help-23

[lean otter]

here they arent saying make 1 team

theyre saying make 2

[hidden parcel]

Yes but its the same concept

Make 2 playlists from 100 songs (where each song is distinct) is the same as making 1 playlist with 15 songs and 1 playlist with 85 songs

[lean otter]

in the playlist analogy you dont even care abour the remaining songs but here you care abour the remaining kids

[hidden parcel]

By breaking the first playlist into 15 songs, you've already created the second one

[fickle yoke]

in this question our sample space is to assign into 2 teams of 5

[lean otter]

Yes i agree but like, you still want to see the possible outcomes of that arrangement

[fickle yoke]

@lean otter

[lean otter]

yea

[hidden parcel]

The outcomes of the 2nd arrangement dont matter?

[lean otter]

they do

[fickle yoke]

so when u assign 5 kids for the team A the rest will be assigned for team B u understand?

[lean otter]

yeah i get that but we want the combinations for how possibly both groups can look like

so i count both

[fickle yoke]

look

if u assign group A, B will be grouped itself

like

think we have ten kids

if we put five of them in team A

where the other 5 go? to team B

so we dont need to count them

u understand?

[lean otter]

yea

now count all the possibilities for those outcomes

[fickle yoke]

its C(10,5)

[lean otter]

uhm

• 2?

😭

[fickle yoke]

second question?

[lean otter]

no

like times 2

[fickle yoke]

no

why times 2?

[lean otter]

Think about it, i dont see how this could be right because say they told you to put the kids into 1 group of 5 you’d literally do what you just did

and i dont imagine them saying to put them in 2 groups now would be the same

the same answer you know

[fickle yoke]

look brother after reading 5 months about combinatorics analysis dont say im wrong ik what im saying

look

u choose

[queen ingot]

we can prove it with a small example

put 4 kids into 2 teams of 2

you will get C(4, 2)

[lean otter]

i didnt say you are wrong im telling you what im thinking

[fickle yoke]

ik bro its just that if u have 2 groups when u choose for one u dont need to count the other rest it would be overcounting because we already assigned 5

[fickle yoke]

leon look

u choose 5 out of ten people for team A ok?

C(10,5)

the rest 5 for the team B which is C(5,5) = 1

now u get it?

@lean otter bro

[lean otter]

im thinking

i think i get it?

[fickle yoke]

i hope so

[queen ingot]

i think this is exactly what nCr is designed to do in the first place

[fickle yoke]

bro let us not confuse leon

lemme see what he says'

[lean otter]

so its like

10 kids

{1,2,3,4,5} , {6,7,8,9,10}-> one possibly

where (6,7,8,9,10) was already implied?

[fickle yoke]

bro why u ordered them

look

[queen ingot]

the teams are sets

[fickle yoke]

we have 2 teams

lets name ten people

1,2,3,4,5,6,7,8,9,10

[lean otter]

Ok

[hidden parcel]

leon i believe in u

[fickle yoke]

first team can have 1,3,5,7,9

[hidden parcel]

u got this

[fickle yoke]

or

1,2,3,4,5

or

[lean otter]

thanks bro

[fickle yoke]

3,4,5,6,7

[lean otter]

yea

[fickle yoke]

so there are C(10,5) you know what C() is?

[lean otter]

combination

k to 1 mapping

[fickle yoke]

we are choosing 5 random people from 10 people

[lean otter]

It takes a permutation and maps it’s elements to a single set for each duplicated one

[fickle yoke]

now that we chose for team A we want to choose for team B

we already chose 5 people

for team A

[lean otter]

Yes

the rest are already grouped

is that what you mean

[fickle yoke]

5 rest and we want to choose 5 for team B

[fickle yoke]

yes

[fickle yoke]

out of 5 people that remained choosing 5 is C(5,5) = 1

[lean otter]

okay that makes sense

no i get it now

[fickle yoke]

So the answer is C(10,5)*C(5,5) = C(10,5)

[lean otter]

i don’t think the C(5,5) is really part of this

its just like you said picking 5 kids already leaves another 5

the thing is I misunderstood what they wanted me to count

turns out they want you to count like both arrangements as 1

[fickle yoke]

exactly im just saying it for u to understand

[lean otter]

so you split the kids into the 2 groups thats 1 outcome

you split them again that’s another outcomes

the 2 groups next to one another is 1 whole outcome

[lean otter]

yes thank you bro

[fickle yoke]

ofc bro

[lean otter]

@hidden parcel @queen ingot thank you guys

[fickle yoke]

any other question>

?

[lean otter]

can we do part b

so theyre asking what are the chances alex and jose are in the same team

[fickle yoke]

for part b think we fix alex in one group

[queen ingot]

ye that's why the other person was talking about ordered pairs ({}, {}) two groups next to each other

[lean otter]

oooh yeah that makes sense lol

i mean now i see it I ignored that earlier

because even when i did {(),()} I knowledged 2 groups (although i did it wrong) but i didnt count them properly i shouldve counted them once

but anyway

[lean otter]

why

I thought of fixing both

or something

[fickle yoke]

no

[lean otter]

because they want both in one group

and that would be an event E ⊆ sample set

[fickle yoke]

look bro

think of it this way

alex is in some group

either A or B

we want to see the possibility that jose be with alex

[lean otter]

okay

[fickle yoke]

the whole sample space is that we put jose in one of the 10 places

the event E is we put jose with alex

[lean otter]

yeah

so { jose, alex } x { 8 kids } x {7} x {6} x {5} ?

[fickle yoke]

so if we fix alex in one group, the group that has alex in it have 4 possibilities for jose to be there

think of 10 boxes

we group 5 box together and other five together

we put alex in one of the boxes

the group that contains Alex in it we want it to contain jose too

[lean otter]

i dont get why were fixing him

[fickle yoke]

we have 4 boxes left to put jose in

[lean otter]

you mean like

you mean youre treating them both as one slot?

[fickle yoke]

because alex is already in somewhere u agree?

[lean otter]

theyre both somewhere

but we wanna narrow it down to where they are in one group

right

[fickle yoke]

they both can be anywhere thats the whole possibility

[lean otter]

yes

[fickle yoke]

we fix one of them

either alex or jose

[lean otter]

Why

[queen ingot]

i think both approaches work

i got the same answer two ways

[lean otter]

i see

whats up with the fixing way tho

i dont get it

What i do is i treat them both as one slot

[queen ingot]

vijan you'll need 10! in the denominator right?

[lean otter]

I thought we were looking at 1 group

which is 5

[fickle yoke]

i mean u can fix both too

[fickle yoke]

hm no, why?

[queen ingot]

10 * 4 * 8! / 10!

[fickle yoke]

the answer is 4/9

think about it

we assigned alex somewhere, 4 remain that we choose jose, the whole places where jose can go is 9

[lean otter]

again i dont get why we assign alex somewhere

[fickle yoke]

explain a bit more bro

[lean otter]

like i dont get it

[hidden parcel]

if alex is the first one to be picked it doesnt matter which teams he picks

all that matters is that jose is on the same team

this is what i meant w/my law of total probability approach earlier

P(Alex & Jose are on the same team) = P(Alex is on Team b)P(alex&jose | jose is on team b) + P(alex is on team a)P(alex&jose|jose is on team a)

but idk if youve learned conditional

prob

[fickle yoke]

bro u making it hard for them with conditioning😭 i mean thats literally what we doing but ye

[hidden parcel]

im just giving a diff approach it might make sense

if it doesnt leon js ignore it

[lean otter]

I don’t understand

[queen ingot]

you can put both of them on the same team

it leads to the same answer

[lean otter]

I thought thats what you’re supposed to do

[fickle yoke]

yes

[queen ingot]

i think so too because of part A, the denominator should be C(10, 5)

[lean otter]

because you literally want them on the same team

[hidden parcel]

is ur confusion that you think the answer should be (10 * 9)/(5 * 4)?

[queen ingot]

who are you asking?

[hidden parcel]

leon

[fickle yoke]

if u do that approach it'd be C(8,3)/C(10,5)

[queen ingot]

you need a factor of 2 but yeah

[fickle yoke]

which is same as 4/9

[hidden parcel]

i just want to know what he thinks it might be so we can correct that instead of just trying to replace his understanding

[lean otter]

im just asking about the arrangement

[lean otter]

.

thats what I thought initially

but also that * 2

[hidden parcel]

its not necessarily that youre fixing a person, but in order for them both to be on the same team you need one of them to be on a team to begin with

[lean otter]

you need both on the team tho

[fickle yoke]

leon think u fixed both ok?

[hidden parcel]

yes

[queen ingot]

{jose, alex, ?, ?, ?} {? ? ? ? ?} count these possibilities
then multiply by 2

[fickle yoke]

why multiply by 2

[queen ingot]

because they can also be on the second team

the teams are distinct

[fickle yoke]

we already chose for second team

C(8,3)

[queen ingot]

calculate it

[hidden parcel]

alex and jose can also be on the second team

this counts for them just being on the first team

[fickle yoke]

nooooo

bro

thats overcounting

[lean otter]

i don’t understand

its a set of 5 kids

[queen ingot]

two sets of five kids

[lean otter]

{ jose, alex } x { 8 kids } x {7} x {6} x {5}

= ( 2 · 8 · 7 · 6 · 5 ) * 2

right or wrong

[queen ingot]

are those meant to be cartesian products?

idk what that means

[fickle yoke]

ok yes i think

hm

[lean otter]

yes

they are

[queen ingot]

why are we doing 5-tuples?

the teams are unordered

i don't think you meant a cartesian product

but idk what you're trying to say

[lean otter]

2 · ( P(8, 3) / 3! ) · 2! = 2 C(8,3) · 2! = 4 C(8,3)

@queen ingot

[fickle yoke]

over 4!?

??

[lean otter]

because it duplicates

[fickle yoke]

ah

@queen ingot bro is cooked

[lean otter]

bruh

Why am i cooked

[fickle yoke]

can u think this way for a sec

u fix 2 people why because u need them to be in 1 team right?

[lean otter]

yes

thats what I did

{ alex, jose }

fixed

[fickle yoke]

so when u fix u should assign the 3 remaining ppl

for team that they are fixed in

for example think alex and jose are in team A

we should assign the 3 people for that team from the 8 people

the rest will be choosen themselves for team B

so its C(8,3)

[lean otter]

@fickle yoke

rookie mistake

I accidentally added an extra guy

is that right

[fickle yoke]

u added 2! randomly

[lean otter]

because alex and jose can sit in 2! Different orders

next to each other

[queen ingot]

their order on the team doesn't matter

[fickle yoke]

no brooo its not permutation

[queen ingot]

the teams are unordered

[lean otter]

oh true

oops

[fickle yoke]

its a team order doesnt matter

[lean otter]

yrah yeah

so 2 C(8,3)

[fickle yoke]

yeah over C(10,5) bc we already know the sample space

im done bro i got tired

[lean otter]

2 C(8,3) / C(10,5)

yesssssssirrrrrr

thanks yall

@fickle yoke @queen ingot @hidden parcel I appreciate the help alot

should i take this opportunity to do the last part 🤣

[fickle yoke]

allahu akbar

[queen ingot]

idk do you feel like you need a break?

[lean otter]

i have a final soon …

Final one then ill go 😴 inshaAllah

[lean otter]

always

[fickle yoke]

inshallah brotha

so

here

u want to assign 5 girls

[lean otter]

Yeah

[fickle yoke]

so fix all 5 there is only 1 way

[lean otter]

thats P(5,5)/5!

maybe

[fickle yoke]

for both A and B so 2 * 1 then the whole prob = 2/C(10,5)

leon how old are u?

[lean otter]

wait

[lean otter]

i dont wanna say here

[fickle yoke]

ok

[lean otter]

but probably younger than you

[fickle yoke]

im 16 anyway

[lean otter]

oh

[fickle yoke]

but yeah

[lean otter]

Bro no im older LOL

mashaAllah you know alot

[fickle yoke]

reading for olympiads

[lean otter]

thats humbling ngl

[fickle yoke]

dw bro u good just practice a lot

[lean otter]

yes inshaAllah

im new to counting

so

[fickle yoke]

have u ever took a combinactoric analysis course before>

?

[lean otter]

mo

no

this class is discrete math

[fickle yoke]

idk any good book for that

[fickle yoke]

ahhhh now i see

[lean otter]

Yea

[fickle yoke]

well

u need combis a lot

[lean otter]

true

alright

so now

[fickle yoke]

did u understand the question?

[lean otter]

{ 5 girls } x {4} x {3} x {2} x {1}

/ 5!

[fickle yoke]

just assign 5 girls

[lean otter]

Theres 1 way for each team

[fickle yoke]

ye

u got it bro gg

[lean otter]

thanks man, wait one last thing

i saw you multiplied by 2

to count for both teams

[fickle yoke]

1+1 i meant

[lean otter]

but here we didnt do that

oh

wait i don’t understand

[lean otter]

did you mean to count for 2 teams

[fickle yoke]

ye

[fickle yoke]

we did count for 2 teams lol

[lean otter]

the 2 here doesnt come from counting for both teams though

[fickle yoke]

ye

[lean otter]

it comes from the product rule

[fickle yoke]

look its different

[queen ingot]

i forgot the 2 on part C 😭

[fickle yoke]

u assign 5 girls on team A

[lean otter]

okay

[fickle yoke]

5 boys go to team B so one way

1

now u assign 5 girls on team B

5 boys go to team A

1 again

1 + 1 = 2

[lean otter]

why didnt we apply the same logic on part B

for alex and jose

[fickle yoke]

Axe brother

im done

[lean otter]

we only counted their arrangement in 1 team

[queen ingot]

we did, alex and jose can either be on team A or on team B

that's where i got the factor of 2

[lean otter]

alright

[lean otter]

yes but did we count for that is what im asking

because we only arranged them in 1 team

[queen ingot]

i did, but i didn't understand your notation so i don't know if you got the factor of 2 the same way

[lean otter]

2 is from the product rule

{ jose, alex } x { 8 kids } x {7} x {6}

= 2 · 8 · 7 · 6

[queen ingot]

i still don't know what that means

[fickle yoke]

me too

[lean otter]

cartesian product

to put in 1 group

of 5

so divide that by 5!

[fickle yoke]

idk why u doing it with cartesian its just that u think of it in a hardway u would get in trouble solving harder questions like this

[lean otter]

Wait

[queen ingot]

why are there always so many different ways to count the same thing 😭

[lean otter]

No

that should be

im gonna crash out bro

what is this

[fickle yoke]

Why i hate combis bro

[lean otter]

What is going on dude

order doesnt matter

i forgot

[fickle yoke]

It doesnt

[lean otter]

{ jose , alex } x { 8 } x { 7 } x { 6 }

= 2 · (8 · 7 · 6 )/3!

= 2 C (8,3)

now thats 1 team

and the other team

[queen ingot]

there's no 2

[lean otter]

why not 2 · ( 2 · (8 · 7 · 6) /3!)

[fickle yoke]

Oh no u counted for both team rn literally

[lean otter]

to count for team B like we did with the girls

[lean otter]

how

i put them in a group of 5 only

They’re together in one team only

[queen ingot]

i have to go to bed

[lean otter]

goodnight bro thanks for the help

[lean otter]

?

[fickle yoke]

Idk bro my brain is not braining anymore

Idk how u doing cartesian rn

[lean otter]

Because thats how it is defined

[lean otter]

how did we not count for the second team 😭😴

im so done

ah man

BRPOO

<@&286206848099549185> help please

Hello

[low echo]

Still on this question?

[lean otter]

theres progress

but one confusion tho

[lean otter]

@low echo

is that right for part b

[low echo]

Is the answer not just 50%

Or am I wrong

[low echo]

I don't know what this is

[lean otter]

what

No it cant be

This is getting frustrating

im ngl

reposting for reference

part b

{ (jose , alex) } x { 8 } x { 7 } x { 6 }

= 1 · (8 · 7 · 6 )/3!

= C (8,3)

= 2 C(8,3) / (10,5)

now can someone tell me whats going on here

because either i did something wrong or we didn’t account for the second team

[low echo]

4 situations

Alex: g1, Jose: g1
Alex: g1, Jose: g2
Alex: g2, Jose: g1
Alex: g2, Jose: g2

2 situations in which they are in same group and 4 total

2÷4 = 0.5

[low echo]

When one person has gone into the group, the chances of whichever group the other guy goes in is still the same no?

[lean otter]

oh wait i was wrong what the hell

bro i put them together may times

nonno no

To cancel that I gotta do

i give up

[low echo]

With what

[lean otter]

i have no idea man

[lean otter]

part b

[low echo]

This a simple question

[lean otter]

bruh 😂

[low echo]

If a guy goes in a group

The chances of the other guy going

remain the sames

It's

[lean otter]

why is it “when a guy goes ina group”

[low echo]

group 1 or group 2

Nothing else

[lean otter]

i dont get the thought process

[low echo]

Like

There's 10 spots

You're thinking that

[limpid lodge]

WWouldn't It be 4/9..?

[low echo]

So you think when Alex goes in a group. The chances of that group go down to 4/9 and the other to 5/9 ?

[low echo]

Was about to ask him that

[lean otter]

wait am i even wrong

wait

[low echo]

That is irrelevant, I think, because the amount of space in the group doesn't matter.

[lean otter]

i have 0 clue whats going on man

[low echo]

You're overthinking it

[low echo]

Ignore that

[low echo]

.

[low echo]

!!!

[lean otter]

Waaaait

i figured it out

waiy wait

its { (alex, jose) } not { alex , jose }

[low echo]

What

[lean otter]

i cant 😂

[limpid lodge]

erm consider alex got into team A

[lean otter]

Why

[limpid lodge]

consconsider team B then

[lean otter]

why not both

[limpid lodge]

WWHAT

[lean otter]

why not both alex and jose together

[limpid lodge]

thts the probability we're trynna find

[lean otter]

Look at my thought process

{ (jose , alex) } x { 8 } x { 7 } x { 6 }

= 1 · (8 · 7 · 6 )/3!

= C (8,3)

Look

then to count for both teams

2 C(8,3)

then 2 C(8,2)/C(10,5)

[limpid lodge]

would u word it?

[lean otter]

= 4/9

[lean otter]

I wish i can just tele communicate

whats it called telekeniesis

whatever that is

okay so

[limpid lodge]

wait whats in the answer key

[lean otter]

its 4/9

[limpid lodge]

okayy

[lean otter]

@limpid lodge both alex and Jose being in the same team is a ⊆ of the sample space

so think of creating that proper subset

and I mean it makes sense cause youre talking about both of them being in them same team

i can’t continue im tired

@low echo thoughts?

[limpid lodge]

does thth acc simplify to 4/9?

[low echo]

Hmmmmmmmm

[lean otter]

yep

think of all scenarios where both are on the same team

[low echo]

So

[lean otter]

thats literally just

{ (jose , alex) } x { 8 } x { 7 } x { 6 }

[limpid lodge]

wait a sec whats the doubt

[low echo]

It's not half

Hmmmm

[lean otter]

it cant be half because were talking about 2 kids being in a team together, not 5

i mean intuitively it cant be half because its just 2 kids it can take alot of times for them to end up together

correct me if im wrong

[fickle yoke]

omg leon u didnt understand it yet?

[lean otter]

i did bro

Im explaining to them

[limpid lodge]

..?😭

[lean otter]

not anymore i guess

[limpid lodge]

wtaf is happening here?

[lean otter]

chillin

[low echo]

Person 1 goes to G1
(0.5 chance)
G1: 4 spots left
G2: 5 spots left
Chance for other guy to go into-
G1: 4/9 (together)
G2: 5/9 (not together)

It's the same thing if person 1 goes to G2 that is: 4/9 chance of being together, and 5/9 of not.

so:

Four situations:

(1/2)(4/9)
(1/2)(5/9)
(1/2)(4/9)
(1/2)(5/9)

So chance of being together

(1/2)(4/9) + (1/2)(4/9)
so 4/9

So

[fickle yoke]

u dont wanna know cherry

[low echo]

it is 4/9 if the chance changes

[low echo]

Yeah that makes sense

[fickle yoke]

are u using graph or smth to explain?

[limpid lodge]

vihan is such a genz name

[lean otter]

sorry i don’t understand this language i speak cartesian product

[low echo]

G mean group

[low echo]

What's cartesian product

[limpid lodge]

DO U HV A DOUBT???😭

[lean otter]

not so far

[fickle yoke]

it's an ancient name wdym and pls dont talk in here let them solve the question

[limpid lodge]

why is this help channel open then🥀

[limpid lodge]

huh its like shanaya🥀 yep ill shutup lawl

[lean otter]

Life theory

[fickle yoke]

im telling brotha to not think about it using cartesian product idk why he keep using it

[lean otter]

sorry i can’t

[low echo]

Which class are you in?

[lean otter]

my brain just adapted to it

[fickle yoke]

u cool mate

[lean otter]

discrete math

[fickle yoke]

WHYYYY

bro neveerrrr

[low echo]

Number?

[lean otter]

because you need it

[fickle yoke]

in combis use cartesian

[lean otter]

permutations and combinations literally come from cartesian product

and this problem used combination

[fickle yoke]

bro the way u think is like solving (1 + 5)^2 = (1+5)(1+5) = 1 + 2 * 5 + 25 instead of just saying 6^2

[lean otter]

LOL

But this is different though

[lean otter]

there is no number but it’s an undergraduate class

[low echo]

Alright

[limpid lodge]

WhWhere did cartesian product come frm

[lean otter]

you never get more humbled than when kids teach you math

[fickle yoke]

look when u solve with cartesian its like u doing an ordered problem because cartesian is like permutation but this problems are combis

[lean otter]

definition

[lean otter]

yes combination comes from permutation

[limpid lodge]

eh but u could js do it directly?

[lean otter]

idk how I raged mid studying the other day and didn’t pick up on the short cuts

[fickle yoke]

see u trying to solve a question from cartesian -> permutation -> combination when u can do combis straight

[lean otter]

i think thats what happened

[limpid lodge]

what r we trynna do here....solve it using Cartesian product..?

[fickle yoke]

exactly im telling him this

[lean otter]

thats a really good question

[fickle yoke]

he just wants to solve it but he only knows cartesian

he cant analys it using combis

[limpid lodge]

but u domt even need combinations

[lean otter]

you do

[limpid lodge]

just throw alex in one grp

[fickle yoke]

u can say alex in one group then jose go to the same group so 4/9

[limpid lodge]

4 favourable seats for jose and total 9 seats

[fickle yoke]

yeah but he doesnt understand why we should fix alex only so i told him try to fix both its the same thing

[lean otter]

idk what yall are saying

[limpid lodge]

ffix jose then (what)

[lean otter]

Jist fix them both to begin with

i dont get why youre putting one of them alone

[fickle yoke]

fixing both will cause C(8,3) ways to put other kids

it can be done in two ways bc of two groups so 2 * C(8,3)

now the whole ways we calculated is C(10,5)

[limpid lodge]

yeah could do tht too

but fixing one is js simpler

[fickle yoke]

but he doesnt understand why

[lean otter]

why does fixing one even make sense

[limpid lodge]

okay do u have any other method to begin with?

[fickle yoke]

because its the same thing u want to fix one and see in how many ways jose can sit with alex or whatever his name was

and it comes out to have 4 places to be with alex

from 9 remaining place

[limpid lodge]

it is jose. Its pronounced fancy tho.

[fickle yoke]

josè so french

[lean otter]

yes group tjem both

[limpid lodge]

then u would proceed liek this

what exactly doesn't make sense to u?

[fickle yoke]

i just told u the method

[lean otter]

how do you do this

[fickle yoke]

lemme cry lemme cry

[lean otter]

sorry bro

[fickle yoke]

bro if this server had vc

[lean otter]

im trying to be inclusive here and open minded and maybe step out of my cartesian product comfort zone

[fickle yoke]

i would have told u easier

[limpid lodge]

u could do private vc

[lean otter]

do you wanna be my tutor

[fickle yoke]

im younger than u brother

how

[limpid lodge]

depends on ur educational levels rather than age

[lean otter]

so?

[fickle yoke]

idk discrete math i just know some about graphs and combis and sets theorems

[limpid lodge]

whats discrete math

[lean otter]

a class I hate

[fickle yoke]

discrete numbers and stuff like that

discrete prob

graph theorem

sets theorem

[limpid lodge]

OOhhhhhhhhh

[fickle yoke]

number theory

[lean otter]

“Discrete mathematics is the study of mathematical structures that are fundamentally separate and distinct, such as integers and graphs. It provides the mathematical foundation for computer science and is used to solve problems in programming, algorithms, and cryptography. Key topics include logic, set theory, number theory, graph theory, and combinatorics”

[fickle yoke]

logic

[fickle yoke]

thanks

[lean otter]

youre welome

[fickle yoke]

so useful tbh

just dont get deep in it

[lean otter]

not that i want to

[fickle yoke]

just dont think a lot brother stay shallow, yk u can be a good mathematician only if u be lazy

find simple ways

dont go to deep

[limpid lodge]

ohohhh thts discrete math

[fickle yoke]

what grade are u in?

[limpid lodge]

11

[fickle yoke]

same

[limpid lodge]

cools

[fickle yoke]

i think discrete math is for uni

here in my country they teach in 12th grade

[limpid lodge]

UUhhh they teach it in 11th here

[fickle yoke]

ah

[limpid lodge]

i mean some of it

[fickle yoke]

no we have pre-calculus and probability and statistics and

hmm

geometry here

they teach logic a bit in probability

and set theory

[lean otter]

but you need to understand also right

[fickle yoke]

understand it the easy way not the hard way, think intuitivily rather than deep-math shit

[limpid lodge]

eh close this channchannel when ur done

[fickle yoke]

ye clos it

brother

u been here for 3 hours

[lean otter]

hahaha

Alright thank you for your help brother

[fickle yoke]

ofc bro inshallah

[lean otter]

God bless you

[fickle yoke]

u will be successful

[lean otter]

inshaAllah

[fickle yoke]

say amin

[lean otter]

you as well

ameen

[fickle yoke]

ameen

[lean otter]

i sent you a friend request

[fickle yoke]

accepted brother u can close this chat

if had any question

just ask

[lean otter]

may Allah reward you

alright i have nothing for now

talk to you insaAllah

thanks again,

assalamu alaykum

.close

[safe radish]

Channel closed

Closed by @wintry depot

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

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[stark ether]

3 lines show that a+b+c=0 for htem to intercept at exactly 1 point

[safe radish]

Please don't occupy multiple help channels.

[stark ether]

.

other one delayed closing i think

[fickle yoke]

make a coefficient matrix

for all lines to meet in a single point det(A) where A is the coeff matrix should be zero

[stark ether]

but i cant do that

the matrix is 3x2

det isnt defined

[fickle yoke]

it will be 3x3 wdym

[stark ether]

the variables are x,y

a,b,c are constants

so in reality its
a b
b c
c a

Ax= b where
b=
-c
-b
-a

[warm warren]

?

Its 3x3

[fickle yoke]

A = a b c ; b c a ; c a b and v = [x, y, 1] Av = 0

[stark ether]

x,y,1 though

1 isnt a variable

[warm warren]

$\begin{pmatrix}a&b&c\
b&c&a\
c&a&b\end{pmatrix}$

[flat frigate]

Annie Maqionde

[warm warren]

something like this

[fickle yoke]

doesnt matter

[stark ether]

the last column isnt coefficients of variables

[stark ether]

how does it not

[warm warren]

there are 3 equations

[fickle yoke]

we want det(A) = 0 to v exist

[stark ether]

and 2 variables

[stark ether]

why

thats not true

[fickle yoke]

bc v should be in null space of A

[stark ether]

you can hae infinite solutions

[fickle yoke]

yk what det(A) = 0 means?

[stark ether]

infinite solutions

you said for v to exist

it will be a line if det(A)=0

[warm warren]

The three lines will be concurrent if and only if $\begin{pmatrix}a&b&c\
b&c&a\
c&a&b\end{pmatrix} = 0$

[flat frigate]

Annie Maqionde

[fickle yoke]

look if det(A) = 0 it means columns are dependent

and dependence means all lines go through the same point

so if u compute det(A) and its equals to zero it means they go through same point and life is good but if it was not equal to zero means we have independent columns which means there is no two vector to go through same line

and it will span the whole space

idk if u understand or not

@stark ether

u understand? life is good?

[stark ether]

sorry i had to respond to some message i got

[stark ether]

but i dont understand how we can use a scalar inside the variable vector

like the det(A)=0

is for equations where each row of A is coefficients of a variable

[fickle yoke]

ahhh

look

we are in R^3

[stark ether]

yes

[fickle yoke]

if we only said v = (x,y) then the constants c a and b cannot be included in the matrix multiplication

this 1 here acts as a place holder for constants

have u read about augmented matrcies?

here we made an augmented variable vector

which means we added a 1 as a placeholder during multiplication

u will see of these a lot in linear algebra

[stark ether]

cant i just check by 2

[stark ether]

nah

but cant i check first 2 lines then second 2

[warm warren]

you could do tha but that'll be a much more cumbersome method

[safe radish]

@stark ether Has your question been resolved?

[stark ether]

but i dont get how you can have x,y,1

and consider it as a R^3 variable

[safe radish]

@stark ether Has your question been resolved?

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[north orbit]

how do i do g

[north orbit]

i don't understand this

these are the conditions on a,b

[open plume]

guys

this chatgpt groupchat is with my friends

please raid it and send random messages about brainrots

[thin bridge]

Please don't promote that stuff in this server.

[safe radish]

@north orbit Has your question been resolved?

[safe radish]

@north orbit Has your question been resolved?

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

[steep magnet]

How would I get the integral of 1/(2 + 3x)?

[steep magnet]

I dont want to know the exact steps, just what method would I use?

[fierce nimbus]

use u-sub

[steep magnet]

So the denom would be the u?

[fierce nimbus]

yup

[steep magnet]

Alright thanks!

❤️

.close

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[rustic chasm]

hi

[rustic chasm]

cud anyone help me with this problem? The chapter is abt artimetic and geometric sequences

[fallow cairn]

What have you tried so far?

[rustic chasm]

i have no idea how to solve it

at all

[fallow cairn]

Since we're working with sequences, a good place to start is to simply identify what our sequence is

Would anything here look like it has potential to be our sequence?

[safe radish]

@rustic chasm Has your question been resolved?

[rustic chasm]

So like it starts with 2 and decreases

Right

[fallow cairn]

I'd agree with that, yep

[rustic chasm]

One sec my moms calling brb

[fallow cairn]

Don't forgot to read ❌ to the bot's message here so the channel isn't closed!

[safe radish]

Channel closed

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[lean otter]

Calculating two weapon damages to decide which one is better at what point

Target info:

Health aka HP: 20
Info: one damage removes 1 hp

Armor points: 20
Armor toughness: 8
Info: armor reduces the damage you take, here are the formulas on how to calculate it https://minecraft.wiki/w/Armor#Damage_formulas
There is also a 64% damage reduction coming from the armors enchantment called protection, this is applied after the armor's damage reduction. more info: https://minecraft.wiki/w/Protection

Weapon info:

We have 2 weapons, both are a weapon called the mace, which increases your damage based on how many blocks you're falling:
A successful smash attack causes a mace to deal 4HP extra damage for each of the first 3 blocks fallen, 2HP extra damage for each of the next 5 blocks fallen, and 1HP extra damage for each block fallen after that.
More info: https://minecraft.wiki/w/Mace
The difference between these 2 is that they contain 2 different enchantments

The 1st mace has the enchantment Density 5, which does the following:
Density increases smash attack damage by 0.5HP per block fallen per level of enchantment.
More info: https://minecraft.wiki/w/Density

The 2nd mace has the enchantment Breach 4, which does the following:
Breach reduces the effectiveness of the target's armor points and armor toughness by 15% per level. Specifically, Breach deals damage as though the enemy's damage reduction from armor was 15 percentage points lower per level. For example, if the enemy's armor reduces damage by 50%, and they are hit with a mace with Breach I, their armor reduces the damage by 50% - 15% = 35%. However, this reduces the effectiveness of only the armor itself, which does not include damage reduction from enchantments such as Protection.
This is the formula used to calculate the damage for the breach enchantment:
damage taken=weapon damage×(1−max⁡(0%,armor effectiveness−level×15%))
More info: https://minecraft.wiki/w/Breach

[lean otter]

My goal:

My goal is to find the point where the density mace becomes superior to the breach mace in terms of damage and the block fallen, for your information: breach deals more damage at less blocks fallen and density at more blocks fallen, and i want to find the exact point where this change happens

I have made the python code below, that uses the formulas in those wiki pages i linked to calculate the exact damage, however, i dont know how to add the "protection" enchantment part, the 64% we talked about earlier in Target info: https://minecraft.wiki/w/Protection

def func(base_damage, armor_points, armor_toughness, fall_distance, density_level=0, breach_level=0):
    # A successful smash attack causes a mace to deal 4HP extra damage for each of the first 3 blocks fallen,
    # 2HP extra damage for each of the next 5 blocks fallen, and 1HP extra damage for each block fallen after that.
    if 0 < fall_distance and fall_distance <= 3:
        damage = 4 * fall_distance
    elif 3 < fall_distance and fall_distance <= 8:
        damage = 6 + (2 * fall_distance)
    elif 8 < fall_distance:
        damage = 14 + fall_distance
    else:
        damage = 0

    # The Density enchantment can be used to increase smash attack damage by 0.5HP per level for each block fallen.
    if density_level > 0:
        density_damage = 0.5 * density_level
        damage += density_damage * fall_distance

    damage += base_damage # Add base weapon damage
    damage = damage * 1.5 # Make the hit critial

    # Calculate how much damage armor removes
    armor_formula = min(20, max(armor_points / 5, armor_points - ((4 * damage) / min(armor_toughness, 20) + 8))) / 25
    if breach_level > 0:
        formula = (max(0, armor_formula - breach_level * 0.15))
    else:
        formula = armor_formula

    return damage * (1 - formula)

[fallow cairn]

I believe protection is factored at the very end, after all armor deduction occurs, and isn't affected by breach nor density. If you're just trying to compare which does more, you can ignore it. If you instead want to find out how much damage is actually being applied, you'll want to apply it at the very end (inline with the return)

From the wiki:

The protection enchantment is applied after the armor's damage reduction.

[lean otter]

yes it is calculated at the end

i know it dosent affect the goal, but i still want to add it but i dont know how

i struggle with percentages

someone told me to devide by 0.36 anoither guys told me use % and im confused

[fallow cairn]

Let's assume a maximum 64% reduction. Then we're dealing

100% of damage - 64% of damage
= (100% - 64%) of damage
= 36% of damage
= 0.36 * damage

[lean otter]

oh its 0.36 * damage and not / damage

thats where i got stuck

lets say, we get the total protection level as an argument

for example 16 for max protection

we do 16 times 4

but

how do we get 0.36 out of 64 we got

idk how percentages work

[fallow cairn]

"Percent" can be read as "per 100", so we have 64% is 64 per 100, or 64/100

[lean otter]

i know its the remaining of it but how to turn 64 into 0.36 in code

[fallow cairn]

That'll be something like

protection_multiplier = 1 - (4 * level / 100)

Or, if its clearer to read

protection_multiplier = (100 - (4 * level)) / 100

[lean otter]

(4 * level / 100) gives us 0.64

but why do we minus it by 1?

that just makes it negative

[fallow cairn]

1 - 0.64 gives us the desired 0.36

[lean otter]

how does it not give us negative

oh fuck im dumb

i read it backwards

sorry lmao

[fallow cairn]

Lol no worries

[lean otter]

okay thanks! ima go code it and i will ping you if i run into any problems

[fallow cairn]

(Also, if we're being pedantic, protection is hard-capped at 20 levels, so we'll want a math.min in there)

[lean otter]

something like..?

[fallow cairn]

Yeah that'd work; I'd probably consider the max overkill since protection level is at least 0

[lean otter]

yep thats an LLM error

[fallow cairn]

Sorry, the level is capped at 20. The reduction would be capped at 80 (4*20)

This limit only matters when cheats are enabled as far as mace calculations are concerned

[lean otter]

yea but it wont hurt to add it

def func(base_damage, armor_points, armor_toughness, armor_protection, fall_distance, density_level=0, breach_level=0, critial_hit=True):
    # A successful smash attack causes a mace to deal 4HP extra damage for each of the first 3 blocks fallen,
    # 2HP extra damage for each of the next 5 blocks fallen, and 1HP extra damage for each block fallen after that.
    if 0 < fall_distance and fall_distance <= 3:
        damage = 4 * fall_distance
    elif 3 < fall_distance and fall_distance <= 8:
        damage = 6 + (2 * fall_distance)
    elif 8 < fall_distance:
        damage = 14 + fall_distance
    else:
        damage = 0
    
    # The Density enchantment can be used to increase smash attack damage by 0.5HP per level for each block fallen.
    if density_level > 0:
        density_damage = 0.5 * density_level
        damage += density_damage * fall_distance

    damage += base_damage # Add base weapon damage
    if critial_hit:
        damage = damage * 1.5 # Make the hit critial

    # Calculate how much damage armor removes
    armor_formula = min(20, max(armor_points / 5, armor_points - ((4 * damage) / min(armor_toughness, 20) + 8))) / 25
    if breach_level > 0:
        formula = (max(0, armor_formula - breach_level * 0.15))
    else:
        formula = armor_formula

    damage = damage * (1 - formula)

    # Calculate how much damage protection removes
    protection_percent = 1 - ((min(20, armor_protection) * 4) / 100)
    damage = damage * protection_percent

    return damage

this should do the job

it seems to be outputting wrong tho

what did i mess up ? @fallow cairn

damage = damage * (1 - formula)

    # Calculate how much damage protection removes
    protection_percent = 1 - ((min(20, armor_protection) * 4) / 100)
    damage = damage * protection_percent

    return damage

only edited that part + adding the armor_prot arg

oh lol

[fallow cairn]

What was the issue?

[lean otter]

something is wrong here

it does not at all make any sense with my tests in game

only the part that armor comes into play

testing without armor is correct

[fallow cairn]

I can skim through the code here shortly if you'd like

[lean otter]

sure, im making a mod rq to show me my fall distance in game so i can test accuretly

let me show you where i get the formulas from

calculating the damage part works perfectly, no issue in that

the armor formula comes from this part of this page https://minecraft.wiki/w/Armor#Damage_formulas
since the devision was the same in both formulas, i simplified the code to only contain it once

and the next part is our protection formula that we just wrote

[lean otter]

@fallow cairn heres the formulas

[fallow cairn]

Alright, give me a moment to look this over

[lean otter]

okay, take your time please

ping me on response

[fallow cairn]

Hmm...

@lean otter Could you provide some examples where in-game differs from the formula? I'm not seeing any issues with the code right now

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

sure

my power went out and don't have access to PC rn but I can pull some examples from the wiki

[fallow cairn]

Ah dang, sorry to hear that

Yeah that should work

[lean otter]

I tried simulating the same scenarios mentioned here
they work exactly like the article in game but the code produces different results

[fallow cairn]

Okay damage calculation for maces is definitely correct

Ah, yep

armor_formula = min(20, max(armor_points / 5, armor_points - ((4 * damage) / min(armor_toughness, 20)  + 8))) / 25

needs to be

armor_formula = min(20, max(armor_points / 5, armor_points - ((4 * damage) / (min(armor_toughness, 20) + 8)))) / 25

@lean otter See above

The issue was that the formula was being interpreted as
[ \text{armor points} - \frac{4\times\text{damage}}{\text{min}(\text{toughness},20)}+8]
instead of
[ \text{armor points} - \frac{4\times\text{damage}}{\text{min}(\text{toughness},20)+8}]

[flat frigate]

@fallow cairn

[lean otter]

ohh I see

thank you so much, I will try it once power comes back in around an hour and let you know

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

nop
hang it man

[plucky elk]

!done

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

[lean otter]

i am not, i just came back and want to continuie it

[lean otter]

alrigght lets test it out

[lean otter]

same result no difference

e = func(
    base_damage=6,
    armor_points=20,
    armor_toughness=8,
    armor_protection=16,
    fall_distance=10,
    density_level=5,
    breach_level=0,
    critial_hit=True
    )

print(e)

[lean otter]

i replaced my formula with the bottom snippet

[fallow cairn]

hm

and what's the expected for this specific example

[lean otter]

above 20 but not more than 21 or 22

either the armor formula is wrong or the protection one

[fallow cairn]

It may be helpful to divide out the logic for computing the damage dealt from the damage received

[lean otter]

that was too many complicated words

i didnt understand it lol

[fallow cairn]

Ah

[lean otter]

there is one way to make sure it is working as expected

take this formula and calculate the damage by hand

[fallow cairn]

basically, divide the logic into two functions, like so:

def calc_damage_dealt(base_damage, fall_distance, density_level=0, critial_hit=True):
  # TODO

def calc_damage_received(damage_dealt, armor_points, armor_toughness, armor_protection, breach_level=0):
  # TODO

would make it easier to reason about it

[lean otter]

oh i get it

however

if we do that

nothing changes coz i have already done that

we know for sure that calc_damage_dealt function works

this part is the calc_damage_dealth function

the rest is calc_damage_received

[lean otter]

we know for sure this part works, i have tested it without taking armor into account and it works perfectly

[fallow cairn]

,w 82.5 * (1 - Min[20, Max[4, 20 - (330 / 16)]]/25)

[flat frigate]

Results provided by WolframAlpha

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

Requested by .kiako

[fallow cairn]

,w 69.3 * .36

[flat frigate]

Results provided by WolframAlpha

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

Requested by .kiako

[fallow cairn]

Your formula seems good

[fallow cairn]

@lean otter What makes you so sure it should be <22?

[lean otter]

First of all, the wiki says this:
The amount of fallen blocks needed to defeat a player wearing full Protection IV netherite armor from full health are the following:
Density V mace: A critical hit after falling 10 blocks.

It says this is the minimum for killing a player with max protection and armor, however, we can still defeat a max player with only 7.2 blocks, not 10

Second of all, in the game it works just like wiki says it does

[fallow cairn]

Hm, let's see here

,w 78 * (1 - Min[20, Max[4, 20 - (312 / 16)]]/25) * 0.36

[flat frigate]

Results provided by WolframAlpha

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

Requested by .kiako

[fallow cairn]

Hm, I'm not sure what's up with that then

[lean otter]

lets do something

lets check armor_formula charecter by charecter, both of us check it
and make sure all of it is exactly what the formula represets

then i will use that to exactly check minecraft source code

charecter by charecter i will check it, but we first need to make sure armor_formula is the correct formula the wiki says, like no extra paranthesis or anything

min(20, max(armor_points / 5, armor_points - ((4 * damage) / (min(armor_toughness, 20) + 8)))) / 25

thats the best i can do

[lean otter]

If you confirm this, ima go compare it to the games source code @fallow cairn

[fallow cairn]

that seems good to me

[lean otter]

under if breach_level > 0:
the max(0 part, here:
formula = (max(0, armor_formula - breach_level * 0.15))

I dont see a world where 0 will get picked as maximum, is this another overkill check like this other one you mentioned? or it can actually happen

[fallow cairn]

with cheats its possible, e.g., with breach level 7+

[lean otter]

i see

oh yea then it exceeds 100%

[lean otter]

protection_percent = 1 - max(0, (min(20, armor_protection) * 4) / 100)

im a bit confused, u said the one i replied to works, but this above is what we were using

ignore the devision by 100, im talkinjg about armor protection times 4 logic

@fallow cairn are you okay with pings?

[lean otter]

<@&286206848099549185>

[fallow cairn]

What about it?

That one is also correct

There's like 4 ways to clamp that value

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

After checking out the games source code this seems to be correct, however in action it still dosent make any sense lmao
Edit: turns out i inputted 4 less armor_toughness lol

[safe radish]

@lean otter Has your question been resolved?

Channel closed

Closed by @gaunt tide

Use .reopen if this was a mistake.

[safe radish]

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[junior canopy]

How would you calculate 1 rotated i°?

[junior canopy]

1 rotated 90° equalling i for example

[visual linden]

Sorry I don't get your question

[visual linden]

This is correct, yes

[junior canopy]

In polar coordinates 1 being rotated 90 degrees is i

What would it be if 1 is rotated i degrees

[visual linden]

Oh god, let me think

[vagrant ice]

it doesn't make sense to rotate by a non-real angle

[junior canopy]

Would it be a quaternion number

[magic junco]

z = 1 being rotated anti-clockwisely 90° becomes i

[junior canopy]

Huh

[visual linden]

I thought there might be some sense at a higher level, complex numbers are messed up man, i^i is a real number🙏

[vagrant ice]

it's like how yes, there technically is a right triangle with sides 1, i, and 0

[visual linden]

That's fair, I should have pointed that out

[vagrant ice]

you can definitely multiply some vector by a quaternion to perform a rotation

[junior canopy]

So assuming i is a second second dimensional number, would rotating 1 by i give you a third dimensional number?

[ember socket]

I don't think so. trying to apply rotation with a theta of i wouldn't give you a rotation at all iinm

[vagrant ice]

you're forgetting that you always need to specify the axis of rotation

[magic junco]

It makes negative sense

[vagrant ice]

when we rotate the vector 1 + 0i by 90 degrees counter-clockwise
that's with respect to the z-axis

really, maths isn't that deep

[visual linden]

IG it could be third dimension if you rotate it with respect to imaginary axis or x axis, but then you gotta have a z-axis term, and that would be too much i feel

[split kayak]

1 i^1 makes sense in complex as a rotation

1 i^i doesnt

Its a number, but not one that makes sense as a rotation in the complex plane

[visual linden]

Sorry but I'm confused, if it's a real number then why can't we rotate by it?

[magic junco]

i is not a real number

[visual linden]

i^i is though

[split kayak]

with A being a real number

A* i^n

defined a rotations in a cycle of fourths

so, i^0 is 1, so no rotation

i^1 is i, so it moves 90deg

etc...

and you come back to 1 with i^4

[visual linden]

So wouldn't i^i exist somewhere on the x-axis?

[glacial meadow]

Second dimensional number? 🥀

[twilit spindle]

writing a+bi as (a,b) then i(a,b)=(-b,a), dotting (a,b) with (-b,a) gives 0. Which is the general idea behind why i encodes a 90deg rotation

[glacial meadow]

Yeah, on the point (e^-(π/2),0)

[split kayak]

the fact that it works like that, is specifically because you have

$e^{i\frac\pi2 \cdot n}$

[visual linden]

Alright I see, so we cannot rotate by it, but it does exist on the plane right?

[split kayak]

which is just i defined with the eulers identity and multiplication of exponents

[glacial meadow]

You can rotate by i^i, it's a real number like any other, it being of any use or interesting for something is another matter

[vagrant ice]

yes i^i actually makes sense in re^(i theta) form

but the definition of an angle is always a real number

[visual linden]

Yeah e^(i*pi) = -1, we can derive i^i from that

[visual linden]

Alright I see

[vagrant ice]

there are other ways to perform rotations, such as using complex numbers or quaternions as you said

[split kayak]

now, what would this be if you define it like this:
$i^i = (e^{i\frac\pi2})^i$

[vagrant ice]

but those are not angles

[split kayak]

If you use multiplication of exponents, you get:
$e^{-\frac\pi2}$

which is just a real number

[visual linden]

I see, so we can use it for rotation then yeah? But like Prim said it may or may not be of use

[junior canopy]

I have another question but let me find the message I'm following up

#help-7｜zen1thxyz message if you do the same for i instead of π it approaches a different constant, what is this constant and how do you calculate it?

[split kayak]

goddam my internet is bad today

[visual linden]

Cos(i)!?

i cannot be angle if I'm not wrong

[junior canopy]

Oh wait

I'm stupid

[vagrant ice]

using the exponential definition that does exist

[twilit spindle]

cos(...cos(x)...)=x, holds only when x is the Dottie constant

[vagrant ice]

as a complex number

[visual linden]

You can have cos(x) + i*sin(x) though

[junior canopy]

I used deg instead of rad this time

[split kayak]

there is a definition for complex trig functions

[vagrant ice]

yeah like if the limit exists, then you must have cos(L) = L

[junior canopy]

It's the same constant 😭

[glacial meadow]

That's the limit of a sequence defined by a_1=cos(i), a_n=cos(a_n-1),

[junior canopy]

Okay well thank y'all

[visual linden]

Wait, e^(i*i)?

[junior canopy]

.close

[safe radish]

Channel closed

Closed by @junior canopy

Use .reopen if this was a mistake.

[vagrant ice]

$\cos x = \frac{e^{ix} + e^{-ix}}{2}$

[flat frigate]

south

[vagrant ice]

seems to exist

[twilit spindle]

cos(i)=cosh(1)?

[visual linden]

Okay so (1 + e²)/2e

[glacial meadow]

Wasn't cos contractive if I remember correctly?

[vagrant ice]

I have no idea if that generalises to the complex domain

[glacial meadow]

Though Idk if that generalizes to C

[vagrant ice]

but yeah for the real numbers it's a contractive map

Banach fixed point theorem tells you that it would exist

[visual linden]

.Oh wait, wasn't there something similar for hyperbolic functions?

[vagrant ice]

but I don't see a problem with the Lipschitz definition for C

you just replace the norm, so instead of the absolute value, it'd be the Euclidean distance in R^2

[glacial meadow]

Yeah, should work with the norm metric

[vagrant ice]

yeah so $\cosh x = \frac{e^x + e^{-x}}{2}$

[flat frigate]

south

[glacial meadow]

So that should converge to something

[split kayak]

the cos(cos(cos...(i)...)) also limits to dottie

[vagrant ice]

sub in x -> ix into the definition for cos(x) and you get cos(ix) = cosh(x) lol

[visual linden]

.Damn, didn't know the hyperbolic functions and imaginary numbers were so closely related (we aren't taught in that manner here)

[split kayak]

tbh complex algebra is relatively easy once you get the hang of it
and complex analysis is well behaved compared to real analysis

there are a few quirky rules of complex algebra that is pretty easy to break on accident tho

[visual linden]

.Any idea when we're taught that?