general discussion

[vivid gulch]

an evil magma in a suit

[hollow ice]

$ai + bj + ck = \langle a,b,c \rangle$

[vivid gulch]

an evil magma in a suit

an evil magma in a suit

[hollow ice]

$-\frac{2}{\sqrt{42}}$

[vivid gulch]

an evil magma in a suit

[hollow ice]

$\cos \theta = -\frac{2}{\sqrt{42}}$

[vivid gulch]

an evil magma in a suit

[hollow ice]

$\theta = \arccos \left(-\frac{2}{\sqrt{42}}\right)$

[vivid gulch]

an evil magma in a suit

[hollow ice]

If and only if $\vec{\mathbf{u}}$ and $\vec{\mathbf{v}}$ are orthogonal does $\vec{\mathbf{u}} \cdot \vec{\mathbf{v}} = 0$.

[vivid gulch]

an evil magma in a suit

[lethal wigeon]

Try this

[dusty swallow]

What is it

[lethal wigeon]

Vector feilds!

[dusty swallow]

Ohh

I See

Looks cool indeed

[sour sinew]

pretty cool

what are the vector fields

[dusty swallow]

I coded a 3d vector field viewer for magnetic fields once

It looked fancy

[lethal wigeon]

The rainbow one is visualizing x^5 on the complex plane

[sour sinew]

what does this even mean
if it is prime, it is either odd or even still

[lethal wigeon]

The cyan and yellow one is

[sour sinew]

ah

[sour sinew]

this one is really boring

imo

[lethal wigeon]

fair

[sour sinew]

imma try to make the x^5 one

[lethal wigeon]

if im not mistaken

[ancient helm]

$(a+bi)(c+di) = (ac - bd) + (ad + bc)i$

[vivid gulch]

r•eⁱˣ = r•cos(x) + ri•sin(x)

[ancient helm]

@lethal wigeon a and b would not multiply in on eachother (same with c and d)

[lethal wigeon]

whoops

what other cool things have i done with math

Ih

Oh*

I memorized Runga Kutta 4

[lethal wigeon]

Nobody stopped more than 1 correct answers

[sour sinew]

ok imgonna do it
so since (x-10)^2002 >= 0 we need that x =/= 10, we will remember that, and remove that factor
since (x+1)^2000 >= 0 we need that x =/= -1, we will remember that, and remove that factor
then since (x-12)^2001 has the same sign as (x-12) we will make that replacement, and similarly for (x-3)^1999 => (x-3)
so then we need the number of integral solutions of (x-12)/(x-3) < 0
keeping in mind that x =/= 3 we can multiply by the positive number (x-3)^2 to result in (x-12)(x-3) < 0
finally note that this is zero for x = 3, 12 and as such is negative for 4,5,6,7,8,9,11, which is an odd prime number

[hollow ice]

This is such an easy problem bro come on

Its A,C with seven integral solutions

[lethal wigeon]

Ah i forgot when i sent that question

[sour sinew]

is there a closed form for the recursive function f(0) = c, f(x + 1) = 1 + 1/(f(x))^3

or even f(0) = c, f(x + 1) = 1 + (f(x))^a

more general

i know there is one for f(x + 1) = 1 - 1/f(x)

[topaz cobalt]

https://tenor.com/view/litty-mlg-wow-gif-22702489

same colours

[lethal wigeon]

image with the same function

[lethal wigeon]

yoohoo

[sour sinew]

anyone wanna try this

[lethal wigeon]

i have no experience with that

[sour sinew]

well,

try f(x + 1) = 1.5 - 1/f(x) first

really fun challenge imo

nvm that one sucks

edited (in other words, fixed)

[lethal wigeon]

alright

[obtuse zinc]

Assuming the multiplicative subgroup of a finite field Z_p whereas its objects are all numbers relatively prime to p, and is denoted by U_p. Some conditions must be met for this group to be cyclic

Now, let's assume that a group A contains all all numbers { x | 1 <= x < p and x is natural }

In what cases is A cylic?

Is it possible with numbers over N? or some conditions must apply to some field F, such that we're talking about all the elements that meet the conditions stated, but belong to F/F_n

[tight lagoon]

Lagranges Zero one block has to be one of the most coolest things I have learned in mathematics till now.

[sour sinew]

i love using lagrange interpolation to write “not enough information” on every find the next term puzzle

[tight lagoon]

Even better if it is a multiple choice question and there is an "all of these" option then that would be the correct answer

Anyways Lagrange is a freaking genuis

He just broke pattern recognition.

[sour sinew]

answer i came up with:
||3/4 + s/4*tan(x*arctan(-s/3) + arctan((4c-3)/s)) where s = sqrt(7)||

it seems that f(x + 1) = 1.5 + 1/f(x) is a harder problem

i have no solution for that

[sour sinew]

nvm i have a solution but its gross and complex numbery

[tight lagoon]

We have talked before haven't we?

You had helped me with that parabola question right?

[sour sinew]

perhaps

[sour sinew]

question

for what functions f is this (the part in the range 0 < x < 1) invertible

obviously x works

we can define z = e^(1/x + 1/(x-1)), x = (ln(z) + 2 - sqrt(ln(z)ln(z) + 4))/(2ln(z))

seems pretty unhelpful

[sour sinew]

maybe this is easier to solve?

[versed comet]

Helppo

[sour sinew]

#1015578016606343218 or #1020426321261756536

[versed comet]

@sour sinew its neither

Its a question I made up. Have been trying to solve. And have failed to solve

[sour sinew]

ah ok

i will try to help

[versed comet]

Its been wracking my brain for the last two weeks

[sour sinew]

well clearly the sphere will go outside of the tetrahedron

[versed comet]

the point is proving

[sour sinew]

just consider a regular tetrahedron

no 3 collinear points

sphere will go outside

[versed comet]

Thats what im struggling with

[sour sinew]

ok

[versed comet]

Yes but mathematically prove it

E.g show the radius of the sphere would pass through the plane on which any side exists

Its obvious that it will go outside but it’s finding a proof of it

thats the problem

I left it open ended just to throw intuition into it

[sour sinew]

can you just

wlog set the base having vertices (0,0,0) (1,0,0) (0.5,sqrt(3)/2,0)

actually you can

because i only need one counterexample

[versed comet]

There would be 4 vertices

and those 3 are co-linear

[sour sinew]

no they are not

[versed comet]

Yes they are. Along z = 0

[sour sinew]

that is called being coplanar

any 3 points are coplanar

[versed comet]

Well then I misworded the question

Wait no

Colinear works

[sour sinew]

yes

z = 0 is a plane

[versed comet]

Coplanar wouldnt work though as then a tetrahedron would be impossible to form

Those are colinear though

As the z component of each is 0

[sour sinew]

i told you z = 0 is a plane

[versed comet]

So how would I phrase it so that this isnt allowed cause that was the point of adding the colinear part

[sour sinew]

uhhhhhhhhh

any regular tetrahedron will be similar to that one

[versed comet]

You can form a tetrahedron without the need for a mutually shared x,y or z component in 3 points

[sour sinew]

since moving points around is continuous,

slightly adjusting the points by which i mean moving them 0.00000000001 away from the z = 0

it won't change anything

[versed comet]

But the point of this is a challenging proof question

So you could choose points where it satisfies the conditions and have a counterexample

[sour sinew]

well anyway here's my counterexample

clearly the distance to the nearest point is less than the distance from that plane

(this is a regular tetrahedron)

[sour sinew]

i have a question

if Q(x) is the indicator function of the rationals

what would the integral from 0 to 1 of Q(x) be

it should be 0

but if you define it with riemann sum it will be 1

[elfin kraken]

@rancid cosmos

[rancid cosmos]

1. Lines and angles
2. Trig basics
3. Log basics
4. Graphs and functions basics

3 are just basics

Okie

[elfin kraken]

Give me some names of book

[rancid cosmos]

Now what do you think a line is Vansh

Use imagination

A straight line

[elfin kraken]

Ok

[rancid cosmos]

How would you describe it

[elfin kraken]

Let me get on laptop

[rancid cosmos]

Me too

@wheat crescent you come here too

[wheat crescent]

I WAS TRYING TO FIND THE CHANNEL

I had no idea it was on top

[rancid cosmos]

It's someone elses

We stole ot

[wheat crescent]

dayum

well if it works

[elfin kraken]

so

@rancid cosmos

[wheat crescent]

yes

Vansh

[elfin kraken]

ax + by + c

[wheat crescent]

no

ax+bx+c is an equation

Tell me what a line is

[elfin kraken]

keyboard math is trivial

[elfin kraken]

@wheat crescent

[rancid cosmos]

ok on laptop now

[wheat crescent]

Stop

stop giving me equations

What do you think is a line

[elfin kraken]

i did not equate it to zero

[wheat crescent]

BRO

STOP

[rancid cosmos]

ye we start with basics

lmao

[wheat crescent]

What comes to your mind when you think of a line

[elfin kraken]

a straigh set of points which has no end?

[rancid cosmos]

and Vansh have desmos open in background 24/7 while learning this

[wheat crescent]

good

[wheat crescent]

lmao

[rancid cosmos]

what can we say about set of points ? any relation between them ?

no issues if you don't find any relation

[elfin kraken]

x coordinates and y coordinates?

[rancid cosmos]

I wanted something else but this is better

whats relation between x coordinate and y coordinate

now lets take a line

[elfin kraken]

i am visualising those sets of points on a cartesian plane

[rancid cosmos]

y = x

[elfin kraken]

set*

[elfin kraken]

derivation?

[rancid cosmos]

how much does y increase per x

[rancid cosmos]

nah thats the first line I give you

[rancid cosmos]

tell me this

per unit x, how much y increase ?

[elfin kraken]

if i were to increase x by 2 y will also be increased by 2

since they are equal

[rancid cosmos]

ye

[elfin kraken]

by they i mean x and y

[rancid cosmos]

so if I were to increase x by 1

how much will y increase ?

[elfin kraken]

1

[rancid cosmos]

good job

now thats the meaning of slope

[elfin kraken]

[rancid cosmos]

how much y increases per increase in x

[elfin kraken]

delta y / delta x

[rancid cosmos]

yup

thats our slope

[elfin kraken]

i remember this from last years physics

[rancid cosmos]

Ooo noice

now lets say you have an equation

y = 5x

[elfin kraken]

ok

[rancid cosmos]

how much will y increase per x now

[elfin kraken]

5

[rancid cosmos]

per x means unit x

yes

y = 10x

now ?

[elfin kraken]

10

[rancid cosmos]

5y = 20x

[elfin kraken]

15?

[rancid cosmos]

nope

make it like other ones

[elfin kraken]

4 times 5?

[rancid cosmos]

you won't subtract y from x will you ?

[elfin kraken]

no

[rancid cosmos]

all of these had 1 for y coefficient right ?

[elfin kraken]

y will increase 4 times??

[rancid cosmos]

and when they had 1, you simply took x coefficient and that was answer

yes

4 times

[elfin kraken]

ok

[rancid cosmos]

now we start with real work

so until now we have this

y = mx

and m is the slope

[elfin kraken]

o\

ok

[rancid cosmos]

now imagine I had y = mx + 25

when will this touch the y axis ?

any idea ?

[elfin kraken]

let me think

[rancid cosmos]

okie, take your time

if you want hint tell me

but hint will give straight answer

[elfin kraken]

ok wait

since m is the slope so we subsitute by change in y axis upon x axis?

[rancid cosmos]

nah m is useless for this question

[rancid cosmos]

want hint ?

[elfin kraken]

no wait up

[rancid cosmos]

okie

@elfin kraken where you at ?

[elfin kraken]

@rancid cosmosi cant figure it out

[rancid cosmos]

okie now what was our goal ?

finding which point it will intersect y axis correct ?

[elfin kraken]

yep

[rancid cosmos]

what do you know about y axis ?

[elfin kraken]

its perp

[rancid cosmos]

y axis is at x = 0 ?

so your x coord is already found ?

[elfin kraken]

oh on either +ve y

or -ve u

y*

[rancid cosmos]

all is allowed

but a straight line only intersects once y axis or x axis

[rancid cosmos]

if you know x coord

can you find y coord ?

where you Vansh

[elfin kraken]

back

people in general are so stupid nowadays

[rancid cosmos]

ikr

wanna give Zrekon trusted for time being ?

[elfin kraken]

not sure

[rancid cosmos]

okie

[elfin kraken]

he was muted himself quite a while ago

[rancid cosmos]

I mean he has been mod before 🙄

[rancid cosmos]

oh

okie then

ok back to question

y = mx + 25

any ideas now that you know y axis lies on x = 0 ?

@elfin kraken

[elfin kraken]

y = 25?

[rancid cosmos]

yup

now give me coordinates

[elfin kraken]

0,25

[rancid cosmos]

yess

now we make big equation

y = mx + c

c is called y intercept

y intercept means point where line meets y axis

x intercept is where it meets x axis

now we enter into calculus

@elfin kraken understood everything till now ?

[elfin kraken]

yep

[rancid cosmos]

now what we learned is y = mx + c m is slope

slope is also called derivative

and gradient

differentiation is finding derivative

[elfin kraken]

so finding the slope

[rancid cosmos]

yes

now what if I want you to find slope of y = x^2

[elfin kraken]

what tis the logic behing naming it this?

[rancid cosmos]

differentiation ? finding difference between 2 points maybe ?

oh wait i know

[elfin kraken]

0

[rancid cosmos]

differentiation is breaking a curve into a super small line

[rancid cosmos]

nope

what is slope of y = x ?

[elfin kraken]

didnt i had to find y intercept

[rancid cosmos]

nope

lol

[elfin kraken]

x intercept then?

[rancid cosmos]

nah

we want slope

no need for intercepts

wait lemme tell you why

if you have y = 5

whats slope ?

its a straight line right ?

[elfin kraken]

ye

its a straight line

[rancid cosmos]

and its never gonna change y value ?

so slope is 0 ?

[elfin kraken]

ye if its a straight line then it wont

and yes slope is zero

[rancid cosmos]

yup

so no need to find intercept ?

because constants have slope of 0

[elfin kraken]

ye[

[rancid cosmos]

back to y = x^2

y = mx m is out slope

whats your first idea ?

by seeing this ?

remember we can write x^2 as xx

[elfin kraken]

is the slop x lmao

[rancid cosmos]

now thats close but wrong

why did you say its x ?

because x is multiplied to x ?

[elfin kraken]

i saw xx

[rancid cosmos]

ye

now either I teach you product rule now or I teach you logical way

lets use logical way

product rule another day

[rancid cosmos]

each x is multiplied to 1 x right ?

[elfin kraken]

oh then the slope is 1

[rancid cosmos]

you have to add whatever each x is multiplied to seperately

[rancid cosmos]

nah

[elfin kraken]

2

[rancid cosmos]

nope

1sst x is multiplied to x

2nd is also multiplied to x

x + x

2x

did you understand what happened ?

[elfin kraken]

no

sowwy

[rancid cosmos]

issoke

whats your 1st x multiplied to ?

x right ?

x x

[elfin kraken]

yep

x * x

[rancid cosmos]

so we add 1 x

now whats 2nd x multiplied to ?

1st x

right

[elfin kraken]

1x to where?

[rancid cosmos]

x1 * x2
lets label them like this

but both are same in end

x1 is multiplied to x2

and x2 is multiplied to x1

so our final answer is x1 + x2

we add what each of our x is multiplied to

[elfin kraken]

shit

time to sleep

its about time

[rancid cosmos]

oh okie

good night ✌️

[elfin kraken]

cya tommorow

good night

[rancid cosmos]

cya , sleep well

[dire dew]

I've got a mean question for anyone who wants to try figure it out

is there a specific channel I send it in?

[sour sinew]

here is fine

[dire dew]

Aight

I made it myself in geogebra cause I got bored 🤣

[sour sinew]

so PS || QR, SPQ is 90, PQ = SR, PS = 7?

[dire dew]

Yup

Im assuming || means parallel

[sour sinew]

well clearly PQRS is a rectangle then

[dire dew]

indeed it is 🤣

[sour sinew]

am i meant to assume that QS is horizontal

[dire dew]

the arrows are north lines

so with that you can see that from the North to QS it is 90*

[sour sinew]

psq = 69.3

[dire dew]

so it is horizontal, yea 🤣

[dire dew]

I wont tell you if you're right or wrong from here on

but good luck, although I dont think you'll need it

[sour sinew]

49 tan(69.3 deg)

i think this could have been more mean

[dire dew]

it could definitely be

[dire dew]

If that is your final answer, it is incorrect

I dont think it is your final answer tho

[sour sinew]

oh i totally misread the problem

QS and RS are equal

mb

it's not a rectangle
it would be 1.5x that

1.5*49*tan(69.3deg)

[sour sinew]

what was this

[dire dew]

😄

[lethal wigeon]

2x+(1+1i)

[topaz cobalt]

I rember watching something interesting like this

[lethal wigeon]

x^2+2x+1i

[lethal wigeon]

i was inspired by 3blue1brown

[topaz cobalt]

Lemme see if I can pull that up

[topaz cobalt]

Have you seen the Summer of Maths Exposition 2

[lethal wigeon]

Mhm

[random iron]

https://youtu.be/idpOunnpKTo

[lethal wigeon]

Cool

[lethal wigeon]

A;; tjos re[resents is finding the fixed points

Not the solutions

[sour sinew]

have you tried plotting zeta

there’s probably pictures online but just as a fun challenge

[sour sinew]

i can find nothing about why it’s called the derivative

interestingly

also please don’t teach the ““logical”” method ever again

/lighthearted

[vague dagger]

-ban @kind frost nsfw videos

[calm ginkgo]

Why did you ban him?

[vague dagger]

I wrote the reason @calm ginkgo

[sour sinew]

amazing

oh i forgot this is what middle school students are interested in

[agile roost]

cool, what's 791⁹

you have 5 seconds

times up, it's obviously 121223927776935534071210711

[dusty swallow]

Trivial

[ancient helm]

Easy Mental math

the discord math sticker

Half of the things on the sticker makes no sense looking at it

[normal arrow]

nerd

[ancient helm]

True

[topaz cobalt]

What'd you expect from people working at discord?

[sour sinew]

trueee

[ancient helm]

Makes sense

Don’t even wanna know what a youtube based math sticker would be like

Half the youtubers I’ve seen can’t do basic adding on camera

[dusty swallow]

https://tenor.com/view/the-gates-of-irony-irony-ironic-welcome-gif-14697709

[ancient helm]

Shush

[dusty swallow]

[sour sinew]

are you saying reixrcosxrisinx can't do basic adding on camera either

[dusty swallow]

Nono

I’m saying he can’t do basic adding with or without cameras

[sour sinew]

ah

[ancient helm]

To be fair I can’t talk to you without using a device with a camera so I have no way to prove I can

*Without cameras

I can prove it with cameras

[jagged basin]

X - ((.18% of x + 15)*1.5768e+11) = 9,572

How do I solve for X here? I don't know exactly what I am doing wrong and it's been a really long time since I've done stuff like this.

i haven't done math in a long time honestly...

[sour sinew]

you mean
x - (0.0018x + 15)(1.5678*10^11) = 9572
?

[jagged basin]

yeah. I always use E.

for you know, exponent.

because I talk numbers a lot more than use them I use e.

[sour sinew]

just multiply
x - 0.0018*1.5768*10^11*x - 15*1.5678*10^11 = 9572

like terms

and this is going to have a ridiculous answer

[jagged basin]

i know it has a stupid answer.

it's kinda the point.

[sour sinew]

x(1 - 0.0018*1.5768*10^11) = 9572 + 15*1.5678*10^11

and divide

[jagged basin]

wait pause for a sec

x - 0.0018 * 1.5768 * 10^11 * x - 15 * 1 .5678 *10^11 = 9572

My dyslexia is kicking in trying to read this...

[sour sinew]

math is hard to read

[jagged basin]

taking a second to read it.

okay i think I see it... but what happened to the X that was being subtracted?

[sour sinew]

well the first x is at the start

[jagged basin]

yeah I see that

[sour sinew]

and the 2nd x came to the 2nd term

[jagged basin]

2nd term?

[sour sinew]

- 0.0018 * 1.5768 * 10^11 * x

[jagged basin]

x(1 - 0.0018* 1.5768* 10^11) = 9572 + 15 * 1.5678*10^11

but where did it go in here

[sour sinew]

i factored it out

[jagged basin]

how and why?

[sour sinew]

it's being multiplied by 2 things

x - x*somestuff
=>
x(1 - somestuff)

[jagged basin]

ah...

okay... I think I get it.

but why is it that and not 2x then?

[sour sinew]

why 2x

[jagged basin]

idk, been a long time since I've done factors

So... X(-283823999) = 2.3517e+12?

but wouldn't that mean X becomes a negative?

[sour sinew]

yes, x is about 15/(-0.0018)

~~ -10000

[jagged basin]

yeah but what I am working with it can't be negative so just say it's positive?

[sour sinew]

uhh

[jagged basin]

like X has to be a positive value.

[sour sinew]

if it must be positive there must be some mistake in the equation

or maybe the thing it represents is impossible

or it represents going backwards in time

[jagged basin]

it represent going back in time kinda.

[sour sinew]

well then the answer would be, you know, x ago, ig?

[jagged basin]

X is initial value
.18% of x + 15 is the amount being taken out of the inital value.
1.5768e+11 is the amount of times that occurs.

9,572 is the value after that many occurences.

[sour sinew]

is it .18% of (x + 15)

or (.18% of x) + 15

[jagged basin]

the latter.

[sour sinew]

hmmm

[jagged basin]

X - ( ((.18% of x) + 15)*1.5768e+11 ) = 9,572

it looks trippy I know..

sorry it's a weird thing

[sour sinew]

welp

guess x is negative

that would be the answer

[jagged basin]

but it can't be negative...

how do you subtract something and then make it positive?

[sour sinew]

because, .18% of x + 15

is negative

so youre subtracting a negative = adding a positive, which gets you to 9572

lemme actually calculate x

maybe it's positive

[jagged basin]

I'm doing a nerd thing here to calculate the health of a monster based off a status effect they have been afflicted with for 5,000 year. The status effect does .18% of max hp plus 15 damage every second.

it's dumb I know but my brain is screaming "figure it out."

[sour sinew]

i mean think of it this way

5000 years of .18% of max hp

it would already be 0

and if it's taking 15 away as well

then it would get to 0 even faster

[jagged basin]

yeah that's the issue which makes it weird...

if it was just 15 points of hp it would pretty easy to plug in...

When I plug x-(((.0018x) + 15)*1.5768e11)=9,572 into a calculator it gives me 572.

which that doesn't make sense at all.

[sour sinew]

are you sure it's not reading that as 1.5678*11*2.71828

[jagged basin]

16183.075 is the value I get after removing the comma. Which makes even less sense as that seems way to low for that rate of decay over that period of time...

2.71828 i don't know where you are pulling it from

[sour sinew]

that's the number e

[sour sinew]

oh

[jagged basin]

did i put it into this calcultor wrong?

[sour sinew]

1.5768^11 is quite different

you want 1.5768*10^11

[jagged basin]

yeah comes out negative...

[sour sinew]

should be about -8000

[jagged basin]

yeah that's what is saying.

[sour sinew]

i think the monster situation is impossible

one idea: it takes 0.18% of its current health + 15 away

[jagged basin]

yeahhhhhh... unless he's also health constantly at the same time.

[sour sinew]

that is another possible

possibility

[jagged basin]

Which is possible... but then that's throwing shit like Y in there which is I think impossible to calc as I think in game they don't heal.

[sour sinew]

so no healing

[sour sinew]

this isn't it either because that will lead to some incredibly ridiculous answer

[jagged basin]

kinda the point to know the insane number

as effectively they've been decaying for 5,000 years at the rate I said above - going off the in game status effect of decay - when you fight them

trying to reverse that value to see what their HP would have been 5,000 years ago.

[sour sinew]

i mean like

significantly larger than that

[jagged basin]

where/how did you get that?

[sour sinew]

that is if it takes 0.18% of its current health away

without even taking away the 15

and finishes at 9572

it has to start at thta

since 5000 years is a very very long time

[jagged basin]

can you show me the math

[sour sinew]

alr

so if it takes 0.0018 of its current health

thats basically like multiplying by 0.9982

[jagged basin]

in the interview for the game the writer of the game went "yeah the events of the game where all the gods battled one another was 5,000 years ago."

[sour sinew]

aka dividing by about 1.001803

so since we start at 9572 we need to multiply by 1.001803 so many times

[jagged basin]

so... X/1.001803?

[sour sinew]

which leads to the massive number

of 9572*1.001803^(1.5768*10^11)

and since thats not even counting the fact that we remove even more health

(the 15)

so it has to start even larger than that

[jagged basin]

is there a way to count that or no...

[sour sinew]

to calculate it with the +15?

[jagged basin]

couldn't you just multiple 15 by the 1.568e11 and add that number to 9572

[sour sinew]

no

idts

you multiply by 0.9982 then subtract 15

then repeat that

so to undo that, we need to add 15 then multiply by 1.001803

repeatedly

uh and this is kind of annoying to do

[jagged basin]

yeah sounds like it.

[sour sinew]

for fun imma figure it out

[jagged basin]

so....

((9572 * 1.001803^(1.5768* 10^11))
Is function A.

Multiple by 0.9982
is function B

Subtract 15
Is function C

So... Repeat function B and C 1.5768*10^11 times?

[sour sinew]

turns out it didnt really change the answer that much

that is a 2 with 123374271 0s

which probably,

the game can't handle

[jagged basin]

lot's of zeros.

[sour sinew]

so anyway

[jagged basin]

2e123374271?

[sour sinew]

is this just like "the player has been fighting this monster for 5000 years"

backstory

but not actually real gameplay

in which case the game devs probably screwed up

[jagged basin]

nah it's more that the monster/boss has been decaying for 5,000 years and you show up to put him out of his misery.

[sour sinew]

maybe the decay rate is much slower than 0.0018

[jagged basin]

the game says that's the rate of damage of the rot to other enemies and yourself

but how did you add in the 15 difference?

[sour sinew]

i used some math that adds up geometric series

[jagged basin]

you said it was really annoying but you did it pretty fast.

can I see how you plugged it in?

[sour sinew]

because the 9572 gets multiplied by 1.001803, L times
the first 15 gets multipled by 1.001803, L times
the 2nd 15 gets multiplied by ^, L - 1 times

etc.

the last 15 gets multiplied by ^ 1 time

[jagged basin]

L being?

the time?

[sour sinew]

1.5768*10^11

[jagged basin]

gotcha

[sour sinew]

and then you add all those together

[jagged basin]

I actually don't think that's how it would work though would it? Why isn't it just 15 times L?

because 15 isn't coming from a percentage

[sour sinew]

because you add 15 every single second

[jagged basin]

15 is just a flat rate

[sour sinew]

and that contributes to the health multiplier

[jagged basin]

oh I think I might have compeletely messed up something okay.

[sour sinew]

did you figure out the actual equation

[jagged basin]

.18% of health isn't from the current health.

but the original value

Whatever the max health is.

So if something's max health was 1,000 it would always subtract 1.8+15

[sour sinew]

ye

that is what we originally tried

and it led to the negative value

[jagged basin]

alright. well just gonna slap 2e123374271 on it and call it a day

[sour sinew]

alr

[jagged basin]

as it's technically an impossible math problem I guess

[normal arrow]

@jagged basin @sour sinew FYI use LaTeX

$x - 0.0018\cdot 1.5768 \cdot 10^{11} \cdot x - 15 \cdot 1.5678 \cdot 10^{11} = 9572$

[vivid gulch]

John Math

[solar quarry]

Is it normal that I find differential geometry hard?

[open whale]

i can help with that stuff

if you want

[open whale]

as a guy who never tried, no

i never found differential geometry hard (i never worked on it)

[solar quarry]

Uhh

[lethal wigeon]

im not asking for help

[dusty swallow]

Yoav get absolutely destroyed

[burnt nest]

$A = 9x² - 6x + 1 +( 1/8 - (1/16)x )$

[vivid gulch]

jado

[burnt nest]

$= ( 3x - 1)^2 + (1/√8-(1/4)x)(1/√8+(1/4)x)$

[vivid gulch]

jado

[plucky storm]

hello guys !!

[elfin kraken]

heyo

[ornate thunder]

There's this combination puzzle. I've made a simulation, available at https://jsmeansjauhesammutin.github.io/newerpuzzlegame

Rules are as follows:
Clicking a green cell cycles it and orthogonally adjacent cells according to green -> red -> white
Clicking a red cell cycles it and orthogonally adjacent cells according to red -> green -> white

When analysing the game, we found out that certain positions, such as this one, are impossible to turn all green

here are two grids which can be used to calculate invariants

if you use the following scheme:
white: 0
green: 1
red: 2

and take a board state, turn each square into a number, and multiply it with the number on the same square on the invariant grid, no matter what legal move you make, the sum of the products remains in the same residue class mod 3

[ornate thunder]

the invariants derived from these two grids are independent

As can be proved with the invariants, the graph of all positions is not connected. A brute force search yielded the following results:

there are twelve components. the first one and the last three have the same invariants, but are still not connected.

the first one is just the all-white board

the last three are almost exactly three times smaller than the other components

i'm trying to figure out what the reason for this "split" is

[ornate thunder]

Rules are as follows:
Clicking a green cell cycles it and orthogonally adjacent cells according to green -> red -> white
Clicking a red cell cycles it and orthogonally adjacent cells according to red -> green -> white

[sour sinew]

i am quite confused about what the rules even are

oh you explained

[brave surge]

https://cdn.discordapp.com/attachments/624314920158232618/1119245815270080655/390895986106564609-20.png

Can someone tell me how they'd go about solving this?

I don't really think it's worth making a help post over

[sour sinew]

is that for help in school/university

[brave surge]

No

[sour sinew]

alr this is fine

[brave surge]

It was brought up in general and I asked how to solve it, but they just memed and didn't help at all

So I thought maybe general wasn't the place to take it seriously?

Idk I'm new here

[ancient helm]

Thats just Coffey

[brave surge]

Oh

[sour sinew]

coffey is the only one to meme?

[ancient helm]

Not the only

[brave surge]

Idk, the one-word answers and "it's just basic trig" kinda threw me off

But yeah, I just wanna know how to solve it. I'm curious

[ancient helm]

Is there a double angle formula for sec?

[sour sinew]

well yeah

[brave surge]

I mean you could interpret it as 1/cos and cos does have a double angle

I was thinking of going that route but I'm not sure it helped

[sour sinew]

sec(2x) = 1/(2(1/sec(x))^2 - 1)

i do not think it helps

sec(8pi/7) = -sec(pi/7)

and sec(4pi/7) = -sec(3pi/7)?

[brave surge]

I did go that route actually

https://cdn.discordapp.com/attachments/1119253096120463470/1119254215487918141/358822645225095170.png

It is equivalent to this, I'm pretty sure

[sour sinew]

yep

[brave surge]

Apparently the answer is -4

[jagged basin]

So I’m running into an issue and I don’t know why it’s occurring where in theory these should be the same answer but after doing the calcs several times they are different and I don’t know why.

I have two speeds basically and trying to find the median or mid speed or whatever for the time frame directly in the middle.

First speed is .33 and the other is 1 speed. Now if I figure out the time frame for those speeds to cross a distance, and then figure out the middle number I get a value like… 6 or whatever.

But if I go middle speed of .665 over the same distance for the time gram I get a value of 5…

Why?

[sour sinew]

there is a difference between mean speed and mean time to go a given distance

mean*

one of those is the harmonic average

[jagged basin]

It’s weird… like 10/.33 and 10/1 take those numbers and get the middle you get 20.15. But if you take 10/.665 you get 15.0375

[jagged basin]

Not sure what that word means

[sour sinew]

indeed

those 2 are in general not equal

[solar quarry]

This is quite a peculiar fact.

[sour sinew]

like
if you go at 1 m/s and someone goes 2 m/s
the average speed is 1.5 m/s but the speed needed to take the average time to go a certain distance would be 1.333333m/s

it biases to the lower one

this leads to the famous paradox where you run around a racetrack and the question is asked, how fast would you have to run another lap to have an average speed of 2x as much

[jagged basin]

But… why…. Thats… weird

[sour sinew]

the naive answer is 3x as fast

3 + 1 over 2 is 2

however that is not correct

[jagged basin]

So… which is better to use to determining a mean/average time frame for speed stuff? Middling the speed or middling the time?

[sour sinew]

depends on your use case?

if you're comparing cars and gas mileage or something

this comes into play

i watched a video at least where that was a factor

[solar quarry]

Average speed of 1km/s and 1m/s for 1km is close to 1km/s,
But average time is closer to 1000sec, so based on this you get 1m/s.

[sour sinew]

wouldnt it be close to 0.5 km/s

and ~2 m/s harmonic average

[solar quarry]

Ohh

Right, I miscalculated

Still, quite a difference

[jagged basin]

How fast something can react. I know this thing can react to time frames between 10m/.33c and 10/1c time frames consistently. So figuring out the middle to use.

[sour sinew]

yep

[solar quarry]

And gives a hint why such difference happens.

[sour sinew]

indeed

[jagged basin]

It’s dumb and nerdy I know

[sour sinew]

hmm

is that c as in the speed of light

[jagged basin]

Yes. It gets weird… I’m a nerd and I like trying to calc video game feats

It helps me relax during times of stress

[sour sinew]

so the question is
would you use 0.66c or .5c

i have no idea

you could go in the middle

[jagged basin]

Wouldn’t middle of .33c and 1c be .665

[jagged basin]

No it’s the thing from above

[sour sinew]

didnt i say that-

[jagged basin]

The middle reaction speed if I do the time frame between the 10/.33c and 10/1c is basically an event happening in something like… 6.somethingE-8 seconds

But if I do 10m/.665c it’s close to 5E-8 seconds

[sour sinew]

here the time frames are between 30 and 10

so the middle reaction time would be 20

i think that actually makes more sense than giving the average in terms of speed and distance

[jagged basin]

30.1 something something…

But why would that be more accurate than the time frame average?

Like you said it’s sorta a math paradox

[sour sinew]

the question is, which seems more reasonable:
average reaction time for something going a certain distance?
or the average, like, distance something goes before you react?

this is a subjective

thing

[jagged basin]

Average reaction time

I think…

[sour sinew]

well then it would be 10/0.5c

[jagged basin]

But that’s not making too much sense in my brain… why did I stumble into a paradox math thing

[sour sinew]

math is everywhere

[jagged basin]

As like in my head it doesn’t make sense that you would go .5c rather than .665c for the average for what a character would be able to react to if the speed ranges they react to is .33c and 1c

So was I right to do my initial thing of
((10/.33c)+(10/1c))/2?

[sour sinew]

idk

[jagged basin]

To get the more accurate time frame stuff?

As that’s finding the median time frame between the two speeds. While 10/.665c is the median between the two speeds… I think I’m trying to figure out speed relative to something relative to the character so I think I got to go the route of the speed median rather than time median.

But that paradox is weird… what’s the paradox called?

[sour sinew]

probably doesnt have a name

[jagged basin]

Does it work practically?

Like have people done the whole drive at 1 kph see how long it takes to go 1 km, same with 2. Then doing the math for the average time frame between the two, and then drive the median speed of 1.5 kph and see if it lines up?

[jagged basin]

Like this math is kinda confusing me…

[sour sinew]

well no, no point

1 kph 1km is 1 hour
2 kph 1km is 30 mins
average time is 45 mins
1km/45mins = 1.333 kph

[jagged basin]

That’s… weird…

So wait going median speed then makes you go faster than the average time?

That’s… weird…

[sour sinew]

there are 2 averages and for whatever quantity you take the mean with, the other average will bias lower

very weird

[jagged basin]

Then… huh…

I’m then still not sure which average to use to determine the proper time frame of reaction. Because determining speed is the big thing here…

[sour sinew]

the 2 methods give 1.5 kph (mean) and 1.333 kph (harmonic mean)
if you look instead at average time, the 2 methods give 45 mins (mean) and 40 mins (harmonic mean)
harmonic mean is always lower

[jagged basin]

For what I am doing

[sour sinew]

hmm

so

the player reacts on the same frame as something 10 m away?

[jagged basin]

Basically lighting attacks or light based attacks the player character can easily dodge and or react to something that is 10 meters away. I could technically math it out to be closer but 10m is easiest

[sour sinew]

well that is just impossible

lol

[jagged basin]

It’s video games

Video game characters can punch a moon in half

[sour sinew]

yeah

but this isnt about reaction speed

this is about they cant possibly know the light attack is happening until its on them

unless

light moves slower in air

[jagged basin]

They dodge lasers and such.

You got Jedi out here blocking those by the hundreds

[sour sinew]

the jedi just stop bullets

i. assume

[jagged basin]

Blasters in SW are said to approach the speed of light. Star Trek straight up says speed of light

Actually jedi have harder time blocking bullets

[sour sinew]

wow

wh

[jagged basin]

Because they go molten and hit their body

[sour sinew]

lesson learned if you face a jedi bring a gun

[jagged basin]

Madalroians use buck shot specifically to counter jedi

And it works most of the time because muscle memory from jedi

That’s a canon thing btw look it up. It’s pretty funny

But yeah I think gonna just put their reaction speed at .665c and sigh at weird paradox

Kinda wished I knew how fast people “saw” as the character above can react to things happening using 10/.665c thing in a time frame of 5e-8 seconds. But not sure how much faster something would have to be to be invisible to them.

Humans can see things in a time frame of about .022 seconds.

.25 is their reaction… wait a second…

So humans for visual can see things about 11.36 times faster before they can react. At least to visuals

So that reaction time got to multiple it that much for for what a character can see

[sly burrow]

Why do clones and stormtroopers wear their white chainmail if it doesn't protect from blazer shots?

[normal arrow]

i think its more of a uniform than something to actually protect the stormtrooper

[sly burrow]

In priquels Palpating worked on plates for soldiers of more durability made from godzilla

[normal arrow]

made from what now

[sly burrow]

If you watched Clone Wars 😂 you have to memorise that beast was brought to Courusant

[normal arrow]

bro i watched some star wars movies a long while ago i didnt know they had added godzilla 💀

[sly burrow]

Dude star wars is iceberg. Movies are top and comics/cartoons/fanfics/encyclopedias are base

[normal arrow]

damn

[sly burrow]

Palpatin's plan was to mix cloning tech of Kaminoans, skin of Godzilla and biskar stell of mandalorians

[brave surge]

How the hell did Lagrange think of Lagrange multipliers

It’s insane to me how you’d come up with something like that with no way to visualize any of the math

He had no way of easily seeing the graphs and going “Oh hey look, their gradients would be the same”

[dusty swallow]

Think about someone like Riemann

He had no way to visualize what he was saying

Now we can make cool ass pictures with hard computations and higher dimensions but he literally just had paper and pen

Yet he came through and basically invented a new branch of mathematics

[solar quarry]

Some people can visualize internally, like, they can imagine some partition of 4d objects.

[dusty swallow]

But to be fair, Lagrange multipliers also have a visual understanding

Maybe not as intuitive as other stuff in math but it’s not out of the blue

[solar quarry]

What are Lagrange multipliers?

[dusty swallow]

They are commonly used to find minima and maxima of a function with additional constraints

[solar quarry]

https://en.wikipedia.org/wiki/Lagrange_multiplier This?

[dusty swallow]

Yes

I watched a good vid on it a while ago

If u want I can find it

[solar quarry]

Perhaps I am naive but it just looks like.. using contours for finding local minima/maxima in constrained case

And contours are more or less easy to visualize.

[dusty swallow]

Do u mean by parameterizing the constraints and then solving it in R rather than R^n?

[solar quarry]

I mean, we do it for R case then generalize to R^n

[dusty swallow]

I mean the thing that in my opinion not directly is intuitive, especially when u don’t have a good image of it, is that they are parallel

[solar quarry]

Parallel? Hmm

[dusty swallow]

I’m talking about $\nabla_{x,y}f = k\nabla_{x,y}g$

[vivid gulch]

Dappity Doppity Doo

[solar quarry]

Yea I do not know why this seems obvious to me for 2 dimensional case, and it seems obvious that it generalizes to higher dimensions

[urban echo]

how to rotate graph function

y=f(x)

[normal arrow]

replace x and y with their rotated analogs and solve for y

i actually did a desmos demo earlier

https://www.desmos.com/calculator/ycik3bjizm?

https://www.desmos.com/calculator/b1tqer39fv

the problem is, however, that you get a set of functions

(or implicit equations if you're LAZY)

because graphs do not pass the vertical lines test

[urban echo]

thanks

that is pretty complex to me

[sly burrow]

Why mandalorians repeat without end:" That's the way"? I suppose it is part of code of conduct. But why Sabin Wren doesn't use such expression, although she must be young and rebel ?

[lethal wigeon]

@elfin kraken ok

Just a min

[elfin kraken]

with what you need help?

[lethal wigeon]

Sorry to make u wait

I needed help in polynomials, like the basic thing about it

I got an exam in a few days and haven't even touched the chapter

[elfin kraken]

i am sending you a video

[lethal wigeon]

Coordination and number system was all easy

Ok

[elfin kraken]

watch that and then go through NCERT

[lethal wigeon]

Yes

[elfin kraken]

and write whatever they say like make very short notes

[lethal wigeon]

Ncert cover concepts well

Ok

[elfin kraken]

and do the questions what they show

[lethal wigeon]

Also

Random request

[elfin kraken]

after that do NCERT exemplar also

[lethal wigeon]

Examplar?

[elfin kraken]

https://ncert.nic.in/pdf/publication/exemplarproblem/classX/mathematics/jeep202.pdf

this thing

[lethal wigeon]

Ok

[elfin kraken]

just do the problems from this book

then you are good

😄

@lethal wigeonhttps://www.youtube.com/watch?v=a4Maqqxb1wI&t=1518s&pp=ygUUY2xhc3MgMTAgcG9seW5vbWlhbHM%3D

this is pretty good

[lethal wigeon]

Ok, i have the book

[elfin kraken]

now , i have to go

bye

[lethal wigeon]

Ok ig

[terse pebble]

Hello, in the lambda calculus you have (lambda x expression) for an anonymous function. Could you instead have (lambda positions expression), where the positions is a list of positions in the expressions to substitute into, so you don’t have to deal with problems like variable name conflicts.

[strange lance]

i'm trying to write a script that evaluates how effective various card shuffling techniques are. one way i'm considering doing this is, for a deck of N cards, labeling all of the N! possible permutations with a number between [1. N!]. then, for a given shuffling technique, run it a ton of times and see how uniformly the resulting decks' labels sample [1, N!].

the problem is, i can't think of an efficient 1-to-1 way of labeling the N! permutations. i briefly looked into symmetry groups hoping to find a cyclic generator g such that every permutation is equal to some g^k, and hence k would be my label, but no such luck. any ideas?

[sour sinew]

you could define it as (position of N)*(N-1)! + (position of N - 1 if N is removed)*(N-2)! + (position of N - 2 if N, N - 1 are removed)*(N-3)!... + (position of 2)
where the positions go 0, 1, 2.... N - 1

this is splitting the N! possibilities into N groups, then splitting whichever group its in into N - 1 groups, etc

[strange lance]

oh huh, this works great! i had to draw out a tree to make sense of the formula, but this is a really clever scheme

[versed comet]

just did a proof of the product rule and the proof for it is so beautiful

[brave surge]

Differentiate the IBP formula

🧠

[pulsar beacon]

[brave surge]

Yesterday I tried solving a physics problem I posed myself like last year, and I had no idea just how complicated it really is

I tried solving it back then not knowing what it really was, and had no idea why it didn't make sense, but now I tried again, and uhhhh...it's a second-order non-linear, most likely non-separable differential equation by the looks of it

So yeah, checkmate, no chance

This is a piece of my fruitless attempt. Ignoring friction, the opposite leg of this triangle starts at an h0 and increases at a constant dh/dt. I want to find an expression for what velocity the box would move at once it reached the bottom

https://cdn.discordapp.com/attachments/1119253096120463470/1121831742463033464/358822645225095170.png

This is what I reasoned must be true, but the height is a function of time as well, so I have absolutely no idea how to analyze this properly

[brave surge]

Update on that, I realized I was wrong about the differential equation itself

https://cdn.discordapp.com/attachments/1119253096120463470/1122157144389718036/358822645225095170.png

It would actually be this, which is even worse

[short zodiac]

Hey, I was wondering how to do something with probability. For instance there is a game with six players who are shooting a ball into a goal who score different points and have a chance of not attempting. Only one can score at most each trial since theyre shooting a ball. Each attempt from a player is a score.

Player B scores 36 points when they score,
Player C and Player E score 33.6 points when they score
Players D and F score 28.8 points when they score, ```
```Players A, D, E, and F attempt 5% of the time, 
Player B attempts 20% of the time, 
Player C attempts 10% of the time. ```
What is the formula for finding the number of attempts that should be tried in a game so that there is a 75% chance of scoring at least 100 points, and whats the calculation for the standard deviation?

I know how to do this for one player at a time like bincdf but i do not know how to combine the averages

[sour sinew]

those 40 + 40 + 20 are disjoint, then?

[short zodiac]

Yes. They’re independent but only one can occur at most

[sour sinew]

so like pick a number from 1 to 10

[short zodiac]

During each trial

[sour sinew]

and if it's 1, A, 2, D, 3, E, 4, F, 5-8, B, 9-10, C

[short zodiac]

I probably shouldn’t have had them sum to 100% bc that’s confusing

[sour sinew]

yeah in this case it is guaranteed to be at least 100 points after only 4 turns

[short zodiac]

i edited the chances to make it less confusing hopefully

now it sums to 50% not 100%

im more interested in the formulas to determine the averages

[short zodiac]

i know how to calculate the number of trials needed on average for 75% chance to get 100 points at the given rate if only one player is playing but i dont know how to average it across them because they all score different points. how do i combine the averages?

[sour sinew]

for at least 75% chance?

[short zodiac]

yea

it finds how many trials must be done on average to have a 75% chance of succeeding with 100 points but i only know how to apply it to one player at a time

and not all of them at once

if j is the probability of attempting for a specific player and 1-j=g then the probability that they dont attempt on the trial "n" is "g^n". so 1-g^n is the probability they score.
so if h is the number of times that player needs to score to get 100 or more points then we can use 1-g^(n) > h to find the number of trials we need to attempt. So its log format is n>log g (-h+1).

how do i apply it to all players at once for an average and standard deviation?

i could also do the same with a sequence of binomial distributions or or if i wrote the binomial distribution in summation form but

idk how to combine it for the average

[sour sinew]

epic distribution after 1m ...thingys

number of times it got to 100 points on that turn

i guess you can find the exact expected distribution of points after a certain amount of trials

but what we really want is the distribution of trials after a certain number of points

[short zodiac]

yeah, im sure theres a way to just pull the expected number of trials with the formula without simulations though

do you think it would be easier for me to simulate a bunch and just store the base data like a normal distribution chart bc i dont know how to do it mathematically?

[short zodiac]

also this does seem v epic, i assume bottom is the expected number of trials to reach 100 points and the left is how many took that many?

how did you combine the averages for each player to put it in a simulation like that?

[short zodiac]

ah so true thanks ill fiddle around with some simulations and see if i can get it working in google sheets for the data im working with

easier than making formulas

thank you :)

[short zodiac]

fantastic

so this means array starts at 0 trials done right?

because player a can score 52.8 meaning the third is trial 2?

[sour sinew]

yeah

the 3rd is the 1/400 chance

should actually be 2500
pretty close

[short zodiac]

Yay :)

[brave surge]

new Float32Array(n)

[fresh marlin]

If we are generating an income of 250$ every 6 seconds and we can turn every 1$ into 0.04 income increase(so for example after spending 100$ we are going to get 254$ every 6 seconds). How can I calculate the fastest way to reach 20000$ if we are starting from 0$?

[nocturne spear]

why does the values match btd battles cash values

[fresh marlin]

idk😆

[sour sinew]

my intuition tells me the way will be

spend every 1$ as soon as you get it

then there will be a point where you stop spending money entirely and ride the income to 20000$

so maybe you can find and solve the maximization equation

[fresh marlin]

Yeah I figured out that much too and tried to make a formula to calculate the time needed but it indeed went wrong cuz the formula I made assumes I get the income upgrades instantly(i mean before even having the cash for it)

[sour sinew]

wdym

once you get the 1$ it takes time to go to the store?

[fresh marlin]

nope I meant my formula adds up to the income before even having the cash for those upgrades wait a sec

so what I thought about was

time=(goalCash+(income-250)/0.04)/income*6

so this formula works like it adds the price to the goalcash so if 20k$ is the goal then the upgrade cost is added to it

income is a variable that I changed from 250 to 2000, 1 by 1 using a simulation

and I did a minimum search

but it resulted in giving me 2000 being the most ideal income which is wrong cuz I cant instantly upgrade the income to 2000

[sour sinew]

if you have a certain rate of income X and you just got to that so you have 0$
then you are going to take 20k/X seconds to reach $20k
the question is, when is it equally good to spend another 1$ and go faster or go straight to 20k
so we have in the spending case 1/X + 20k/(X + 0.04) = 20k/X
X + 0.04 + 20kX = 20k(X + 0.04)
=>
X = (20k - 1)(0.04)

then, this implies that getting to 800 is best

or 799.96

one of those 2

but that could be a minimum or a maximum

[fresh marlin]

one thing I dont understand is what is that 1/X

[sour sinew]

how much time you will lose just by getting from ur point to the 1$ spend

because that's a time loss

small one, but still

[fresh marlin]

yeah but 1/X would be really small that's why it is suspicious for me like if the income is 800 which u just said then 1/X is 1/800 which is added to the 20k/800 sec

[sour sinew]

suspicious?

you have 2 options when your rate is 800 $/s

take 1/800 + 20000/800.04

or just go 20000/800

if you don't factor that small time in, more rate will always be better

which is wrong

[fresh marlin]

I just meant that adding 1/800 to the num doesnt really make any difference that's why it was confusing why it is there

but I see now

thank you haha this is genius

[sour sinew]

of course if you're doing this in a video game context you also probably want to take into account your reaction speed and things

[sour sinew]

this is also 4800 $ every 6 seconds

[fresh marlin]

the funny thing is that getting to 4800$ income would take approximately 455 seconds and with 4800$ income it takes 25 seconds to reach 20k$ so it is 455+25=480 seconds. Whereas in game you start with 250$ income and 20000/250 is 480 seconds also lol

cash=0
time=0
income=250
for i in range(80):
    print(f"time={time}, cash={cash} income={income}")
    time+=6
    cash+=income
    income+=cash*0.04
    cash=0

[sour sinew]

interesting

[azure aurora]

Hi, are there any people who are into complexity theory, boolean algebra or binary decision diagrams? (theoretical CS)

[lethal wigeon]

$A\coloneqq {a \in \mathbb{Z};|; {-5}<a<5}$
\newline
$A={-4,-3,-2,-1,0,1,2,3,4}$

[vivid gulch]

vazpera

[sour sinew]

what's this

[lethal wigeon]

set theory

[sour sinew]

ik

what's it for

[lethal wigeon]

just testing my knowledge

[peak sentinel]

hello