help-27

[restive river]

• its first derivatives can't be defined at origin since the vector function is discontinuous there

[wicked rover]

this theorem is an "if then". just because the assumptions dont hold for an electric field doesnt mean its not conservative

if x is a dog then x is an animal. but if x isnt a dog that doesnt necessarily mean x isnt an animal

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[exotic saffron]

how do I do this

it’s so hard

no clear piece of paper no nothing

<@&286206848099549185>

help

my brain hurts

[restive river]

could you zoom in on the graph

[exotic saffron]

is that good

the squares r so small bro

[devout snow]

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[rugged jewel]

How is the point (0,1,2) found?

I randomly picked x=0 and solved for y and z. Hopefully this is the correct way?

[dapper gazelle]

Are you looking for points on this line?

[dapper gazelle]

If so all points on the line must satisfy the equation

So if you artificially add more constraints you can get a unique point from the line

[rugged jewel]

Yes

[rugged jewel]

🧐

What do you mean exactly

[dapper gazelle]

$z$ is already constrained to a plane.

[woven radish]

草w

[dapper gazelle]

So you just added $x=0$ to find a specific point, given that a relationship between $x$ and $y$ exists

[woven radish]

草w

[rugged jewel]

Yes

My first thought was correct, thanks

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[stiff coral]

Hello

[stiff coral]

I’m confused on what it’s asking for the values

[worthy tundra]

I'm trying to model a tangent around a wave and idk how

I got close tho

[lusty sapphire]

!help

[devout snow]

Please read #❓how-to-get-help

[lusty sapphire]

If the edge length is given, find the volume

If the volume is given, find the edge length

[stiff coral]

How would you find it?

Could u give me a idea with the first one

[lusty sapphire]

The object is a cube

Do you know how to find volume of a cube?

[stiff coral]

No I haven’t been shown that yet

But I kinda have a idea it’s just the power of the 3rd?

[lusty sapphire]

If the side length is $s$, then the volume is $V=s^3$

[woven radish]

SWR

[stiff coral]

Ah

Alright I got it thanks for the help

.close

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[real galleon]

Hello guys,
Context: I'm working on a 3D project where I have a camera moving arround the Origin (0, 0, 0) and always directed to it
I need to set 2 points in a way they always seems to be at the same place on my screen, wherever my camera is
A bit like If i just marked a big dot on my screen and make my camera moving (the dot wont move because it's marked on the screen and not in the 3D space)

[magic thicket]

just take lines starting from your camera (maybe rotating as well if the camera can rotate). Make sure they're in the field of view. Pick a point on this line.
Basically using the fact that a pixel corresponds to a direction

[real galleon]

The camera will move arround a sphere and will rotate to always be in the direction of the Origin
How do you take lines (I'm struggling to understand lines equation in 3D) (ps: sorry for my english i'm french 🙂 )

[magic thicket]

alors on peut aussi parler français en fait

si tu considère que tu as un repère local associé à ta caméra c'est simple

[real galleon]

Incroyable ^^
Du coup pour être plus précis sur mon problème, j'ai une caméra qui pourra se déplacer sur n'importe qu'elle point de mon espace 3D mais sera toujours orienté en direction de mon Origin
Ce que je cherche à faire c'est avoir un point qui semble complètement immobile sur mon écran malgré les déplacements et rotation de ma caméra

J'ai cru voir que j'allais avoir besoin d'équation de droites dans l'espace

[magic thicket]

sinon vu que la caméra peut tourner en place il faut prendre ça en compte d'une manière ou d'une autre

[real galleon]

Tourner en place c'est à dire ?

[magic thicket]

tu peux regarder le même point depuis le même endroit en mettant ta tête à l'horizontale

et à ce moment là l'image a tourné de 90°

[real galleon]

Je suis d'accord

Les seules informations que j'ai aussi sont les coordonnées de ma camera et les coordonées initiale du point dans l'espace

[magic thicket]

t'a pas d'orientation de la caméra ?

elle peut pas tourner ?

[real galleon]

Elle peut tourner mais elle s'oriente toute seule vers (0,0,0) je regarde si j'ai un moyen de récupérer ca 🤔

[magic thicket]

car si il y a possibilités comme ça il faut le prendre en compte et selon l'implémentation des rotations, ça se complique

[magic thicket]

où alors tu programme juste séparément le truc pour s'afficher à telle position sur l'écran plutôt que de poser un truc dans l'espace non ?

[real galleon]

J'ai pas accès à la rotation de ma caméra mais elle peut se calculer avec ses coordonées non ? 🤔

[real galleon]

J'ai vraiment besoin que ce point reste dans l'espace pour lui appliqué d'autres choses après 😦

[magic thicket]

ok

[magic thicket]

si tu sais comment elle tourne oui

mais sinon à une position correspond tout un cercle d'orientations secondaires

[magic thicket]

toutes les directions possibles de l'axe menton-nez si tu veux

[real galleon]

Oui, pas sur de tout comprendre mon niveau de math est resté coincé à la première et encore ^^
Si tu veux je peux te montrer avec un partage d'écran la problématique ?

[magic thicket]

je vois le truc, mais sans connaître l'implémentation c'est compliqué de savoir qu'est ce qui ferait une bonne solution

car visiblement la rotation de ta caméra se fait implicitement, or on veut la connaître

[real galleon]

Oui exactement

[magic thicket]

d'où l'intérêt d'un repère local qui donnerait l'orientation

[real galleon]

Mais pourrait on déterminer sa rotation connaissant sa position et sa direction qui est tout simplement son point (C) vers O => CO (vecteur)

[magic thicket]

rotation et déplacement sont à priori indépendants

idéalement elle tourne pas

mais selon comment c'est codé...

t'utilise un logiciel type unity ou unreal engine je suppose ?

[real galleon]

Enfaite j'ai des spheres qui sont affiché et je peux tourner en "orbite" autour de celles si (pour que mes spheres restent toujours dans mon écran)

J'utilise ThreeJs et D3js

[magic thicket]

donc tu code tout ça toi même en javascript ?

[real galleon]

J'aurais préféré xD

Oui tout à la main 😄

[magic thicket]

donc tu t'est pas encore posé la question de l'orientation de la caméra

tu sais pas où sera le haut de l'écran

[real galleon]

Si la caméra est toujours toujours orienté vers l'origin

[magic thicket]

on est en 3D

il y a 2 angles en sphérique

[magic thicket]

juste parce que tu définis ce qui est au milieu ne dit pas si tel point voisin sera dans la moitié haute ou la moitié basse de l'écran

[real galleon]

C'est à dire je ne comprends pas le problème que j'ai du coup

[magic thicket]

donc c'est gênant pour fixer un point sur l'écran si on sait même pas où il va apparaître

[real galleon]

Je sais ou il apparait initialement

Est ce que tu peux vocal sinon je peux te montrer visuellement ce que j'ai déjà

[magic thicket]

vocal ça va être un peu dur

[real galleon]

On est pas obligé de parler c'est plus pour t'apporter un support visuel

[magic thicket]

je suppose que tu as un objet caméra dans l'un de ces modules

[real galleon]

Oui

[magic thicket]

quand tu le fais pointer vers l'origine, tu peux pas définir une orientation secondaire de la même manière ?

[real galleon]

Qu'est ce que l'on appelle une orientation secondaire ? 🤔

[magic thicket]

je programme pas des jeux moi

mais logiquement t'a 2 informations d'orientations pour ta caméra

[magic thicket]

ça devrait être documenté quelque part lol

[real galleon]

Elle est géré automatiquement par D3js
Je sais que sur mon écran (le centre aussi bien en x que y est toujours l'origin)

[magic thicket]

et dans quelle direction est (1, 0, 0) par exemple ?

vers le haut, le bas, la droite, la gauche ? Si tu veux fixer un point sur l'axe des x positifs de ton écran il faut savoir quelle direction c'est en 3D

[real galleon]

Dans ce cas là mon point serait à droit là

[magic thicket]

peu importe l'emplacement de la caméra ?

[real galleon]

Du coup non si ma caméra n'est plus en (0,0,1) mais en (0,0,-1) la ca sera inversé et du coup ca serait à gauche

[magic thicket]

en si elle est en (-1, 0, 0) il est au centre

donc il est pas du tout toujours à droite

si il est détaché de l'origine

[real galleon]

Là il serait toujours à droite pour moi 🤔

[magic thicket]

t'es même pas cohérent

[real galleon]

Je suis perdu là

Reprenons, on va dire que ma camera se déplace à distance fixe (on rajoutera le problème de zoom plus tard) du centre O
Elle peux donc avoir pour coordonnées n'importe qu'elle point sur la sphere de rayon (distance Caméra à O)
Elle sera toujours orienté de sorte que le point central de mon écran sera O
et j'ai besoin d'afficher un point sur mon écran de manière fixe sur un plan 2D on pourrait dire (0, 90% de mon écran)

[magic thicket]

tu veux afficher quoi d'ailleurs ?

[real galleon]

une sphère

[magic thicket]

est-ce que tu sais dans quelle direction réelle est le haut de l'écran ? i.e. le point (0, 1) (si (0, 0) est le centre) correspond à quelle direction depuis l'origine ? Car il faut savoir comment la caméra est tournée

savoir si la ligne (x, 0) de l'écran correspond à l'axe (t, 0, 0), (0, t, 0), (0, 0, t), (0, t, 2t) ou autre

en gros c'est ça le problème

[magic thicket]

une fois que tu sais ça c'est facile de placer un point à (0.45, 0) sur l'écran

[real galleon]

Je dois comprendre ce que c'est une direction réelle (pour moi une direction c'est un vecteur)

[magic thicket]

le vecteur (1, 0, 0) définit l'axe (x, 0, 0) par exemple

évidemment

oh wait

à chaque point correspond tout une ligne

[real galleon]

Oui je suis d'accord avec ca ^^

[magic thicket]

donc une ligne de l'écran correspond à une partie de plan

j'avais oublié

la question reste, en soit, on peut dire
la partie du plan associé à (x, 0) (l'axe horizontal de l'écran), à une profondeur telle que l'origine soit dedans, correspond alors à quelle direction ?

ce qui est pas forcément facile à savoir selon l'implémentation en fait

t'a pas un lien vers la documentation de ta caméra, si elle est bien ?

[real galleon]

Je vais te trouver ca attends

J'ai ca : https://github.com/d3/d3/blob/main/API.md

[magic thicket]

elle est où la caméra la dedans

[real galleon]

Tiens voilà j'ai un truc vraiment comme ca en therme de caméra : https://vasturiano.github.io/3d-force-graph/example/controls-orbit/

J'ai pas l'impression que ca soit vraiment documenté enfaite je peux juste set un type de graph: ForceGraph3D({controlType: "orbit"})

[magic thicket]

visiblement la caméra est toujours tournée de la même manière si elle est dans la même position

donc il suffit de connaître cette orientation

[real galleon]

okay si tu veux je peux générer des coordonnées avec ma caméra et des points ?

ca peut nous permettre de déterminer son orientation

[magic thicket]

i.e. prendre un point de l'espace et trouver sa position sur l'écran ?

idéalement c'est quand même accessible quelque part

[real galleon]

De mémoire D3js utilise la caméra de Threejs en fond jje vais fouiller dans le code source

Je devrais avoir sa direction par défaut

Il existe une fonction

Il semblerait que ca soit ca par défaut : -0 -0 -1

[magic thicket]

qui est la direction de quoi ?

[real galleon]

la camera en direction de O

Ca serait sa direction

[magic thicket]

elle commence en (0, 0, 1) ?

[real galleon]

oui

[magic thicket]

tu viens donc de remarquer qu'elle pointe vers l'origine

ce qui serait pratique serait l'orientation qui permet de dire "quand je regarde depuis le vert clair, le rouge est en haut à droite"

plutôt qu'en bas par exemple

comme ça on peut déterminer que la droite c'est en gros le bleu clair

[devout snow]

@real galleon Has your question been resolved?

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[devout snow]

Please don't occupy multiple help channels.

[pseudo basin]

.close

[devout snow]

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[barren pike]

Someone make this make sense

[devout snow]

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[spare hawk]

is this the same thing as assuming that p and q are coprimes?

[sick fulcrum]

well that's the definition of coprime

[spare hawk]

ahh tank you ^^' then i will continue with, whole values are refering to integers in this case right?

[sick fulcrum]

yeah

[spare hawk]

ahh thank you ^^

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[restive river]

Given are two parallelograms ABCD and AECF with common diagonal
diagonal AC, where E and F lie inside the parallelogram ABCD.
Show:
The circumcircles of the triangles AEB, BFC, CED and DFA have a point
in common.

[restive river]

tried with coordinates but is there a smarter way

[eternal marsh]

do you have a diagramm of this ?

[restive river]

think you can help?

[eternal marsh]

yes, i will think of this let me some times

[restive river]

ok

[devout snow]

@trim sleet Has your question been resolved?

[sick fulcrum]

.close

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[sick fulcrum]

user alr left the server

[eternal marsh]

oh ok

[devout snow]

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[restive river]

I'm doing inverse trig functions can someone help me to do 47 please I dont get it

[restive river]

Like what angle is sin of 4/5

[soft shore]

let arcsin(4/5) be equal to x

[restive river]

Ok

[soft shore]

arcsin(4/5) = x
sin(arcsin(4/5) = sin(x)
4/5 = sin(x), right?

@restive river

the question is asking you to find cos(arcsin(4/5))

which is cos(x) now

and then you can solve :)

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@restive river Has your question been resolved?

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[winged forum]

.reopen

hi

[winter brook]

sup

[winged forum]

i need help on a question that is related to percentages

the q : K invests 400 for 3 years at 2.5% simple interest per year

work out : the amount of interest in 3 years

so im wondering

are you supposed to multiply 2.5 * 3

[pseudo basin]

if you mean to ask whether you can just answer 7.5 and be right, no, you cannot.

but if you mean to ask whether that could be an intermediate step in the calculation, then yes.

[winged forum]

thats what im asking

so basically : 7.5/100 * 400?

[feral agate]

yes

[winged forum]

then what abt : the amount of interest earned in 1 year

[pseudo basin]

do the same calculation but with your time frame set to 1 year instead of 3 years.

[winged forum]

so 2.5 * 1?

that's basically the same isn't it?

[pseudo basin]

no, the interest earned in 1 year isn't $2.5 as you just apparently said.

[winged forum]

it's different?

in what way?

wait

is it just 2.5/100 * 400

@pseudo basin

that equals 10

[pseudo basin]

was trying to get you to be more precise with your wording instead of just throwing numbers around.

[winged forum]

ohh

[pseudo basin]

yes, the interest earned in 1 year is (2.5/100) * 400

[winged forum]

that helps actually ty

the next q : the total amount her investment is worth at the end of 3 years

does this mean you should add?

[pseudo basin]

and again imprecision strikes.

"does this mean you should add?" add what?

add your age to the weight of president biden?

[winged forum]

add the amount of 1 year and 3 years

for the same question

[pseudo basin]

no

... "the amount of 1 year and 3 years" is still a bit too imprecise.

[winged forum]

oh

i mean add 30 and 10

[pseudo basin]

you add the principal to the interest.

[pseudo basin]

again, no.

by your logic, the $400 investment is going to shrink to a mere $40 after all this. somehow.

[woven radish]

Ann

[winged forum]

do you mean that 400 is the principal and 30 is the interest?

or

2.5 is the interest?

[pseudo basin]

400 is the principal, i.e. the amount originally invested

30 is the interest, i.e. the amount you gain on the investment

2.5**%** is the interest rate, i.e. the percentage of your principal which is added to the account every year as interest

[winged forum]

i ended up with 430

that should be correct?

[pseudo basin]

yes...

[winged forum]

alr

tyvm

.close

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[gusty vale]

hello need help with letter b below

[gusty vale]

By the way, above, $\mathscr T_1$ is a topology on the set of real numbers. To answer b, can I use the arbitrary intersection of $U_n = (-1/n, 1/n)$ where $n \geq 2$ is an integer?

[woven radish]

strikersigmaV

[devout snow]

@gusty vale Has your question been resolved?

[gusty vale]

<@&286206848099549185>

[gloomy spear]

Yea

@gusty vale

[gusty vale]

How do you explain why the arbitrary intersection of $U_n$ is not in $\mathscr T_1$? I'm asking to confirm my guess.

[woven radish]

strikersigmaV

[devout snow]

@gusty vale Has your question been resolved?

[vast rain]

are you told that T_1 is a topology or is it just that set given

[gusty vale]

Its a given in the problem.

[vast rain]

I guess yeah, because otherwise b would be trivial

[gusty vale]

@vast rain am I right in assuming I can use any open interval like $U_n$ above? since they are open sets but their arbitrary intersection is not open: ${0}$. so I'm assuming that since its a topology, it can only have open sets

[woven radish]

strikersigmaV

[vast rain]

the topology defines the open sets

you can't use the standard topology's definition of open sets

I don't believe that (-1/n, 1/n) is open in that topology anyway, since all sets in that topology have to be of the form (a, infinity)

and yeah I can see how you would prove that it's a topology

probably the trick here is to use arbitrary intersections to construct an interval of the form [b, infinity) and then it's simple to argue it's not in the topology

[vast rain]

stop giving false information smh

[gusty vale]

How about $U_n=(-1/n,\infty)$?

[woven radish]

strikersigmaV

[vast rain]

yeah seems like that would work

in general, any sequence of numbers that converges from below up to some number

[gloomy spear]

I tried to help

[vast rain]

bruh you gave blatantly false information about something you didn't know about

how is that more helpful than just rolling a die and giving an answer based on the number of it

even chatgpt is more helpful than that

[gusty vale]

since the arbitrary intersection of this new $U_n$ is still ${0}$. does the same logic apply?

[woven radish]

strikersigmaV

[vast rain]

it's not {0}

it's [0, infinity)

[gusty vale]

oh sorry my bad yeah you're right its this one

[gusty vale]

anyway thanks again @vast rain

.close

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[rich barn]

Can someone help me with this question?

[rich barn]

can some one please help me with this question?
specifically the second part
"What if Max wants to know..."

the answer is this but I dont understand
the formula that I have for geometric distribution has (1-p)^x-1(p)
this one is missing the p
what happened to it?

[devout snow]

@rich barn Has your question been resolved?

[supple knot]

yes that's the density

[rich barn]

why is it that the more trials i do the probability goes down?

[supple knot]

You have to know what expression equals P(?)

what is ?

[rich barn]

(1-P)^x-1(P)

[supple knot]

what answer are you looking for

[supple knot]

$P(?) = (1-p)^{x-1} \cdot p$

[woven radish]

riemann

[supple knot]

What's the left hand side

[rich barn]

x=6?

[supple knot]

Specifically $P(X=6)$

[woven radish]

riemann

[supple knot]

So here $x=6$

[woven radish]

riemann

[supple knot]

But again, you're not asked to compute $P(X=6)$. what are you asked to compute?

[woven radish]

riemann

[rich barn]

X>-6

X is at least 6

[supple knot]

You're making the same mistake as before of applying the formulas you memorized without appropriately interpreting them

Interpreting the formulas in probability is very important

[supple knot]

Yes.

[rich barn]

but why is it that as X bound increase the probability goes down

should it not be the other way

[supple knot]

what does "X bound increase" mean

[rich barn]

for example should not at least 6 be smaller then at least 7

[supple knot]

why should it

use math to justify

[rich barn]

because chances of not happening at 6 should be lower then chances of it happening at 7

because the more you try the more you are likely to encouter a defective light bulb

intelectually i dont unerstand it

[supple knot]

you're not backing up anything you're saying with math

"should be" isn't justification

[rich barn]

i dont know how to use that TeXit it

[supple knot]

you don't need to write latex to type math

P(X=6) is perfectly fine

[rich barn]

i dont know how explain in mathematically

say ur trying to win the lottery

[supple knot]

stop

if you can't explain it in this simple problem

[rich barn]

the more you play the more chances you will encouter the ticket

[supple knot]

you're not gonna be able to explain it in a more complicated lottery instance

[rich barn]

ok then what should i explain?

[supple knot]

.

[supple knot]

in the context of your problem

[rich barn]

so my chances of encountering a defective light bulb is 0.04

the first time i try the probability is 0.04

the second time i try it is 0.0384

the third time in try it is 0.0368

i feel like the probability should be going up

because the more light bulbs i test the more chances of me finding the defective light bulb

im sorry i just dont understand

[supple knot]

math doesn't work around your feelings

[rich barn]

can u please help me inteectually understand

[supple knot]

Do you agree that $P(X=6)$ and $P(X=7)$ are two disjoint events?

[woven radish]

riemann

[supple knot]

errrr independent events

,w plot 0.96^x for x>0

[woven radish]

Results provided by WolframAlpha

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

Requested by riemann#2529

[rich barn]

which one is which?

[rich barn]

yes they are independent

[rich barn]

yes they are independent

[rich barn]

hello?

[supple knot]

Convince yourself that P(X > 5) = P(X=6) + P(X>6)

Or 6 and 7

Then compare which one's larger

[rich barn]

yes that makes sense

wait what

[rich barn]

could you explain why the mre light bulbs you test the less ur odds become of finding a defective light bulb

[supple knot]

.

[rich barn]

i donnt understand

[supple knot]

does this make sense

[rich barn]

probability of finding a def on 5 or bigger is proability of finding a defect on 6 or bigger then sixth?]

yes that makes sesne

[supple knot]

apply it to your problem

[supple knot]

Compare which one's bigger $P(X \ge 6), P(X \ge 7)$

[woven radish]

riemann

[rich barn]

X>7

[supple knot]

use this relation

[supple knot]

whenever you answer, you should ask yourself if you're using math or just emotion

if you're using emotion, that's not an answer

[rich barn]

emotions? what are those

[supple knot]

things like this

[supple knot]

and this

[rich barn]

.close

[devout snow]

Channel closed

Closed by @rich barn

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dreamy cedar]

how do you get the 1 from 1- 1/21?

[wanton pecan]

It's a probability axiom. The probability of the compliment of an event occurring is 1 - the probability of the event

[dreamy cedar]

when would you know when to do this?

how*

[wanton pecan]

If the result is not odd, it has to be even. Thus the event of it being odd and even are complimentary

[devout snow]

@dreamy cedar Has your question been resolved?

Channel closed

Closed by @dreamy cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

i think

[restive river]

i might be confused about how bijections work on sets

sorry functions

im used to funcitons being defined

by like

for instance defined on f(x) = x^3

but not using just non empty sets without some equation

[vast rain]

wdym

can you give an example of the function

[restive river]

where x y are non empty sets

like this just makes no sense to me

[vast rain]

so the f: X -> Y means that the domain is X and the codomain is Y

f is some function, but they don't tell you what it is, i.e. what it does to every input in X

[neon aspen]

The domain and codomain are part of the defintion of the function

What it does to each element in the domain is also part of the definition

[neon aspen]

Here f : R -> R

[dusty wigeon]

You do $f$ first, then $g$. $f$ is not a surjection means that there exists some $y \in Y$ such that there is no $x \in X$ such that $f(x) =y $. $g$ is not an injection means that $g(y_1 ) = g(y_2)$ for some $y_1 \neq y_2$.

[woven radish]

DavidL1450

[sick fulcrum]

chatgpt user?

[inland seal]

doesn't seem like chatgpt

[sick fulcrum]

fair

[neon aspen]

Chath gpt does not render math text like that

[inland seal]

yeah lmao

dont just assume

[sick fulcrum]

thats why I asked

-.-

[vast rain]

it does write LaTeX

[restive river]

uh okay sorry where do i star

[vast rain]

but it doesn't put the dollar signs

[sick fulcrum]

weirdly enough maybe you can try a diagram

[neon aspen]

It just seems like normal symbols you would use in text, not latex per se

[sick fulcrum]

I think it uses \( and \)

[neon aspen]

Like I haven't seen it use latex commands with backslashes

[sick fulcrum]

eh ive seen it use \boxed

[dusty wigeon]

Since $g$ is not an injection, $g(y_1) = g(y_2)$ means you must "lose information" when applying $g$. To make $g \circ f$ bijective, make $g$ lose information on elements that are outside the range of $f$.

[woven radish]

DavidL1450

[restive river]

huh

[vast rain]

I've seen it use \begin{align*} and \leq; it usually uses it if you give input in LaTeX

[restive river]

wait sorry can i ask about the question i asked

[vast rain]

yeah so david's hint is pretty applicable here

[neon aspen]

We should back track a little

[neon aspen]

Does the statement make sense now

[vast rain]

so you know that you can make X=Z and g circ f the identity, since you're asked for a bijection anyway

[restive river]

like idx?

[vast rain]

yes like id_X

so pick g and f such that this works but f is not surjective and g is not injective

[restive river]

my understanding of identities is rlly bad

[vast rain]

by identity I mean that $(g \circ f)(x) = x$, i.e. it spits the same thing out

[woven radish]

Saccharine

[warm fulcrum]

Just make, like, Y comically large, and X = Z = {1}

[vast rain]

well yeah, that's the idea

[restive river]

like in my notes

the teacher would denote it with like idA or whatever

[vast rain]

all that means is that it puts out the same thing it takes in

[restive river]

ohhhh

[warm fulcrum]

$id_{A} : A \to A$ is the function that maps every $x \in A$ to $x$, that is $id_{A}(x) = x$ for all $x \in A$

[woven radish]

Mikkel

[warm fulcrum]

It won't make my "id"'s fancy

[vast rain]

$\text{id}$

damn didn't work

[restive river]

so for it to not be a surjection or a bijection it needs to spit out an identity

[woven radish]

Saccharine

[vast rain]

no

[restive river]

im completely misunderstanding then

[warm fulcrum]

It's just that the identity-function is bijective, so it is an obvious choice for a function

For $g \circ f$

[woven radish]

Mikkel

[restive river]

what so g circ f = h(x)

because it will literally spew out the same thing

well

g circ f (x)

[warm fulcrum]

Are you allowed to choose the elements in X, Y and Z, or do you need to keep it somewhat arbitrary?

[restive river]

is the only thing they say

i think try to keep it arbitrary though

[neon aspen]

Most probably allowed to specify them

[upper schooner]

[I think you can pick the sets X, Y, Z to be as you want them to be]

[restive river]

okay

[upper schooner]

(unlike the other exercise, this is an "existence" exercise rather than a "for all" type one)

[neon aspen]

Do you get what an identity function is

And why it's bijective

[restive river]

yeah

if it outputs itself

then everything will have a unique output

for every unique input

[neon aspen]

Yes

[restive river]

surjectivity

and

injectivity

[neon aspen]

Try to imagine sets

[restive river]

sorry

that was injectivity

[neon aspen]

And an arrow between them

[restive river]

idk like x = {1, 2, 3}

[neon aspen]

Sure

[restive river]

so like x, y, z = {1, 2, 3}

[warm fulcrum]

Because if you are allowed to specify the elements chosen in X, Y and Z, you can just choose f : {1} -> {1, 2} defined with f(1) = 1, which is obviously not surjective, and g : {1, 2} -> {1}, defined by g(1) = 1, g(2) = 1 which is obviously not injective. Here you will get (g ∘ f) : {1} -> {1} such that (g ∘ f)(1) = 1, which is obviously bijective.

[neon aspen]

There's just an answer

[warm fulcrum]

I should really get out of the habit of writing "obviously" this much, when 50% of what I write is bull crap

[restive river]

that hurt my brain

can i ask more questions

[warm fulcrum]

No. Only 1 question per life time. Come again when you're reincarnated

[vast rain]

you write obviously when you don't have a proof for it and the hw assignment is due in 15 minutes

[restive river]

i want to be reincarnated

into a differnet major

[vast rain]

uh oh another business major coming up

[restive river]

no

wait

YES

YES

IM TRANSFERRING TO BUSINESS

LOLLL

[warm fulcrum]

Well... Obviously

[restive river]

HAHAHA

[warm fulcrum]

Bruh, I had one economics course, and I hated it

[restive river]

i wrote a proof but uh

its a little sus

uhh where did i go wrong

cries

[warm fulcrum]

https://hugelolcdn.com/i/216365.gif

Me when I see the square-y thing at the end of proofs

[restive river]

they force us

[upper schooner]

What does the set [n] represent? The integers from 1 to n, or?

[vast rain]

dopamine I believe in u

[warm fulcrum]

I don't

[vast rain]

obviously you can do it, and the obviously isn't because the assignment is due in 15 minutes

[restive river]

no

[warm fulcrum]

obviously

[restive river]

its due at 2 am

like thats the late deadline

[warm fulcrum]

It's 2 AM in 10 minutes for me

[vast rain]

it's ok I took the L on a lot of assignments in university

my math major friends made fun of me

but look I'm still breathing

[warm fulcrum]

Can you just like, choose not to do your assignments

[restive river]

set of natural numbers from 1 to n

but yeah i think my proof is like very wrong

did i even prove injectivity correctly

[upper schooner]

If this is where you proved it, not really

The aim of proving injectivity is that you assume that you have outputs being the same and show that you force the inputs to be the same

[warm fulcrum]

I don't know why you're making such a big deal out of it. You could just have said "The proof is trivial and left as an exercise for the grader", and it is practically proven already

[vast rain]

hey at least you got a function that worked

[upper schooner]

Whereas you’ve assumed the inputs are the same

[vast rain]

MY FAVOURITE PHRASE EXERCISE TO GRADER

[restive river]

uhh so i did it reversed?

did it in reverse

[upper schooner]

Yea, you (tried to) show that it was well defined (that is, each input has a unique output) whereas for injectivity you need to show that each output has a unique input basically

Still reading through it now though

I would say being well defined is trivial and left as an exercise to grader (sorry couldn’t resist!)

It’s not entirely clear to me how you’ve shown them to be equal

Let me check the next page you have for you now!

[neon aspen]

Do you know who is this

Seems familiar

[restive river]

cries cries

[warm fulcrum]

Nooooooo

I got a B in Linear Algebra 🥲🥲

[upper schooner]

Assuming case 2 here is that 1 is not in either of the sets X and Y?

But otherwise happy

[restive river]

https://math.stackexchange.com/questions/70243/bijections-from-a-to-b-where-a-is-the-set-of-subsets-of-n-that-have-e

...

[upper schooner]

And no, I'm uncultured lol

[neon aspen]

Isn't that above average

[neon aspen]

Np

[warm fulcrum]

Only by a little 😭😭

[upper schooner]

That's basically the injectivity and surjectivity bits that you need, from the top answer

[vast rain]

I got A+s and As my first two quarters and then it slid to A-s and B+s, and by the end of my degree

we were at C-

if you drew a line through it

[restive river]

whwat did u study

[vast rain]

I did computer science and statistics

a doublemajory thing except one was an online 10-week master's degree

[restive river]

is it {n} or {1} that i use

im suffering through cs

[warm fulcrum]

I want to get my master's 😭😭

[upper schooner]

You can use {1} too, the argument is almost identical

[restive river]

okay cool

[neon aspen]

Shouldn't you be graduate+ then

[vast rain]

idk the master's degree was a joke so probably not LOL

[warm fulcrum]

If it's in computer science, wouldn't it be graduate++

[restive river]

do you guys enjoy math

[upper schooner]

Well played, made me giggle

[vast rain]

some aspects

[restive river]

okay can i ask more questions

[vast rain]

other times it's very frustrating

but hang in there

there are very rewarding moments

[restive river]

IM NEVER LEAVING MY HOMEWORK FOR THE LAST MINUTE

dont worry

this is the first and last time

[vast rain]

and it's pretty cool that you can use math to read about really cool things elsewhere

[warm fulcrum]

Me when I accidentally complete a master's degree. Whoopsi

[restive river]

i have no clue how to approach this

[vast rain]

every day I'm more convinced it was a money grab from my university

[warm fulcrum]

Can't you accidentally solve the Riemann Hypothesis next time around

[upper schooner]

Of course the first step I would suggest is writing down definitions

[vast rain]

bro wtf are these questions

do you have a teacher who likes torture

[warm fulcrum]

I'm one of them cool kids that doesn't pay for tuition

[vast rain]

mine gave generous financial aid for the first 4 years, but those 10 weeks of online classes cost me $12000

like holy cow

all my internship money poof

[warm fulcrum]

[vast rain]

I took intro CS for my last quarter there and got a B 😎

[restive river]

my school

love torture

i actually want to die everyday that im here

like no cap

[warm fulcrum]

But like, think how sad mom will get if you die

[restive river]

i wont know

naw i chose this life

school is a menta l game

ill be okay

[vast rain]

hmm okay so for this problem perhaps it's easiest to simply construct the input for any possible output

[warm fulcrum]

School will be a tiny fraction of your life that you just have to pass

[restive river]

i tried

lol

[restive river]

maybe

loll

my attempt

cries

okokksdokoakosakd

asokdoafkgobgkdsz

[neon aspen]

Mind your language.

[warm fulcrum]

[restive river]

im trying to date a mathmajor so that i can get better at math

[warm fulcrum]

Math majors don't exist

They are a hoax

[restive river]

haha no

false

every math major loves poh shen loh

[warm fulcrum]

[neon aspen]

We don't fuck with people like that where I'm from.

[warm fulcrum]

[restive river]

i gotta fend for my survival

[vast rain]

I once dated someone who failed high school math, but she absolutely loved making me teach her random things about linear algebra

of course she never learned anything, but that was an interesting type of crazy

[restive river]

yjust eah IDK

im sufferijngefisjdfajewq

[warm fulcrum]

Just prove it by assumption that it's true

[restive river]

huh

[warm fulcrum]

"If we assume the statement to be true, it is obviously true. Therefore the statement is proven"

[upper schooner]

Think I'm happy here may want to justify the bottom line a bit, but good
[bottom line holds because f is injective]

[restive river]

okay what about the bottom

sorry the top

[vast rain]

probably should add in the brackets for sets yeah?

[restive river]

like for a1

[warm fulcrum]

What course is this for?

[restive river]

my funeral

[warm fulcrum]

Damn

Didn't get an invitation

I see how it is

🥲🥲

[upper schooner]

https://tenor.com/view/mati-bodoh-bangang-keranda-menari-gif-16794421

[vast rain]

you also need to somehow write a_1 = a_2

[warm fulcrum]

Maybe that could be a proof-strategy. State that it is true, say you have a proof for it, die before you can show it

Dopamine's Last Theorem

[restive river]

fuck my university

all this work is making me insane

[vast rain]

well you don't know that you weren't insane already

[restive river]

i guess i did attempt to date a mtha major

[restive river]

wait whats wrong with this

[vast rain]

like what do you mean by F(Y) = f^(-1)[a_1]

this isn't true in general yeah?

[restive river]

right..

[vast rain]

basically you need to show that f(a_1) = f(a_2) implies a_1 = a_2

[restive river]

yes for injectivity

[vast rain]

F takes in subsets of B, by the way

so maybe you could take F({f(a_1)}) and demonstrate that this produces a_1

[restive river]

uhhuhu'huhujbhn m,

confusion

[vast rain]

actually probably easier is to assume that f is not injective and then prove that F is not surjective

[restive river]

do i have to change the part i got right

💀

[vast rain]

you need to change your proof for ->

you have a lot of choices

pick whichever one is most intuitive

[restive river]

none

[vast rain]

okay how about I'll prove it this way:

assume that f is not injective and then prove that F is not surjective
and then you try to fix your proof maybe with some ideas from it

idk

[restive river]

i should take the L

[vast rain]

dopamine we can't be taking Ls so fast

[restive river]

i am ready to drop out

[vast rain]

LOL don't

I promise it gets slightly better

[restive river]

i should transfer schools

i need an easier out

[vast rain]

idk if that'll help

LOL

[restive river]

change to business

[vast rain]

pls we don't need more of those

[restive river]

i hate carnegie melon

[vast rain]

LOL it's not a bad school is it

[restive river]

wdym

bad for my health yes

[vast rain]

hmmm maybe you should take a lighter courseload and spend more time pondering things

math takes a little time to get used to

[restive river]

naw

this is standard track for cs

[vast rain]

oh if you're doing CS, then this + linear algebra is probably all the math you ever need to take

you could go into something that doesn't involve it

[restive river]

calc 1, 2, 3, 2 discrete math courses and lin alg

[vast rain]

also math gets more approachable as you gain experience in it

[restive river]

yes

im a math baby

its true

[vast rain]

meth baby

[restive river]

i just have no experience in this type of math

usu

uw

u

uwu

uwuwuwuwuw

[vast rain]

unfortunately this is used everywhere LOL

usually, this just amounts to writing out definitions

and then trying to say things about them

for example, going with the approach I said before, let's assume f is not injective and try to prove that F is not surjective

f not injective means that there exist a_1 and a_2 such that a_1 != a_2 and that f(a_1) = f(a_2)

let's call f(a_1) = f(a_2) = b

[restive river]

ok..

[vast rain]

Then, what's F({b})?

[restive river]

the inverse

[vast rain]

if we pick F({b}) = {a_1}, then F is not surjective, because we cannot find any input that will give {a_2} [to justify this "because," show that if F(x) = {a_2}, then x = {b}]

and the same argument if you pick F({b}) = {a_2}

basically big F cannot generate both {a_1} and {a_2} if you have this collision, so F cannot be surjective

now try it the other way: assume that F is surjective, and try to prove that f is injective

so say that f(a_1) = f(a_2) = b, and now try to show that a_1 = a_2

LOL your messages in the artificial intelligence server are absolute chaos

[restive river]

STOP

[vast rain]

is this your freshman year?

because I hate to be the party pooper, but uh second year gets MUCH HARDER LOL

[restive river]

STO-

I enjoy programmingokay

[upper schooner]

Programming

[vast rain]

yikes that statement just made you deserve all of your suffering

[restive river]

we are learning pre and post fix

i love c

< 3

[vast rain]

doubly so

[upper schooner]

Anyways, wanna try this out?

[restive river]

i want to drop

okay

yes

[vast rain]

okay I swear I'm not sociopathic and I actually have a lot of empathy for these people, but one of the funniest things to do when I was in university was look up when the assignments were due for the intro CS classes and then study near where the TAs were holding TA hours / help right before the deadline

and then just people watch

[restive river]

uh

its easier to leave programming to the last minute then math

because i just put the programming crack music on

and then i just draw the fuck out of my ipad

and solve the problem

most errors are almost always solved by print statements

debugging is good

[vast rain]

debug my AI code and I'll do your math homework

how about that

I've spent days begging chatgpt to help me

[restive river]

damn deep learning moment?

whatcha into

[vast rain]

im trying to make something recognize chessboards

but really just trying to better understand the related problems of VQA and captioning

[restive river]

Im trying to learn about rl and q learning

in highschool i was into a lot of comp vision shit

[vast rain]

so I took an efficientnet to digital chessboards and now im trying to get a Transformer to generate text from it

but the stupid thing is training to give garbage

[vast rain]

I used to know a lot about that, because one of my internships was doing random stuff with that

but it's all gone

just like most of the knowledge I got

[restive river]

damn wait chat gpt moment

whyd it use transitivity

[vast rain]

wait I swear I've seen this problem

someone else posted it didn't they

[restive river]

yeah bc it was me

okay id be suffering less

if i didnt procrastinate this

but i did

so its on me

[vast rain]

one direction is really easy

like you can show that if the subset relation holds, then f is an injection pretty easily

and then the other way was okay

oh yeah chatgpt actually gave a decent proof for it

[restive river]

NO STOP

[vast rain]

well the right ideas kinda hard to parse

the "for some x in S cap T" is kinda unjustified LOL

[restive river]

since f is an injection is that for two subsets of A say C and D is if f(C) = f(D) then C=D and f(S) intersect f(T) means some variable x is in f(S) and f(T) while f(S intersect T) means some variable y is in S and T

[vast rain]

is that even English

[restive river]

yes\

[vast rain]

SyntaxError: invalid syntax

[restive river]

this si transitivity

[vast rain]

chatgpt's argument is basically if you have an element f(x) in f[S] intersect f[T], then, you have f(x) = f(y) for some y in S and f(x) = f(z) for some z in T

but since f is injective, x = y = z

and therefore x is an element of S and an element of T

and therefore x is an element of S intersect T

and therefore f(x) is an element of f(S intersect T)

[restive river]

that mkes sense

[vast rain]

you don't actually need the x either

[restive river]

Yeah why did they do it transitivity way

[vast rain]

you could call it an element b in f[S] intersect f[T]

well it relies on transitivity

oh wait you don't

LOL

well

chatgpt is weird in a way I guess

[restive river]

I am actually okay at relations

Functions are just

[vast rain]

functions are just relations

[restive river]

Proving this question with transitivity is the equivalent of using a for loop in the range of 1 million instead of a while true

[vast rain]

sounds like something you'd do

[restive river]

I might be bad at this type of math but I’m not a dumbass

Can I just use transitifictu

[vast rain]

not sure what you mean; transitivity is just a little part of the proof

but no you need to use injectivity somewhere

[restive river]

no but can i just do it the transitive way

[vast rain]

what transitive way

[devout snow]

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[orchid tulip]

how do I prove that modular inverses are unique?

[orchid tulip]

What does unique even mean in this case? That given a(mod k), there is only one other integer (x) at most satisfying ax(mod k) = 1?

But with the example, 3(mod 5), the modular inverses could be 2, 7, 12, 17, etc.

So what does "unique" exactly mean?

[stone stump]

mod 5 those are all the same

only one of the numbers between 0 and n-1 is a multiplicative inverse for k

if b and c are two inverses of a, then b=b1=b(ac) = (ba)c=1c=c

[orchid tulip]

but doesn't unique imply equivalence rather than congruence?

2 and 7 aren't the same number, they are congruent

[stone stump]

congruency is an equivalence relation

or what do you mean

[orchid tulip]

I'm just getting confused with the terminology "unique" used

I thought unique implies that there is only one distinct number (x) that satisfies the ax(mod k)=1

[stone stump]

a unique equivalence class

/congruency class

[orchid tulip]

Ok so unique in this case really means the set of values that share the same remainder class modulo k as x

The set of all congruent values is "unique"

[stone stump]

when doing modulo you are always doing everything with equivalence classes

the equivalence classes themselves are the elements, the numbers you write down are just representants you choose

just like with fractions you dont make any distinction between 1/2 and 2/4

if I said there is a unique multiplicative inverse of 2 in Q then it is clear that I mean the equivalence class of 1/2 and I dont care about 2/4 or other ways to write it

[orchid tulip]

Ok thank you!

That clears it up a lot

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[heady gull]

can someone explain this too me i dont know where to start

[lusty sapphire]

Do you know the formula for arc length of a curve?

[heady gull]

yeah i do

[lusty sapphire]

Cool

Do you have any guesses on how you can use it here?

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[red helm]

Hello

[red helm]

This is my matrix

-1/2 + i is an eigenvalue, can someone please confirm that the vector (0,1) isn’t an eigenvector associated to that eigenvalue ?

My teacher ended up with that eigenvector in class but it can’t be right, i found this :

Vecteur propre = eigenvector

[lusty sapphire]

(0, 1) is not an eigenvector

You can prove by inspection

[red helm]

Thought as much

Wtf was he on that day, got every exercise wrong

[red helm]

What’s inspection ?

[lusty sapphire]

Inspection is just putting in the values and seeing whether they are right or wrong

[red helm]

Oh yes ofc should have done that, smart

[lusty sapphire]

Let me clean up those fractions

[red helm]

Welp his whole correction of that exercise is wrong in that case

[lusty sapphire]

As someone who was wrong a lot yesterday, I know the feeling

[red helm]

Happens to the best of us

We suck just as much haha, should have corrected him in class

Could you try and find the solution to X’ = AX ?

[lusty sapphire]

yes

Redemption arc

[red helm]

It’s super long tho, might take you a while

[red helm]

Hahaha love you bro

[lusty sapphire]

Way easier than yesterday's since now there is no degenerate eigenvalue nonsense

[red helm]

Yep the matrix is diagonal

Still 3 matrix multiplications though, so easy to make one tiny mistake

Ended up finding this

[lusty sapphire]

That's exactly what I got

[red helm]

Lets goooo 🤝

Thx man ❤️

I have another question

[lusty sapphire]

happy to help

[red helm]

You probably won’t be able to help but you never know

[lusty sapphire]

[red helm]

I’m not sure about the English terminology 😦

Does stable point mean anything to you ?

[lusty sapphire]

Of that last problem?

[red helm]

A solution to the differential system that doesn’t depend on time

That’s the definition ( in my words granted haha )

[lusty sapphire]

Damn I've done stable points before...

I wish I wrote down the problem or book or chapter or anything!

Okay

[red helm]

Hahahab😂

[lusty sapphire]

Here's a guess

A stable point means the solution does not change with time

[lusty sapphire]

So derivative with time must be 0

[red helm]

Yes that’s exactly it

[lusty sapphire]

So take derivative of solution and find the t that makes the matrix 0

[red helm]

I have a question regarding the fixed point but this might all be a little too distant for you 😔

In my lesson, an affirmation is made :

(I’ll try my best to translate)

The stability of a fixed/stable point for the non homogeneous equation is equivalent to the stability of (0,0) for the homogeneous equation

I have no idea why this is true

Can’t figure it out

[lusty sapphire]

Good question

I remember learning that too

But do not remember the reasoning

[lusty sapphire]

My only book for differential equations does not go into stability, so I must have used a different book in school.

[red helm]

No problem this question is a little specific haha, was kind of a stretch

This whole paragraph is taken out of context too, you don’t even have the system we’re looking at

My bad

It’s fine i’ll think about it some more and try and figure it out, I’m fairly sure it has something to do with the general solution including Xe in it

Yep can’t quite figure it out

Anyway i’ll free up the room for other people, thx for the help yet again @lusty sapphire you’re a legend ❤️❤️

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[chrome creek]

how are these equal?

[magic pine]

is the +2 included in the product?

[chrome creek]

no

the +2 is out

[magic pine]

what is p_i

[chrome creek]

p_i is 2^{2^{i}}

[magic pine]

so $\prod_{i=0}^nP_i = 2^{2^n}\prod_{i=0}^{n-1}P_i$

tex is dead

[chrome creek]

i guess so

i think

[magic pine]

is this 2^2^n included in the product

[chrome creek]

no

it's not

incl. in the product

mhm

[magic pine]

i don't think they're equal then

[chrome creek]

i see

thanks ig

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[magic pine]

might have spoke too soon

i'll mess with it and lyk if i come up with something

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[mild basin]

Is this supposed to say "f o g (x)"?

[lusty sapphire]

[mild basin]

or "f o g" is the same thing as f(g(x)), the x is implied?

[lusty sapphire]

It's implied

[mild basin]

hmmm, OK

[lusty sapphire]

f and g are called the functions

[mild basin]

I have never seen it written like that, normally it's with (x)

[lusty sapphire]

So is f o g and g o f

[magic pine]

the name of the function is f o g, so you'd find the domain of f o g, not f o g (x)

[lusty sapphire]

f(x) and g(x) are how the functions f and g are defined

[magic pine]

f(x) is a number, f is a function

[mild basin]

hmmm OK

so if I write f(g(x)) = sqrt(3x^2)

that's fine? or it should be written f o g = sqrt(3x^2)

[magic pine]

either f(g(x)) or (f o g)(x)

[mild basin]

OK

Just for practice, but looks good?