I recently stumbled upon the N body problem, that; intuitively is very hard to think of, but what if you think of it in just fundamental particles.

[mild hazel]

I mean you are thinking of it as the gravitational field when considering the N body problem so yeah

Also grg sorry

[night wadi]

oh yeah nws

good bye!

have a great day ahead

was nice talking with ya.

[mild hazel]

No worries, best of luck

[dreamy wyvern]

Hm

[wide hull]

Is there an everywhere differentiable function f from R to R such that f' has a point discontinuity?

I've been thinking about this like, once a week for the past year

And I don't know lol

Sorry, jump discontinuity

[silver drift]

they lose energy

[night wadi]

how tho

and why do you know this/where do you know this from at all? (I don't mean where YOU know this but this idea, what gives physicists this idea)

[silver drift]

essentially their frequency. Spacetime redshifts all photons.

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

We thank astronomers and cosmologers, generally, for discovering this. I don't know when it was confirmed, but it was post Hubble. He merely found that the universe was expanding.

[night wadi]

isn't that redshift only observable when it hits a particle?
and isn't it a classical physics' wave phenomenon?

[silver drift]

No, redshift is always observed from the source. Yes, it is basic wave theory

[night wadi]

the whole concept of doppler's effect is when a light wave hits a particle, it gets compressed so we observe a red shift.
And this, is not applicable to the first wavelet as it does not get compressed when it hits the particle.
it's applicable only if it hits something tho right?

[night wadi]

how does the emitter of the photon/wave observe it?

only the reciever should be able to observe it right?

[silver drift]

? we observe the emission

CCD, before that was photographic plates

[night wadi]

how do we observe the emission? like we can only observe the waves that hit us and not the waves we create

[fresh comet]

no, Darboux's theorem forbids it

[night wadi]

I don't think something signifies the existence of light waves to it's own emitter

like how does an electron know the type of wave it emitted

the wave just goes over

and no other phenomenon in my opinion can tell the electron/particle about the wave's locations and etc..

[night wadi]

sure it may know how compressed the wave would be, but that's only when it hits a particle

[silver drift]

I was talking about infinite travel and why they lose energy, not self-awareness of light waves, lol

[night wadi]

right... hmm

[wide hull]

Oh thank god!!!!

[night wadi]

but, why is it that the photon that is emitted is connected to which electron it was emitted from?

[wide hull]

I would have been really mad if there was such a function

[night wadi]

what if another electron jumps in between the wave and the other electron

[wide hull]

Thank you @silver drift !

[night wadi]

I'm just saying, if the wave is 10 metres long and it travels 1 metre per second, there's absolutely no reason for an electron to meet it only when it touches at the other edge

electron B can jump in at 5 metres only

so what happens to the other 5 metres of the wave?

why are we considering a wave phenomenon here?

[silver drift]

electrons are wave phenomena

[night wadi]

they're particles, no?

and photons are wave phenomenon in terms of classical physics

but the wave phenomenon does not make sense at all

[silver drift]

not when you're constructing hypotheticals which are answered by them being quantum fields, no

[night wadi]

but even in quantum fields

they're not like a wave...

they're force carries that move anywhere

a wave has a destined place it tends to

[silver drift]

they quite are

have you heard of superconductivity

[night wadi]

okay what is the wave equation of an electron? does it tell you if the electron is gonna move North or south? doesnt the electron move anywhere it wants?
and does this wave equation end at all like the light waves? because unless you put in extreme energy, I don't think mass really ends you know

[night wadi]

oh I haven't

what is it?

[silver drift]

electrons are massless

[silver drift]

it's the field of electrons behaving like a field and not particles

practically zero electrical resistance at cold temperatures

[night wadi]

how

do they not have a mass?

I heard from someone that they do have mass tho

[night wadi]

Hmmm

[night wadi]

Are you saying that if an electron /atom is perfectly still and not vibrating, then the electron gives no repulsion?

[vivid halo]

[vernal iron]

1 electron is approx 9.109x10^(-31) kg

anything that moves slower than the speed of light in a vaccuum has mass

and if anyone say otherwise they're stupid or lying to you on purpose

[night wadi]

hmmm

[latent edge]

for application purposes it's basically zero approximately where approximately means equal

[vernal iron]

yes it is basically zero

but saying massless is just wrong

I hate rounding ngl

[night wadi]

are electrons a wave equation?

[vernal iron]

I am not a physicist, but I am pretty sure all elementary particles are waves in some field but again Idk

[night wadi]

Ah I see

okay.

[vernal iron]

but the amplitude of the wave would be the probability of finding the electron at a location and time

it is weird

I think treating it like a particle only is better

as opposed to light which acts like a wave and a particle in a more traditional sense

[vernal iron]

(Cause this would be quantum field theory I think)

[night wadi]

hmmm

[vernal iron]

Idk it is kind of freaky

[night wadi]

yea.

do you know about charges? and what exactly are they?

[vernal iron]

no

no clue

ummm

[night wadi]

oh cool.

[vernal iron]

ask @latent edge

He also may not know

[night wadi]

yea sure

[silver drift]

he was talking about speed of light in a vacuum then switched to electrons, my bad

[vernal iron]

ah

[silver drift]

yes, everything is fields

[night wadi]

oh wait I think you mis understood the plot

I was not asking about the electrons in the example of "what happens if an electron comes in the middle of a 10 metre wave, it obsorbs the 5m but what about the other 5m"

I was asking about the light wave there

[brave epoch]

Furry

Furry

Furry

[silver drift]

I don't know how to understand an electron coming in the middle of a 10 meter wave or how it absorbs 5m

[idle steppe]

in quantum mechanics electrons are described by a wave function

the shrodinger equation describes how this wave function evolves over time

but the answers you get are probabilities

[silver drift]

particle man, particle man,
when he jumps in the water does he get wet?
or does the water get him, instead?
particle maaaan

[brave hemlock]

Redshift in this case is not due to doppler's effect

[night wadi]

I see. what is it due to then? how do u know that photons lose energy over time.
what does being reddish mean over here? why can't a blue, 50 watt energy photon stay like a blue 50 watt energy photon forever as it travels

[brave hemlock]

Because of emission spectra

[silver drift]

because space[time] is expanding, and that photon's moving thru it

[brave hemlock]

They are supposed to be a certain wavelength, but they are not

[night wadi]

what exactly is emission spectra. I'm assuming the photon loses its energy to the em field because intuitively I don't think energy can just dissapear. And we've found vaccum has energy as well, so is it due to the field and the photon's nature of not being able to perfectly shift a chunk of energy without losing residue as it travels?

but if it is not, then how do you explain this emission spectra? we certainly can't use wavelengths idea over here because qm treats photons as a particle /a force carrier.
so how do you explain the change of colour in the photon~ why does energy have colour if so.

[brave hemlock]

See https://en.wikipedia.org/wiki/Emission_spectrum basically because positions of electrons in atoms are quantized they can only change their energy by specific amounts, and that means they emit photons of specific frequencies

[night wadi]

so in that sense, if there already have been particles that have been there. and the photon is travelling beside a lot of particles,
Still space time expands? and does that mean space time contracts after something passes through? how does that make sense? can we not treat it as a vacuum field

[brave hemlock]

It can just disappear

Or at least that's the current thinking

Maybe quantum gravity will say it doesn't actually disappear, who knows?

[night wadi]

why is it not that it loses its energy gradually to the em field.
because the em and higgs field have shown us that vacuum without any particles or any energy providers, can have energies and create masses with pairs of anti and real particles

[night wadi]

my idea is that, because photons are just energy carriers. they're not like actual particles even though behaving like one. I'd like to re iterate the idea of a ripple in the field, but it's pointed out to a single particle like area that's moving

[night wadi]

and due then, the idea of it losing energy gradually to vaccum becomes possible

or is this idea wrong? but how?

[night wadi]

hmmm. quantized, I need learn more about why electrons cannot move wherever the heck they want to emit any type of photons.
But I can agree with you on this.
Yet, this still doesn't answer my question of how the photon changes frequency mid air after the electron actually emits it

because redshift, is not the idea of electrons emitting a different kind of photon right? as far as I'm thinking it says about the photon itself

[brave hemlock]

Well, if it's a wave that has dimension in space, then space expanding would make it longer

[night wadi]

it feels counter intuitive to think about space expanding inside a space that has already expanded.
Let me explain myself clearly, I do agree space is expanding. from cmb we know it is, but like why are you considering the space inside it to be expanding as well? why not the sphere's boundary expanding and not the space inside the sphere.
You may think that's the same, but the area that's affected is near the outer edge of our universe and it's not exactly space surrounding earth and other areas

[brave hemlock]

Well, that wouldn't explain the red shift

Also no, that's definitely not the same, I don't think that

[night wadi]

but, the idea of a photon gradually losing energy to vacuum may explain it right? I mean why isn't that possible? why does photon have to dissapear gradually, without sharing it's energy with diffusion. it's like mathematically dissapearing, I don't think that's really a correct answer here. I might definitely be wrong but how about this idea?

[night wadi]

hmm I see.

[brave hemlock]

I mean you aren't wrong. You can try to come up with some model where waves are dampened in some way

[night wadi]

for a matter of fact, do we actually know that the photon is definitive and fixed?
in my idea, the photon's not a real particle but behaves like a particle because of the dynamics.
the photon's just energy that's travelling through space, it's the same energy that the vacuum in the field surrounding contains, just more definitive and higher

[vivid halo]

No the whole idea of “tired photons” that you are referring to doesn’t really work

[night wadi]

hmm it wouldn't if we actually know the photon was a fixed true particle

[vivid halo]

There aren’t any mechanisms in QFT that would naturally give rise to this and it’s not compatible with observation

[night wadi]

or what other idea are you reffering to here

[night wadi]

but how do you explain the mathematical dissapearance of energy then?

where does the energy go

counter intuitive to make a theory about it just vanishing

[vivid halo]

I am referring to the idea that redshift is photons losing energy to the vacuum rather than being a Doppler shift due to expansion

[brave hemlock]

Not compatible with observation is the big deal.

[night wadi]

Hmmm, if that idea would not work.
then what idea explains photons losing energy?

[brave hemlock]

Honestly, there is no reason energy should be conserved?

[vivid halo]

Doppler shift due to expansion lol

[foggy meadow]

What are you up to ngroupoid?

[vivid halo]

Redshift doesn’t violate energy conservation simply because the energy lost due to redshift is compensated by the energy needed to drive the expansion that leads to redshift in the first place

Like you don’t just get expansion from nothing without vacuum energy or cosmological constant or whatever

[night wadi]

what gives a reason for the energy to not be conserved then? there's no reason for it to not be conserved as well.
And as far as everything we've observed that i know, energy is conserved and it wouldn't be right making a theory about energy vanishing without being conserved
When most if not all of our other observations convey it tends to be conserved, and we even have ideas like the field itself having energies randomly and force carriers just moving through it so the idea of them diffusing into their own becomes possible.

[night wadi]

What is the idea that backs up this theory very well

not my theory, the theory of it mathematically dissapearing without giving anyone it's energy

[night wadi]

Hmmm

mind explaining me this doppler shift in terms of a particle

because my previous experiences of the doppler effect was on the basis of after* something was hit by the photon

And not during it

[vivid halo]

No because you shouldn’t view these wave phenomena in terms of particles

Point particles aren’t real

[night wadi]

I agree with you

photon does not seem like an actual particle to me as well

[vivid halo]

Like are you happy with what Doppler shift means in terms of waves?

[night wadi]

but explain me this wave phenomenon, as far as I see it. it has a lot of seemingly counterintuitive idea

[night wadi]

Yes and no, I agree it happens but in this case it's about losing energy mid air and not after getting recieved

[brave hemlock]

Stupid question, can't doppler shift in terms of particles be just addition of velocities, so the energy transfered on impact is different?

[vivid halo]

In this case no

[night wadi]

would you mind explaining me how the doppler effect gives the redshift of the wave phenomenon.
"mid air"

[vivid halo]

You need a relativistic version of Doppler shift since you’re talking about particles traveling at the speed of light which isn’t being changed

[night wadi]

the doppler effect I studied, compresses the wave after a collision

[night wadi]

and what might that be?

[brave hemlock]

Yeah, I realized that it's always the same speed in this case, but wouldn't special relativity say it has different momentum for moving/non-moving observer

[vivid halo]

Literally read Wikipedia or any other source on this

[brave hemlock]

Which could still explain doppler shift for particles

Or does it not work out numerically?

[night wadi]

I don't think it works out numerically, maybe similar to the n body problem. physicists may have not been advanced enough to build equations of relativity for computation, in a dynamic system.

it's really hard

[brave hemlock]

I didn't mean in the sense that you can't solve it, but rather that does it or not give the same answer

[night wadi]

yeah I understood but we seemingly may not have a way of literally proving it

I'm really not sure how relativity works in terms of ideas though

[brave hemlock]

Also it's not that physicists can't construct equations for n-body problem, it's that there just isn't an expression that solves it

[night wadi]

id rather suggest we see it on a universal frame of reference

[brave hemlock]

In the same way that there isn't equation to solve general quintic. Every expression you CAN write down isn't the correct one

[night wadi]

hmm

[idle steppe]

energy is conserved when there is a symmetry in time translation

the expansion of the universe breaks that symmetry

i think. im not a physicist so beware i might be wrong

[night wadi]

right but the expansion of the universe. is only making it possible for energy to not be conserved at the outer edge of the universe and not the inner edge.
it gradually becomes conserved in my opinion, newer areas form but they remain with the same energy they were given to as they progress.

[idle steppe]

u got it wrong, its not the "edges" of the universe that are expanding. its the space between galaxies which is expanding

[night wadi]

hmm I see

[idle steppe]

galaxies are all drifting apart

the space between them is expanding

[night wadi]

hmm, the symmetry breaks even if they drift closer together? supposedly.

I don't understand something over here tho

how is energy of the photons even related to the reciever moving away?

[idle steppe]

the universe isnt symmetric under time because space is expanding

[night wadi]

it's not like they were destined to meet at a place

[idle steppe]

idk im not a physicist tho

[night wadi]

hmm

I'll try to learn more about this

[brave hemlock]

Well, there is always the classical doppler shift

For regular human scale phenomena

[idle steppe]

the expansion of space streches the photons drifting between galaxies. increasing their wavelength and decreasing their energy

[night wadi]

that only happens when the wave actually hits the reciever, by then the wave getting compressed/depressed matters.
but I don't think it does when the wave/photon is mid air and the seeming reciever moves away

[night wadi]

if you talk about it more, there's only two types of waves/photons over here.
Once that already touched those galaxies and once that are in the way

[brave hemlock]

Wait, nvm i'm dumb it's still the same velocity, so no it doesn't work in this case

[night wadi]

and to both of them , it doesn't matter in terms of what you're conveying.

[night wadi]

Hmm well.

[idle steppe]

this is known as cosmological redshift and is why galaxies far away appear more red

[night wadi]

so you're talking about the waves/photons that have already reached us and have been reaching us. I agree with that.
But like, them moving away still doesn't violate any energy conservation laws though or time symmetry? how is that violated then

[brave hemlock]

Notably, nGroupoid says that energy can still be accounted for

[idle steppe]

they lose energy while travelling between galaxies. regardless of us having detected them

[native oriole]

discussion 2

[night wadi]

Hmm

[idle steppe]

energy is just not conserved in an expanding universe

[night wadi]

I get the whole picture now

but just seems wrong to conclude something on the basis of a wave idea

[idle steppe]

general relativity dosent have some equation that says, that the energy of the universe is conserved

[night wadi]

yet it's the only way u explain redshift

hmmm

[brave hemlock]

Even without general relativity, conservation of energy is an incredibly abstract and non-obvious concept

Like if you came to Archimedes and told him that you can calculate energy and that this number is somehow invariant, he would probably be perplexed

[idle steppe]

the universe just is not the same from t1 to t2, because its expanding

that means there isnt time translation symmetry and noethers theorem dosent apply

[brave hemlock]

Noether is pretty pog

[idle steppe]

noethers theorem is amazing

[brave hemlock]

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

Same Noether

[pseudo topaz]

what is noethers theorem?

[idle steppe]

look it up on youtube

[pseudo topaz]

Alright alright

[warm lance]

,w noether's theorem

[fathom swallow]

Results provided by WolframAlpha

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

Requested by usrcard

[pseudo topaz]

Wait I just remembered. what. it was

😭😭

That's a bit embarassing

[warm lance]

what is it

[north lynx]

Anyone here from ISI(Indian Statistical institute)

[river wedge]

Kya kerna hain

[north lynx]

Nthg i want to talk

R u from ISI

Then dm me

[river wedge]

Nhh broo

[river wedge]

Noether’s theorem is Every symmetry in a physical system gives a corresponding conserved quantity.

[pseudo topaz]

Yes I got to see an example of it while studying particle physics

[river wedge]

Okhh

[pseudo topaz]

Thanksss

[faint light]

https://youtu.be/Ohrl3S2wcBU if you wanna learn about Noether’s theorem, here is a lovely video

[neat lintel]

Hey

[cunning horizon]

,w hairy ball theorem

[fathom swallow]

Results provided by WolframAlpha

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

Requested by parttimebhoot

[stray vector]

I LOVE the hairy ball theorem

[tropic pivot]

,w field extension

[fathom swallow]

Results provided by WolframAlpha

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

Requested by ahitbro

[scarlet thistle]

How does one go from “person X was killed while being black” to “person X was killed because he was black” what inference allows you to do that?

[dusk gulch]

😡 😡

[sick parrot]

https://tenor.com/view/benjammins-context-context-hat-context-meme-give-context-gif-17878213523519376968

[wild lantern]

Do you not believe people have been murdered for their race before?

[jagged forge]

surely not, that would be an outlandish reality

[zealous garden]

That can't happen Doot, that's illegal

[placid shadow]

i wanna go to harvard >.<

[winter cliff]

wrd

me 2

[placid shadow]

Yea!

[magic python]

Same girl :3 you can do it, I believe in you :3

[winter cliff]

i told ppl i wanna go to harvard medical school

they said im too dumb

thats why im locking in rn and studying online

[placid shadow]

well i think most people are dumb before uni but they learn stuff in it and get smarter

[magic python]

WE HAVE A BLAHAJ EMOJI?

[winter cliff]

true

[winter cliff]

whats that

[placid shadow]

No, it's from trans academy

[magic python]

Ikea shark that became trans icon

Aw damnit 3:

[placid shadow]

i wish u luck on ur journey u got this! ❤️

you're really admirable

to even want to do med school

[winter cliff]

thank you! You to

i mean you can still try out many things if one doesnt work thats fine

[placid shadow]

Ty!

[placid shadow]

yea for sure!

[magic python]

Imagine I got into Harvard and then spouted my collatz bs

[winter cliff]

[latent edge]

you should learn proper arithmetic dynamics

[magic python]

Any good books or sources on it?

[winter cliff]

im aiming for john hopkins or harvard med school

heh

[latent edge]

https://link.springer.com/book/10.1007/978-0-387-69904-2

[winter cliff]

thing is my reading comprehension is trash

[magic python]

Thats cheaper than an abstract algebra book

[placid shadow]

i'm aiming for UM

it reminds me of monsters inc because they have the initial M

[latent edge]

It's a really good book

[placid shadow]

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

[winter cliff]

uni of miami?

[placid shadow]

michigan

[magic python]

Bet I'll try to get myself a copy

[winter cliff]

oh nicee

[placid shadow]

mhm!

[winter cliff]

i wanna visit the lakes over there

dang

i admire the people here who do advanced math

[placid shadow]

oo

i haven't seen them

[winter cliff]

its amazing

[latent edge]

It's available online in the link I sent u

It's free for me

[placid shadow]

same!

[latent edge]

should be free for u

[placid shadow]

its so cool

[winter cliff]

is sin and cosine

calculus

i forgot

[magic python]

I need an institution it seems to access for free

[placid shadow]

from my limited (no pun) understanding, it's about integrals and derivatives

[winter cliff]

o

[placid shadow]

have u heard of them

integrals and derivatives

[winter cliff]

yes

ive seen it

[placid shadow]

idk what exactly they are

same

[zealous bronze]

trigonometry (study of triangles)

[placid shadow]

i know that integral has to do with area

[winter cliff]

is that where sin and cosine comes in

[placid shadow]

https://www.youtube.com/watch?v=tt2DGYOi3hc&list=WL&index=15

[visual breach]

They be operators on functions

[zealous bronze]

yeah

[placid shadow]

i really recommend this video!

it's amazing

it's short

[placid shadow]

i see

[winter cliff]

oh ty

[winter cliff]

ill keep it saved

for when i start pre caculus

[slate gulch]

Calculus deals with things over infinitely small intervals

[placid shadow]

Nice!

[placid shadow]

Yea

[slate gulch]

Like slope and area

[winter cliff]

is it hard

[slate gulch]

No

[winter cliff]

i heard its difficult to understand that start

but when u get more comfortable and know it more

[slate gulch]

No

[winter cliff]

it gets easier

[slate gulch]

It's not hard

[winter cliff]

i might have to learn the other stuff before i start calculus

[placid shadow]

it's hard for a lot of people that weren't good at algebra, i think

[zealous bronze]

calculus is easy if you have a good understanding of algebra and trigonometry. if you struggle with that then you will struggle with calculus

[winter cliff]

ic

[slate gulch]

Most of the work you do in calculus is just learning formulas and techniques for differentiation and integration. There's other stuff you do to like finding minimums and maximums of functions, optimizing things, etc. But yeah, this all involves a good understanding of algebra and trig, and if you don't know that then you're going to struggle.

[placid shadow]

College algebra is just trigonometry and precalculus

[slate gulch]

Yep

[winter cliff]

0.0

[placid shadow]

It has limits, etc

[slate gulch]

Well, I think

I've never taken college algebra

[zealous bronze]

i tutor some people in calculus and 90% of the time they get something wrong because of a mistake in their non-calculus work

[placid shadow]

in the US it's just trigonometry and precalculus

[slate gulch]

Yeah, the actual calculus is easy, lol

[winter cliff]

yo pebble

[slate gulch]

Yo

[magic python]

Me when antiderivatives aren't guaranteed to be elementary even if the original function is:

[slate gulch]

sin(sinx)

Always the example I look to for that...

[winter cliff]

im learning alg 1 rn i wanna learn something else should i start with geometry first or algebra 2

[magic python]

I love sin(x²) as that seems to be the main example people give from what I've seen

As well as the general gaussian iirc

[slate gulch]

Yep

e^-x^2

[winter cliff]

^ @slate gulch

[slate gulch]

Uhhh

I don't really think it matters

[winter cliff]

o ok

[slate gulch]

I did Algebra 2 and then Geometry, but most kids do Geometry then Algebra 2

I think probably you could do Geometry first, that would probably be good since Geometry introduces a lot of important things for all math

[placid shadow]

i just finished alg 1 now im doing geometry

[slate gulch]

Yeah

[magic python]

Kids these days don't to Euclidean geometry, what has the world come to where we don't force our children to do compass and straightedge constructions?

[winter cliff]

well i started algebra 2 already

imma finish that ig

[bitter prawn]

GUYS what are some beginner friendly self learning course

[winter cliff]

ill do geometry next

[placid shadow]

Khan Academy is really good!

[bitter prawn]

Do they have stuff related to quantum physics?

[slate gulch]

Lol. I remember doing this in my math class, and I remember doing it in a mechanical engineering class as well

[placid shadow]

XD

[winter cliff]

LOL

[placid shadow]

i'm not sure. They have physics for sure though

[magic python]

Wait it's still taught in math these days?

[slate gulch]

For me it was

[magic python]

Damn 🥀

[slate gulch]

But I went through an advanced math and science program soo

[placid shadow]

@magic python Can i send you a friend request? Because you're really cool

[magic python]

Sure! You seem cool too :3

[zealous bronze]

theres no point in learning quantum physics before classical physics

[placid shadow]

is that AP?

[slate gulch]

No

[placid shadow]

Yayyy!!! thanks!!!

[placid shadow]

ooo

[slate gulch]

It was an entire program at my school for math, science, and technology

[bitter prawn]

no i did do classical and i did math up till calc 3 im js tryna expand and i was js wondering if they had quantum physics

[slate gulch]

I'm still in it actually. I'm doing AP Physics and AP Chemistry right now

[placid shadow]

Awesome!!

[placid shadow]

Are you enjoying them?

[zealous bronze]

are you in university?

[placid shadow]

i really love chemistry and physics

[bitter prawn]

about to be im going to university next year

12th

[placid shadow]

wait lemme check

[slate gulch]

I enjoy physics more than chemistry, but yea

I just did my mechanics final exam

I got a 5

[bitter prawn]

this is facts chem boring

[slate gulch]

yep

[bitter prawn]

i got a 4 on my ap chem test tho

[placid shadow]

i dont think they have it unfortunately

[bitter prawn]

ahh okay but i really appreciate u tho

[winter cliff]

thats good

[zealous bronze]

if you really want to self study quantum mechanics before uni i would start with an introductory textbook, Ballentine's is pretty good

[winter cliff]

cant people cheat on APs if they take it online?

[slate gulch]

I have to think a lot more for physics than chemistry

[zealous bronze]

but once you go to college you can take an actual class in it of course

[bitter prawn]

okay okayy ill keep in mind ty man

[bitter prawn]

yea i js wna get a base lwk thast why

[placid shadow]

YW! they have physics 2 though, which is college physics.
Also, there's a website called openstax and it has this, is this what you want to learn?

https://openstax.org/books/college-physics-2e/pages/29-introduction-to-quantum-physics

[slate gulch]

Quantum physics is weird

[bitter prawn]

Whoaaa tysm i really really appreciate u

[slate gulch]

The double slit experiment especially

Just all of it is weird

[placid shadow]

You're most welcome

[placid shadow]

yea

[magic python]

:3

[placid shadow]

the lambda sign always reminded me of half life 2

i knew about lambda from that before any math or physics

[slate gulch]

In physics we use that as the linear mass density

[placid shadow]

https://tenor.com/view/half-life-gordon-freeman-half-life-2-hl2-lambda-gif-8962483776809262439

[placid shadow]

in chemistry it's half life?

[slate gulch]

Can be

[magic python]

Whenever I see lambda in math I'm like "why the hell is lambda here, this ain't lambda calculus"

[slate gulch]

Well

Wavelength of a photon actually

[placid shadow]

xd

[placid shadow]

is lambda calc used in python

[placid shadow]

in chemistry?

[slate gulch]

yep

$c=\lambda\nu$

[fathom swallow]

pebble

[placid shadow]

ooo

[slate gulch]

I think that's right?

something like that

[magic python]

Not explicitly but I'm pretty sure you can still use it iirc

[slate gulch]

speed of light is the frequency times wave length

[placid shadow]

like this?

[placid shadow]

i see

[slate gulch]

yea

[slate gulch]

That uses plank's constant though

[placid shadow]

heisenberg from physics reminds me of heisenberg from breaking bad

[magic python]

What if the solution to the collatz conjecture lies withing the singularity of a blackhole

[slate gulch]

What if? Prove it!

[placid shadow]

i suppose that's because quantum physics studies the submicroscopic?

[slate gulch]

yes

I was just saying, that's formula communicates something different than what I was saying

[magic python]

I mean, I have something relating to the conjecture that I have proved

[slate gulch]

Main formulas we use in chem are $c=\lambda\nu$ and $E=h\nu$

[fathom swallow]

pebble

[placid shadow]

ah

[zealous bronze]

what is it

[placid shadow]

my sisters took lambda in chemistry

a month ago

[winter cliff]

why is MIT top 1 uni

well

one of the best

[magic python]

It's based on the sequences the numbers take before getting to the 4,2,1 loop, I don't have it typed in LaTeX rn tho

[placid shadow]

well these universities constantly publish the most groundbreaking newest stuff right?

[zealous bronze]

what about them

like what did you prove

[slate gulch]

Nobody has proved it lol

[winter cliff]

true

[zealous bronze]

no he said "i have something related that I proved"

[slate gulch]

Oh, lol

[placid shadow]

and i bet (im just guessing) they're probably some of the most funded, most cooperated with with other unis, etc

[magic python]

Well, it isn't really something to be proved, it's a formula that was proved, and it basically allows me to find numbers that take a certain amount of time to get to 1 for the first time

A number of the form (2^n)m+1 goes to (3^floor(n/2))(2^(n mod 2))m+1 in exactly 3floor(n/2) applications of the piecewise function 3n+1 for odd integers and n/2 for even integers, where n and m are both positive integers

So if one of these goes to one, they both do

This is insanely easy to prove directly

[slate gulch]

Interesting

[magic python]

I have another for (2^(n+f_1(c))m+c but that requires introducing a sum (for f_1(c)) and a function that just complicates it more

[slate gulch]

The collatz conjecture asks whether all numbers will converge at 4 2 1, right?

[magic python]

All positive integers, yes

[slate gulch]

yea

And the rules are if it's even divide by 2, if it's odd, 3n + 1 it?

[magic python]

Yes

[slate gulch]

So the question is, can you pick a number such that an infinite recursion of 3n + 1 diverges from 4 2 1

Well

Actually no, because it could be even at some point in that

But it's an infinite recursion of that piecewise function

[magic python]

Yeah, we have checked up to 2×10^21 atleast last time I checked

[slate gulch]

Yeah

[magic python]

There are two types of counterexamples, a new loop, or a branch off to infinity

[slate gulch]

What I notice is that, any power of 2 is going to lead to a staight chain of dividing by 2 until you get to 4 2 1, and if a number is off of that set of power of 2s, it will require 3n + 1 to get to be a power of 2.

[magic python]

Personally, I feel like this conjecture would get proven (assuming it is true) by having too many requirements that a counterexample must follow, meaning that there won't be any, this seems like the most feasible way due to how it works

As it is easy to show that the smallest counterexample cannot be of the form 2n, 4n+1, or 32n+3, as all of these decrease (to n, 3n+1, and 9n+1 respectively)

[slate gulch]

Yeah

[magic python]

I technically have a formula to generate these however it's clunky and i would need to weed out duplicates such as say, if 64n+5 decreased, it would be useless bc 4n+1 already encompasses it

[slate gulch]

yep

[magic python]

Oh wait, wanna know the other 2 I have for it? They use bigger powers of 2 but are still able to be taken into account

[slate gulch]

Sure

[magic python]

2048n+7 goes to 243n+1 and 1024+11 goes to 81n+1

Iirc I used these 5 things to conclude that any given positive integer has atleast a 76% chance to NOT be the smallest number to go into any given new loop, or any given branch to infinity

[slate gulch]

It's definitely an interesting problem

I'm just not sure how I would feel putting much effort into it since it seems kind of useless, lol

I'd much rather just do physics

[magic python]

I messed with it because I was bored tbh

[slate gulch]

yep

I've done it too

[magic python]

I've had experience with generalizing stuff, my other two things are the "rule of 24" for prime numbers, and a formula for the n-th term in a constant recursive sequence, although I can't really remember that one and it used horrid notation, all of which are almost trivial to prove

[slate gulch]

Yeah

I remember, I think for my precalc class I got a summer homework packet which was like 5 or something pages long. I remember I did it all in my spanish class because I was bored, and one there was like a geometric series, and I hadn't ever learned that yet, so I just figured out the formula for it and used that to solve it.

[magic python]

I think I have the prime number one although the formula may be slightly wrong as I don't have the sheet on me, one sec

$\prod_{i=1}^{n}(p^2-i^2) \equiv 0 \bmod 8\prod_{j=1}^{n}(2j+1)$

For all primes p>2n+1

However this is basically just a worse version of trial division

[fathom swallow]

Definitely human

[magic python]

I think this is the one without the error

[slate gulch]

Oh, that's interesting

[magic python]

And this just comes from the first product being (n-a)(n-a+1)...(n-1)(n+1)...(n+a-1)(n+a)

[slate gulch]

I didn't even know that lol

[magic python]

And using n being prime, we can see what this product must be divisible by

Have you ever just messed around with something in math and found a unique result before?

[slate gulch]

yeah

all the time, lol

[magic python]

Ooo

[slate gulch]

Anyway, I'm gonna get to bed, it's getting late for me

Cya

[magic python]

Kk cya

[fresh comet]

[versed jungle]

why is ts an emoji lmao

[brave coral]

I don’t wanna study

[granite hound]

Then don't! It's Saturday

No studying on Saturday

[warm lance]

,ti _notabot

[fathom swallow]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[granite hound]

Uh it's a bit past midnight here

So technically it's Sunday

[warm lance]

isee

[granite hound]

,ti

[fathom swallow]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[brave hemlock]

Not the actual theory of lambda calculus, that's purely theoretical. Python isn't Haskell.
That said there is the following syntax:

lambda x: 2 * x```
(In this case to define a doubling function)

[brave epoch]

H

[brave epoch]

Hello

[tropic pivot]

hello Mr diamond.

[past wedge]

yo has anyone read the handmaid's tale (the book)

[gilded yew]

no but im about to fail differential equations

[polar temple]

Doesn't matter if you don't want to

Do it anyway

[dry needle]

Keep doing practice questions

[gilded yew]

it feels like i dont understand anything

i have been doing integrals and derivarives since i started college and can do them fine

but i dont understand what im doing

i dont have an actualy understanding of the math only memorize the steps

[polar temple]

Probably

[gilded yew]

if i did this would all be significantly easier

[polar temple]

I feel like differential equations is particularly difficult at first

But you get better at it with time

[polar temple]

When you look at the answer to the question, try to understand where it came from

which parts of the question did you have to look at to define this variable and so on

it's worded questions, right?

[gilded yew]

if u mean questions where its a word problem and you apply the topic to it no

its mostly pure equations and it asks you to find an answer

[polar temple]

oh

give an example

preferably a question you'd struggle on

[gilded yew]

i cant upload images here ill type
A homogeneous​ second-order linear differential​ equation, two functions y 1 and y 2​, and a pair of initial conditions are given. First verify that y 1 and y 2 are solutions of the differential equation. Then find a particular solution of the form y equals c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y'' - 9y = 0, y1 = e^(3x), y2 = e^(-3x), y(0) = 0, y'(0) = 2
Why is the function y1 = e^(3x) a solution to the differential​ equation? Select the correct choice below and fill in the answer box to complete your choice.
A) The function y1 =e^(3x) is a solution because when the function and its second​ derivative, y1'' = [answer goes here] are substituted into the equation, the result is a true statement.
B) The funciton y1 = e^(3x) is a solution becasue when the funciton and its indefinite integral, [answer goes here] are substituted into the equation, the result is a true statement

[placid shadow]

@rustic ridge i used to love soccer but because i was so bad at it (i panicked whenever it was thrown remotely in my direction) my teammates always kicked me off >.<

[rustic ridge]

FR omghhh like

Soccer is such a pain

[placid shadow]

Yea

[rustic ridge]

My classmates are really good at that

Worst part

[placid shadow]

i talked here because i didn't wanna clog up the math discussion with that because it was an anecdote from my real life and not math related

[rustic ridge]

SO THEY KICK REALLY HARD. imagine that reaching your ankles

[placid shadow]

wth

[rustic ridge]

Yeah it's alright :D

[placid shadow]

it's just a game

[rustic ridge]

FR..

[placid shadow]

sometimes the soccer ball hit my face

and my head

it hurt

xd

[rustic ridge]

In my previous school they all bullied me and aimed for me chest / head

[placid shadow]

idk why these people are normal outside of soccer but then when we play soccer they just turn into animals xd

[rustic ridge]

Are you alright?

[placid shadow]

Yea i hope so

[rustic ridge]

FR ☹️

[placid shadow]

What the actual

[rustic ridge]

A soccer ball to the head can be dangerous :(

[placid shadow]

please tell me you moved schools

[rustic ridge]

I did !!

[placid shadow]

Yayyy

[placid shadow]

i have a thick skull

[rustic ridge]

That's actually so good@

[placid shadow]

actually i hit my head in the shower when i was 8, i got a really big bruise

slipped and broke my skull

but i didnt pass out

[rustic ridge]

NOOOOO :(

[rustic ridge]

Are you alright now?

[neat lintel]

I hit my head on a toilet cause I passed out one time

[placid shadow]

well i'm smart i think so maybe i turned out ok

[rustic ridge]

WHAT are you doing alright?

[neat lintel]

Yeah I’m fine now

[placid shadow]

:(( 🫂

[neat lintel]

I used to just pass out when I got up sometimes

[placid shadow]

did you get an xray and someone evaluate you

[neat lintel]

nah

[rustic ridge]

How does that even happen? Low iron?

[neat lintel]

I just got better eventually so

[neat lintel]

no clue lmao

[placid shadow]

i cried and my sister in another room heard me and they gave me an ice pack

i was in iraq

[polar temple]

could you send an image in dm instead?

[rustic ridge]

Maybe you got up too fast. Really, take your time. Take it slow.

[placid shadow]

🙁

[polar temple]

i hate reading math on text

[rustic ridge]

I hope you recovered

[placid shadow]

ty

[rustic ridge]

That must've been traumatic

[placid shadow]

i still have a dent in the same spot

[rustic ridge]

It's okay, I'm happy your okay now

[placid shadow]

Yea! literally every single time since then that i've ever been in the shower i've never forgotten it and i make sure to not do what caused it (i was so stupid)

i make sure my footing is sturdy now

[rustic ridge]

It's alright, I also was stupid. I only cared about roblox back then cuz I DIDNR KNOW IT WAS DANGER INFESTED

[rustic ridge]

I just wanted to make pizzas back then

[placid shadow]

same bro... it ruined my innocense

[placid shadow]

one of the first games i played on roblox

[rustic ridge]

luckily I wasn't a victim. Though I was threathened

[placid shadow]

someone did stuff to me

[rustic ridge]

Roblox says the "danger" isn't a problem but an opportunity. Roblox is so fcaking dangerous.

[placid shadow]

you were still a victim

[placid shadow]

corporations care about harming the world

[rustic ridge]

This is true :[

[placid shadow]

but there are sooo many good people out there that counteract this

and people that do good acts

[rustic ridge]

So sad schlep got banned.

[rustic ridge]

SUE!!!

[placid shadow]

unfortunate, i havent heard of him

[rustic ridge]

I hope you're doing better.

[placid shadow]

can i send u a friend request

[rustic ridge]

sure

[placid shadow]

Okay!

[placid shadow]

Thank you! ❤️

it dint go through :<

[rustic ridge]

Awh :(

I could friend you

[rustic ridge]

Oh wait I know why

I turned it off, scammers kept driending me

[placid shadow]

it says u have to ad me

[placid shadow]

Yikes

[rustic ridge]

I do not want to be friends with tech support guy that accidently reported me

[placid shadow]

Yea

[rose pewter]

this manifold stuff seems somewhat simpler then real analysis

atleast compared to the rudin book

[dusky oyster]

Should negative natural numbers be formalized as an ordered set of two natural number?

Such that negative number N = (a,b)

[rugged orchid]

Yea there is a construction of ℤ as (equivalences classes of) pairs in ℕ, where (a,b) stands for a-b, there's prolly something abt that online that explains it better

[dusky oyster]

If you think about it the only numbers that exists in the natural world are natural numbers as the cardinality of sets.

Therefore, the only natural construction of negative numbers are using natural numbers and addition.

Definition of subtraction: b + (a − b) = a
Definition of numbers as ordered pair (a, b).

This would otherwise, create an interesting perspective for imaginary and complex numbers.

How does one formalize complex numbers under the formulation of negative natural numbers?

[quasi raven]

Hey

[rugged orchid]

Basically in set theory, there is a whole chain of constructions like this, going ℕ ℤ ℚ ℝ ℂ where you build the next one out of equivalence classes of something made of the previous one. For ℚ it's very similar and you can probably guess, for ℝ and ℂ it is better documented online (cauchy sequences / dedekind cuts depending on your religion and algebraic tricks for ℂ i.e closure or simply ℝ[i] and showing it's closed)

[quasi raven]

What the def of
f(a) define
Lim x-)a f(x) exists
f(a)=lim x-)a f(x)