help-27

[karmic moon]

Oh srry, here it is, do you see it well¿

[fluid stag]

,rccw

[fluid stag]

oh ok I see where I fucked up

I also see one mistake

the sign of your first b is wrong. it should be negative

also, there is only one solution to this question

[karmic moon]

Fs?

well, the discriminant is greater than 0 so I don't think so

[fluid stag]

not sure what this means, but you have x^2 = 9 - 3x, which means x^2 + 3x - 9 = 0

[fluid stag]

but do you remember your original equation has a square root and thus a domain limitation?

[karmic moon]

TRUE

Mbbbb

[karmic moon]

yes¿

it is um

[fluid stag]

the radicand cannot be negative. and because you have a principal square root, there's another domain limitation from there too

[karmic moon]

Principal square root¿ wdym

[fluid stag]

positive square root

you know how when you take a square root, you do +/-?

this square root was given to you from the get-go, so it's the positive one

aka the principal square root

[karmic moon]

I don't get the get-go thing, srry

[fluid stag]

get-go = from the start

you're given the square root without having to square root both sides

so this square root is a positive square root

so no +/- involved

which you correctly accounted for

but, at one point you will get x = sqrt(9 - 3x)

since the sqrt is positive or 0, x must also be positive or 0

this is the second domain limitation

[karmic moon]

Yes

[fluid stag]

so combine both of you

....fucking phone

combine both of your domain limitations. what do you get?

[karmic moon]

That x is positive or 0? and also less than 3 i think

[fluid stag]

yes!

so check the value of both solutions

one of them will faill this limitation

reject that

[karmic moon]

ok I'll do 👍🏿

[fluid stag]

also don't forget your sign on the b

[karmic moon]

Yes, tysm

[fluid stag]

nps, glad to help!

anything else you would like to ask though?

[karmic moon]

For now, no tnks

[fluid stag]

aye, then you may .close the channel when done. all the best for the rest!

[karmic moon]

gb

.close

[devout snow]

Channel closed

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[devout snow]

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[coral zephyr]

Hello I had a question regarding vectors

Can someone explain to me intuitively the logic behind doing terminal point - initial point ? How does that give you the vector interpreted at the origin ?

Also, how is adding back the terminal point give you the vector back at its position ?

[coral zephyr]

🤔

[polar chasm]

the blue vector is pointing towards the initial point

red vector is the one we are interested in

Now to translate the red vector to the origin, we essentially need to slide it along the blue vector

kinda like this

notice that what we did is we essentially added the dashed blue vector to the red vector

but the dashed blue vector is just - blue vector, so - initial

so the orange = terminal + (-initial) = terminal - initial

This is also how it works for real numbers kinda,
5 - 1 is the distance, starting from 1 moving towards 5

https://www.youtube.com/watch?v=PIo6C2U1GEY

[coral zephyr]

Oh wait so this whole time terminal point - initial point was just dealing with vectors?

[polar chasm]

The 2nd part of this vid is relevant too and i find it quite interesting

[polar chasm]

you could interpret points as vectors starting at the origin

[coral zephyr]

Also how would you describe that adding back the initial point gives you your original vector in it original position

[polar chasm]

in general, adding corresponds to shifting / translating

Like when I do 3 + 5, i shift 3 by 5 places to the right

[coral zephyr]

Yes but what’s the vectors initial points now

[coral zephyr]

Like I can see that adding your blue vector give the red back but what are the initial points ? Wouldn’t they be gone

[polar chasm]

When I add the initial point, i again just shift it

[polar chasm]

wdym by that?

[coral zephyr]

Like if you had two pints
(a,b) (c,d)

The vector interpretation from the origin is <c-a, d-b>

Now adding back the initial vector gives you <c,d>

Or does that not matter ?

That was kinda dumb ngl

[polar chasm]

you can think of <c-a, d-b> as an arrow connecting (a,b) and (c,d), it's the displacement vector

and yeah, since it's obtained by doing
(c, d) - (a,b), when you add (a,b) back in you end up back at (c, d)

[polar chasm]

Try watching "the geometry of subtraction" part in this vid

[coral zephyr]

Thank you very much I’ll check it out for sure

But one last thing

So is it that we can interpret point subtraction as vector subtraction or are they inherently vector subtraction

[polar chasm]

If you wanna be formal, you should be clear about what is a point and what is a vector

but if you just wanna understand it intuitively, it's often helpful to be a bit more flexible with the interpretations

[coral zephyr]

So is terminal - initial inherently vector subtraction / addition or is it just an interpretation? Are you saying it’s an interpretation and not inherently that way?

[polar chasm]

if those are points, then its a point subtraction

but you can interpret the result as a vector, and its more helpful

[coral zephyr]

You mean the points as vectors ?

Does the video go over geometry of point subtraction

[devout snow]

@coral zephyr Has your question been resolved?

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[elfin cloak]

I need help on optimization for calc ab 😭

can someone try to solve for this and see if their answer matches mine?

[uncut crow]

amazing handwriting

[fair juniper]

why did 2.25 become 2.5

[elfin cloak]

where

OHH

[green crypt]

you're not admiring the artistic value as well

[elfin cloak]

HELP

[green crypt]

yes thats why we are here

[uncut crow]

[elfin cloak]

I DIDNT NOTCIE THAT

[fair juniper]

for some reason it fixes itself on the last couple lines

[green crypt]

wait yeah

lol

[elfin cloak]

yes ive been stuck on this for the past hour

so ive been going back and forth

how did i fix that

😭 😭

[fair juniper]

ah

the fact that there is no minimum means the boat is always optimal

[elfin cloak]

huh

[uncut hemlock]

yeah if the derivative doesn't hit zero you just check the endpoints

[elfin cloak]

and then

so at the point 3.2

[uncut hemlock]

yeah compare the cost at 3.2 and 0 to see which is lower

[elfin cloak]

.close

[devout snow]

Channel closed

Closed by @elfin cloak

Use .reopen if this was a mistake.

[devout snow]

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[obsidian plank]

can anyone example why the graph is starting at the minimum instead of the maximum ?

[obsidian plank]

I thought cos graphs always start at the maximum unless the coeffiecient of the function is negative

[obtuse bay]

x-pi, when x = 0 is equal to -180

degrees

or -pi radians

and cos(-pi) is -1

so 3cos(-pi) is -3

by putting -pi into the function, you have shifted the graph right by pi

if that makes sense

[obsidian plank]

oh I see so it just looks like its starting at the minimum but it really just shifted over by pi

[obtuse bay]

yes

so the max that "should" be at 0

is now at pi

[obsidian plank]

ok got it but why when I add pi its the same exact wave

[obtuse bay]

yes, because the function repeats every 2pi

and the difference between your 2 lines is 2pi

so they are the same

try doing -pi/2

and +pi/2

[obsidian plank]

just did that lol

get ur gay ass crypto scam out of here

[obtuse bay]

they will look exactly the opposite

[obsidian plank]

yep

[obtuse bay]

thats not completely opposite

go -pi/2 on the top one

then it will look perfect

but you get the idea

[obsidian plank]

yea now its opposite

[obtuse bay]

yes exactly

now do you see how the top one is right by pi/2

and the bottom one is left by pi/2

thats it basically

[obsidian plank]

mhmm alright thank you

.close

[devout snow]

Channel closed

Closed by @obsidian plank

Use .reopen if this was a mistake.

[devout snow]

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[hazy leaf]

-# read the chain of replies

i want to understand how to derive these, but i cannot. what even is K (the capital letter in the paper)?

-# and to answer, "constructible" as in "constructible in powerpoint"

[supple knot]

do you mean $\Gamma$

[woven radish]

riemann

[hazy leaf]

no

[hazy leaf]

tl;dr — we can construct a lot of things in powerpoint, including the perimeter of ellipses. we're trying to see if this can get us to other interesting numbers — the equations listed tells us we can have Gamma(1/4) and Gamma(3/4)

[supple knot]

tryyy #advanced-number-theory

[devout snow]

@hazy leaf Has your question been resolved?

[devout snow]

@hazy leaf Has your question been resolved?

[grand edge]

They are very difficult to derive

[hazy leaf]

like, the paper seems to say "this is derivable", but i don't see how...

[hazy leaf]

does this mean that if i have $a$, $b$, and $p$, i can solve for $\frac{\Gamma(1/8)}{\Gamma(5/8)}$?

[woven radish]

ijo Sani

[grand edge]

Well yeah lmao, do you know who authored the original paper

[hazy leaf]

:sigh:

[grand edge]

Well sure, but you would get an elliptic integral in terms of gamma functions

[hazy leaf]

.

[grand edge]

Gamma(1/4) and Gamma(3/4) have no elementary closed forms

[hazy leaf]

well, i don't know, but judging from context, ramanujan

[grand edge]

You can relate one to the other with the euler reflection formula

[hazy leaf]

If we construct ellipses of width $1$ and height $1$, width $4$ and height $4\sqrt2$, and width $3-2\sqrt2$ and height $1$ and let their perimeters be $x$, $y$, and $z$, we can construct $\Gamma\left(\frac14\right)=\frac{y-(\sqrt2+1)z}{\sqrt x}$.

[woven radish]

ijo Sani

[hazy leaf]

that's not a problem, since we can solve elliptic integrals in powerpoint anyways

-# assuming powerpoint ellipses are actual ellipses, which they're not but we don't care

[grand edge]

what do you mean

[hazy leaf]

in powerpoint, you just solve them by... constructing an ellipse, and taking the perimeter

[grand edge]

The perimeter will be in terms of elliptic integrals

[hazy leaf]

but we can just take the perimeter

trust me (or i infodump you)

[grand edge]

It's been known that the general perimeter of an ellipse has no closed form

[hazy leaf]

no closed form ≠ not constructible

[grand edge]

Other than specific nice values having gamma values

[hazy leaf]

ok um

like, it's a known we can construct the length of the perimeters of any curve in powerpoint (again, trust me or i explain)

so i'm trying to see how we can milk that to get other interesting stuff

(e.g. unleashing the length of a parabola (or cubic bezier) gives you ln values)

[grand edge]

Well yeah, but this is an ellipse, the general perimeter of one has no nice closed form

[hazy leaf]

i'm slightly confused, are you doubting that we can construct perimeters of ellipses, or?

[grand edge]

Idk how this constructing thing works but feel free to show me

[hazy leaf]

ok

[typing]

to construct perimeter of arbitrary curve, we connect it with a straight line, use dashes in line formatting, do cursed format changes to make that into a shape, then calculate the length of the original curve by counting number of dashes, multiply by dash length plus gap of each, minus any residue on the straight line

there @grand edge

-# specifically the cursed format changes is copy, paste as enhanced metafile, delete blank objects, copy, paste as svg, convert to shapes, or something along the lines of that

[grand edge]

what makes you inclined to believe that will give you a closed form for the ellipse? have you tried it?

[hazy leaf]

oh, it's not a closed form

i'm just able to straighten the curve in a sense, not that i can get a closed form expression out of it

-# e.g. i can construct a linkage which solves x^5-x-1=0, but that doesn't mean i can derive a closed form for the solution

and therefore, i'm only claiming that, hence, Gamma(1/4) is constructible, not that it has any closed form

[hazy leaf]

therefore, i also do not understand what you mean by "have i tried it" — tried which part?

[grand edge]

gamma(1/4) is not constructible and it has no further closed form

don't all constructible numbers have a closed form

[hazy leaf]

no, that's just not true

simplest example i can think of, if you restrict the notion of a closed form, is its easily to construct cos(42 degrees)*, but it doesn't have an algebraic closed form
-# *: if you want i can show you

[hazy leaf]

^ this is "constructible" within the sense of compass and straightedge

i'm talking about "constructible" within the sense of powerpoint
-# and earlier in one sub-message, "constructible" within the sense of linkages

[grand edge]

Constructible within powerpoint 💀

[hazy leaf]

lol

its the dr. zye video, uh lemme send

https://www.youtube.com/@DrZye

[grand edge]

Okay... regardless I'm not bothered enough to try and construct gamma(1/4) in powerpoint. There's literally no closed form. You can find a closed form in terms of perimeters of ellipses but those perimeters of ellipses will have no closed form either (other than in gamma functions.. and then you're just going in circles)

Someone else can help you with that

[hazy leaf]

i don't need help with the actual construction, i just want to know if i can express gamma(arbitrary rational) as some (finite) combination of perimeters of ellipses

i'm probably committing an X-Y here but i believe it's for good and not evil

[grand edge]

Oh sure that's definitely possible

[grand edge]

You could probably reflection formula and legendre duplication the hell out of this to get something in terms of gamma(1/4)

[hazy leaf]

like, from this, gamma(1/4) is obviously achievable

[grand edge]

Well the first and last results are definitely

Just use reflection formula

[hazy leaf]

yah, so just do some stuff with it

but i wonder if this goes to any gamma(rational)

[hazy leaf]

i see, so applying Legendre duplication formula allows me to express everything in terms of gamma(1/8), and i just solve

[hazy leaf]

how likely is it that something nice exists for any rational x, something something

[devout snow]

@hazy leaf Has your question been resolved?

[devout snow]

@hazy leaf Has your question been resolved?

[rain summit]

He released part 2 btw if you didn't know

[hazy leaf]

i did :-)

[grand edge]

what do you mean?

[hazy leaf]

means i can express Gamma(rational) as some equation, allowing perimeters of ellipses

ooh, i also have perimeters of a portion of an ellipse, where said portion goes from 0 degrees to theta degrees, and theta can be rational, rational (potentially times pi), trig of rational (potentially times pi), and inverse trig of rational (potentially times pi)

i.e. (**incomplete **elliptic integrals of the second type)

[sand wagon]

Hello

[hazy leaf]

hi

[sand wagon]

If you dont mind, could you help me to very briefly illustrate a geometry problem? It's about shadows and sun inclination stuff

[hazy leaf]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[sand wagon]

#help-2

[dense tangle]

woah, didn't expect to see you here, i swear this was complete coinsidence. very shocking! 😭

[devout snow]

@hazy leaf Has your question been resolved?

[stoic thorn]

1+1?

[pliant carbon]

3

[mystic scarab]

Do not troll

[mystic scarab]

1. There you go! Or 10 if you prefer

[devout snow]

Channel closed

Closed due to timeout

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[rocky oriole]

@devout snow

[next saddle]

ok, lets just do 1A first

[rocky oriole]

Ok

[next saddle]

so if i asked you to factorize $x^2+2x+1$, how would you do that?

[woven radish]

Francium

[rocky oriole]

Wait let me do it in copy

[next saddle]

ok, good! now if i gave you the task to expand $(x+k)^2$ where k is some number, what would you get?

[woven radish]

Francium

[next saddle]

close... you're missing a coefficient on your second term

[rocky oriole]

Damm

2

[next saddle]

yep

ok, now going back to the question. The first two terms look like theyre the start of an expanded square, right?

you just need the constant

[rocky oriole]

Yep

[next saddle]

so what do you need to get it in this general form?

[rocky oriole]

-1 ig

Is it?

[next saddle]

why is the 1 negative?

[rocky oriole]

-8
-(-1+9)=-8

[next saddle]

yes, but with that negative it becomes positive

alternatively you can see the -8 as (-9+1)

[rocky oriole]

Oh

[next saddle]

so which number goes with which variable?

[rocky oriole]

+1

[next saddle]

so the 1 goes with the ___ and the -9 goes with the ___ (put x or y in each blank)

[rocky oriole]

X+1 and y-9

[next saddle]

so then how would you factor this whole thing?

you need to put it in the form $a^2-b^2$, where a, b are some expression containing x and y

[woven radish]

Francium

[rocky oriole]

Wait iam in copy

[uncut hemlock]

watch the signs on line 2, -(y-3) should be -y + 3

[rocky oriole]

I didn’t understand

Oh

[rocky oriole]

Thanks

[rocky oriole]

.close

[devout snow]

Channel closed

Closed by @rocky oriole

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[frail beacon]

are
lim x->inf x
and
lim x->inf x^2
equal? or are they not equal because both limits DNE?

[lost laurel]

They both diverge to infty

if their limits were equal $\lim_{x \to infty} x^2-x =0$ would be true, which it isn't

[woven radish]

wai

[lost laurel]

so they aren't equal

I think

[willow helm]

It depends

If you consider infinity as a 'value', then they are both infinity, so yes.

But otherwise you are comparing two things which don't exist

[frail beacon]

i think we say limit does not exist according to our syllabus

so we cant compare two things which dont exist

[willow helm]

Yes, exactly

In that sense, as per usual, infinity is a concept

And not something you can really compare

[woven vale]

like you said, we can't really equate two things that don't exist. but often we are interested in the growth rate of two limits that go to infinity.
i.e., yeah these limits both go to infinity, but which one gets there faster? that's pretty much all we care about since it helps us solve quotient limits

[uncut crow]

they are equal if you include infinity in your number system (which there are reasons to do, and reasons not to, depending on what you’re doing). if those expressions do not exist, then no they are not equal

[mortal tendon]

can we combine these limits if they are both DNE

[uncut crow]

no

[sharp moth]

Even if we include infinity doesnt mean theyre equal, how do u know they diverge to the same thing, infinity isnt a fixed quantity

[mortal tendon]

the analogy of x^2-x being zero if they were equal isnt true then right

[uncut crow]

if we include infinity then they are both equal to infinity, so they are equal

[mortal tendon]

yea

[uncut crow]

no because the limit statement you’re trying to use would be stated only for limits that are real numbers, not when limits are infinity

[mortal tendon]

yea thats what i was thinking

[uncut crow]

they both diverge to infinity. that’s all working in the extended real numbers and writing = infinity means

[frail beacon]

this was the original question
B does not imply A because lim (x-x) = 0 but lim x is not equal to lim x when x is tending to infinity right?

[uncut crow]

growth rate and whatever is irrelevant

[mortal tendon]

it says that limits to inf exist

[uncut crow]

in your book (and generally) limit exists means limit is a real number

[frail beacon]

yeah

[sharp moth]

But doesnt that just mean both are unbounded, u cant say the functions are equal when x tends to infinity

[frail beacon]

but the answer is 6

i think it should be 4

B does not imply A and B does not imply C for the same reason

[mortal tendon]

if limit exists then B does imply A

[frail beacon]

but we dont know if both limits exist

[uncut crow]

yea we do

[frail beacon]

if A is true then both limits exist

[uncut crow]

read the first line again

[mortal tendon]

its written at the top, both limits to inf exit

[frail beacon]

oh

sorry

i didnt read that lol

but if that wasnt given the ans should be 4 right?

[uncut crow]

i don’t really have the energy to argue about this but i’ve been doing analysis for like 5 years and i’m not saying nonsense, i promise

[mortal tendon]

only C would imply A if that was the case i think

[sharp moth]

I mean if the statement literally says the limits are equal, it insinuates both exist and are finite

[sharp moth]

Not trying to argue, i probably dont know im in high school still, i was just curious

[frail beacon]

if either A or C is true then we know limit exists

[solemn hatch]

"The question is not valid" would be the best answer

[frail beacon]

yeah

[mortal tendon]

it isnt about being true in general, if in the particular case C is true then A would be implied

[frail beacon]

why doesnt A imply B

[mortal tendon]

if limits do not exist then we canr just say lim (f+g) is lim f + lim g

[solemn hatch]

You can't split limits if they DNE

[frail beacon]

they do exist if A is true, because we can compare them that means they both exist too right?

[solemn hatch]

That's exactly why we can't compare them

Because they do not exist

[uncut hemlock]

yeah since it says they exist they're finite, so all 6 work

[sharp moth]

The question mentions they exist

[solemn hatch]

Oh right

[mortal tendon]

yes but he was asking about the case when they do not edist

[uncut crow]

if i interpret ‘A implies B’ to mean for all f and g, ‘A implies B’ is true, then without the limit exists condition ‘A implies ab’ would be true vacuously when one of the limits don’t exist

[solemn hatch]

I thought we were still discussing x and x^2 mb

[uncut crow]

so the question wouldn’t really be sensible without that condition

[frail beacon]

if we're considering the case A implies B then we are assuming that A is true which means both limit exist because we can compare them no?

[warm pelican]

oh slayla

[sharp moth]

Yes

[uncut crow]

[void fox]

amen slayla

[uncut crow]

hello celestial grandfather 0lante

[warm pelican]

slayla idk if ur the layla or idk but

do u know madi? she said sorry to u she removed everyone and has deleted her acc . She said sorry for removing randomly

I just wanted to say that bye sorry if i disturbed the help channel

[solemn hatch]

Btw if A-> B and B->A then aren't A->C and B->C the same

[uncut crow]

[warm pelican]

?

[uncut crow]

i don’t know what to say

[frail beacon]

So the answer should be 4 in that case right?

[warm pelican]

maybe then it was someone else sorry

[uncut crow]

no i know madi

[frail beacon]

b does not imply a or c

and the others are true

[warm pelican]

whatever leave it. She js deleted her account anyway. Just wanted to tell u that. Its been idk how many weeks.

[uncut crow]

ok lol

[warm pelican]

good luck yall have a good day

[solemn hatch]

Maths server side lore wow

[mortal tendon]

fire

[uncut crow]

the statement presumably is ‘for all f and g, A implies B’ (even though the for all f and g part is not mentioned). when one of the limits don’t exist, A is false, so A implies B is true vacuously.

[green crypt]

someone said lore?

[uncut crow]

so if you remove the limit exists condition it doesn’t even change anything

[solemn hatch]

It changes if B then A no?

[uncut crow]

yea it does affect that one

[frail beacon]

A implies B means if A is true then B is true
so youd have to assume A to be true to comment on that

[void fox]

do you know basic logic

if the antecedent is false then the implication is trivially true

[uncut crow]

a priori A may be true or false. you just usually ignore when A is false, because in that case A implies B is true anyway

[frail beacon]

so A does imply B

[uncut crow]

yes, even without the limit exists condition

the implication is true for every f and g

[frail beacon]

so the ans in that case would be 4

[uncut crow]

B implies A and B implies C would be false and the other 4 would be true, yes

[frail beacon]

yeah

thanks

everyone

.close

[devout snow]

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[devout snow]

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[tranquil sail]

Got a funky number while hashing this out and wanted to be sure I'm doing it right

[uncut hemlock]

yeah opposite side is sqrt(7) so sin is just sqrt(7)/4

[supple knot]

get used to funky numbers. then they just become numbers

[tranquil sail]

The opposite side of my triangle is something like 1.777

[rocky oriole]

What is sqrt?

[tranquil sail]

How did you get to sqrt 7?

Oh just adding 4 and 3, I see. but then why sqrt if you didn't ^2 the 4 or the 3?

[supple knot]

what's sqrt(4^2 - 3^2) equal to?

maybe you should draw the triangle

[tranquil sail]

It's 2.65

[supple knot]

,calc sqrt(7)

[woven radish]

Result:

2.6457513110646

[supple knot]

you should be leaving your answers in exact form and not rounding unless you're told to round in the answer box

[tranquil sail]

I just don't understand why we're using 7

[supple knot]

can you answer this

[supple knot]

and do this for sec(theta) = 4/3

[tranquil sail]

Yes I am told to round to 2 decimals, I also didn't want to type 9 digits

[tranquil sail]

Yes it is 2.65 or 2.645751311

[supple knot]

have you seen

if you know c = 4 and b = 3, then a = ?

you need a to find sin(theta) if sec(theta) = 4/3

[versed juniper]

As your final answer maybe? but when you're working you should keep it exact

[tranquil sail]

Ah of you put this answer to ^2 then that's why you get 7

I was unaware for how we were getting 7

Thank you

[supple knot]

yes $\sqrt{a}^2 = a$ when $a > 0$

[woven radish]

riemann

[versed juniper]

4^2 - 3^2 =7

[tranquil sail]

.close

[devout snow]

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[fickle moon]

what does the semi colon on the right mean

[versed juniper]

nothing

[fickle moon]

nice

why is it there then

[versed juniper]

sometimes used to separate things in a list

[fickle moon]

mmm i see okok

also

[versed juniper]

the list being the functions/domains making up the piecewise

but its lowk oddly formatted in the middle

[fickle moon]

for this question to find the graph, would setting x =-2 for the bottom be fine

[versed juniper]

uh wh

you just graph the functions

[fickle moon]

but like

i need to find a point

dont i

to find the limit

this is how i did it for the last one

[versed juniper]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[uncut hemlock]

yeah plugging in -2 for both is exactly how you check if they meet up

[devout snow]

@fickle moon Has your question been resolved?

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[ionic jasper]

I need help on following task.
Of the teachers in a country, 25% work at a grammar school (Gymnasium).
15% of the teachers are female and work at a grammar school.
Overall, 72% of the teachers are female.

f)
Determine the minimum number of teachers that must be selected so that, with a probability of at least 95%, at least one of the selected teachers works at a grammar school.

[ionic jasper]

heres the original task from german f)

the answer is 11 i think but idk exactly why

[uncut hemlock]

classic at least one problem, you want 1 - 0.75^n >= 0.95, solve with logs

[ionic jasper]

wait if i understand correctly its P(x>=1)>=0.95 or 1-P(x=0)>=0.95

?

n= ?, p = 0.25 and k = 0 right and then this formula

[uncut hemlock]

yeah exactly, so it's 0.75^n <= 0.05, take logs and you'll get n >= 10.41

[ionic jasper]

oh okay

i got it

thanks

.close

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[viral ledge]

Wait what is finite axiomatisation?

[viral ledge]

In finite axiomatised theory there are still infinite axioms

Am I right in understanding this

Just that instead of a schema we have defined them recursively?

.close

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[velvet coral]

if $f$ is piecwise smooth and $g$ is continuous can we claim that $f \circ g$ is piecewise smooth? what about $g \circ f$? (assume the domains and co-domains match up)

[woven radish]

LXDL

[drifting sierra]

I don't think either is true

[velvet coral]

i see okay, but what if g is also piecweise smooth and we know f is also continuous?

[drifting sierra]

So both are infinitely differentiable except at a few points?

[velvet coral]

i believe so

or sorry i am not clear

When I say piecwise smooth, I mean f is continuous and there exists finite partition $[t_i, t_{i+1}]$ such that $f'$ is continuous on there

[woven radish]

LXDL

[drifting sierra]

,, (f\circ g)' = (f'\circ g) \cdot g'

[woven radish]

Nel

[velvet coral]

yes but the problem here is that say $[t_i, t_{i+1}]$ is a partition on $g$. $f'$ may not necessarily be differentiable on $g([t_i, t_{i+1}]$

[woven radish]

LXDL

[drifting sierra]

Your definition of "smooth" seems to be C^1 (meaning differentiable, with a continuous derivative - I usually interpret "smooth" as C^inf, meaning infinitely differentiable)

[velvet coral]

yeah sry mb, i shouldve been more clear

[drifting sierra]

[velvet coral]

does this make sense

like idk

not sure if i am drwonign in my own mind

because this has been very frustrating and I'm trying to prove but to no avail

and internet/stack seems to only consider smooth, not piecwise smooth

[drifting sierra]

Say both f and g are continuous, and C^1 on (-inf, 0) and (0, +inf)

Say g oscillates over the x-axis many times

Every time g crosses the x-axis, f(g(x)) is not differentiable

[velvet coral]

ah so techncailly this claim is not true then

[drifting sierra]

Example: |sin(1/x)|

[velvet coral]

but sin(1/x) is not piecwise smooth (continuous and derivtiave continuous on closed intervals)

[drifting sierra]

(in blue is |x| shifted up, in red is sin(1/x) shifted up, in green is |sin(1/x)|)

sin(1/x) is C^1 on (-inf, 0) and (0, +inf)

[velvet coral]

yeah but sin(1/x) needs to be differentiable at 0

or one sided limit must exist

maybe not equal, but each of the one sided limits must exist

since we reuqire C^1 on (-inf, 0] and [0, +inf)

[drifting sierra]

If it's C^1 on (-inf, 0] and [0, +inf) then surely it's C^1 on R?

So I don't really understand what you mean by piecewise smooth

[velvet coral]

i mean for endpoints we say one sided differentaibility

[drifting sierra]

Do you have an example?

[velvet coral]

I do I thnk, let me take screenshot of lecture note

this is oriignal lecture note

[drifting sierra]

Oh god that handwriting

I'm not sure that "continuously differentiable" means "has a derivative that is continuous"...

And I can't read this

[velvet coral]

yeah i guessed that means piecwise smooth

[velvet coral]

same bro ;(. I am like left assuming things half th etime. I assume it means derivative is continuous

and that gamma is continuous (since it is a curve)

[drifting sierra]

Honestly I don't know what to answer at this point

[velvet coral]

same i just asked my insturctor an hour ago

and he said "yes" just now

i think im just lost

[drifting sierra]

You asked what?

[velvet coral]

i asked exactly what i asked here i.e.

[drifting sierra]

Ok... Take |xsin(1/x)|

It looks like this

[velvet coral]

yeah so idk why he said yes to this 😭

[drifting sierra]

I mean it is piecewise smooth, but on an infinite number of intervals

[velvet coral]

dang but it needs to be finite

[drifting sierra]

|sin(1/e^{-x})| is even better

No complaining about that 0 point

Also I'm dumb this is just |sin(e^x)|

Well really just |sin(x)| needs an infinite number of intervals

But whatever

I don't know what to tell you

I'm also tired so I'm off

[velvet coral]

okay thanks for the help

@dry robin I'm a bit confused why if $f : \mathbb{R} \to \mathbb{R}$ piecewise smooth and $g: [a, b] \to \mathbb{R}$ piecwise smooth that $f \circ g$ must be piecewise smooth? (at least according to instructor)

[woven radish]

LXDL

[velvet coral]

here piecwise smooth := f is continuous on its domain, and there exists finite intervals $[t_i, t_{i+1}]$ that partition the domain such that $f'$ is cotninuous on there (wtih one sided dfiferentiability being defined)

[woven radish]

LXDL

[velvet coral]

main probelm (as Nel showed) is that $g([t_i, t_{i+1}]$ can cross the point where $f'$ has discontinuity infitnie numbe rof times

[woven radish]

LXDL

[devout snow]

@velvet coral Has your question been resolved?

[devout snow]

@velvet coral Has your question been resolved?

[devout snow]

Channel closed

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[violet wind]

Alice has 7 subjects to take. Her school's timetable is organised into a 7-day cycle, with 7 class periods each day. Each day, Alice attends a class for each of her 7 subjects, and no subject is scheduled for the same period on different days.

Alice wants to join an extracurricular program that requires her to miss one class each day. Can she choose which class to miss such that, over the 7-day cycle, she misses exactly one class for each subject, and each missed class occurs in a different period?

[rancid forge]

What's your question?

[violet wind]

its the thing at the end with the question mark

[rancid forge]

Are you learning like Latin Squares?

[violet wind]

nah it's not from school

[rancid forge]

Oh just like a riddle?

[violet wind]

yeah

[rancid forge]

Idk what the rules are for me answering this.

[violet wind]

ok i can see the connection though

it's not like a contest or anything

just something a friend and i couldn't figure out

i thought about a bunch of points in 3D

none sharing a pair of similar coordinates

[rancid forge]

Try to think of it like a 7x7 chart with rows for each day and columns for the periods. Each subject appears once per row and column.

[violet wind]

hmm

so i need one cell from every row column and "number"

[rancid forge]

Then go through and try to remove 7 different classes 1 class from each day.

[violet wind]

hmm

[rancid forge]

If you can remove a different class each day then yes, if there are less classes then days then you can't remove one.

Does this make since to you?

[violet wind]

not really

[rancid forge]

You have 7 days of classes.

Each day includes 7 periods.

[violet wind]

yeah ok

[rancid forge]

You have to remove x amount of periods x = number of days, for the extra curricular.

[violet wind]

one each day right

so x=7?

[rancid forge]

Yes

If you have 7 periods that repeat each day.

Can you replace 1 period a day with the extracurricular without exeeding x?

[violet wind]

well sure i can select one period from each day to be replaced

[rancid forge]

Does that answer your question?

[violet wind]

not really

how do i know one subject won't get selected multiple times

[rancid forge]

How many different periods do you need to do a different period each day?

[violet wind]

well, 7 ig?

but idk that the subjects will be different

just the periods

[rancid forge]

Yeah so you can do diffrent periods each day.

So that means you need at least 7 different subjects.

How many subjects do you have?

[violet wind]

7

[rancid forge]

So you have enough to replace one each day then.

[violet wind]

ok

so i can do one subject each day

or i can do one period each day

[rancid forge]

Both

[violet wind]

with the same configuration?

ok lets see

would it also be possible if there were 2 days, 2 subjects, and 2 periods?

[rancid forge]

Yes

[violet wind]

ok, lets say math and english, monday and tuesday, period A and period B

Monday I have math period A and english period B

Tuesday I have english period A and math period B

how do i schedule my extracurricular

[rancid forge]

Then you could replace math on day 1 and english on day 2

[violet wind]

but then i'd be replacing period B both times

[rancid forge]

I see

[violet wind]

oh period A lol

i mean

[rancid forge]

Then you can't do it with that

It only works if each period always matches a subject.

[violet wind]

well i cant find any 7 day configurations that dont work

[rancid forge]

If Period 1 was always math and Period 2 was always English then yes

[violet wind]

i tried with 3 day too

and havent found one that doesnt work yet

3 days 3 periods 3 subjects

[rancid forge]

With different subjects for each period? Like period 1 on monday is math then on tuesday its english then on Thursday its like writing?

[violet wind]

yeah

notably all the classes have to be on different periods each day

so if math is period 1 on monday then it can't be period 1 on tuesday

[rancid forge]

Yeah

It seems to work for 3 days

Just not for 2 days

Anything 3+ should be good then.

[violet wind]

hmm

[rancid forge]

The answer is yes to your og question btw

[violet wind]

hmm

i could believe it but i dont see why

[small mural]

all i could think is this diagonal arrangement. this allows different schedules on each day of the week, with 7 subjects and 7 periods, and allows her to miss exactly one class for each subject but instead of each missed class being a different period its every missed class being the same period

[rancid forge]

Yeah the diagonal arrangement is what I was doing.

That's the only way to make it really succeed.

Maybe there is another way I am missing since it is midnight for me, idk.

[small mural]

idk there are countless ways to arrange, but i dont think ive the tools to analyze them

not literally countless

[violet wind]

there are definitely configurations that work

[rancid forge]

I could analyze more on a computer.

[violet wind]

i haven't found any that don't work though

[small mural]

how do you know

[violet wind]

i thought of this problem as like coordinates in 3D space

(x,y,z) is a scheduled class if z = x+y mod 7

then, x=y works as a subset

(1,1,2) (2,2,4) etc

[rancid forge]

Anyways I got to head to bed now.

Feel free to ping me if you come up with anything interesting I will see it tomorrow.

[violet wind]

sounds good

[devout snow]

@violet wind Has your question been resolved?

[devout snow]

@violet wind Has your question been resolved?

[ionic harness]

@uncut crow

maybe fun maybe not

[uncut crow]

if dreyuk cannot solve it then i also cannot

[violet wind]

this really is a slayla channel

[violet wind]

ooh nice

16,942,079 to go

[alpine python]

the question is if she can always do it?

[uncut crow]

i joke i joke (kinda). i cannot beat this newly developed minecraft addiction though so i won’t check the problem out rn

[violet wind]

rip

i believe in you

[finite briar]

m,e,p,c,cs,s1,s2
e,p,c,cs,s1,s2,m
p,c,cs,s1,s2,m,e
c,cs,s1,s2,m,e,p
cs,s1,s2,m,e,p,c
s1,s2,m,e,p,c,cs
s2,m,e,p,c,cs,s1

and then just skip along the m,p,cs diagonal?

[finite briar]

i mean the answers yes?

[ionic harness]

the two helpfuls answering each others' combinatorics questions across their channels rn

love late night mathcord

[uncut crow]

i’m quitting combinatorics for minecraft

[finite briar]

@uncut crow u should play clash

[uncut crow]

no i’m not a 16 year old boy

[finite briar]

🙁

its fun

[violet wind]

yes, for certain schedules it's possible

do we know it's possible even if we don't know the schedule?

[uncut crow]

16,942,078 to go

[violet wind]

[ionic harness]

If the problem is still open in 8 hours when I wake up in the morning I'll take a look

[finite briar]

uh?

oh if its always possible

[violet wind]

yeah

[alpine python]

this can't be completed because there's no way to miss subject 7

this problem seems really hard

[carmine veldt]

@violet wind where's this problem from 😭

this is basically the solved portion of ryser conjecture

[finite briar]

wth is that

[carmine veldt]

open problem in combinatorics

[violet wind]

the what

[arctic field]

oh we're all here now are we

[violet wind]

its from discord

[carmine veldt]

💀 💀 💀 💀

[violet wind]

oh some hypergraph thing

[carmine veldt]

this thing is literally unsolved

only some brute force verification for grids upto 11x11 is done I think

[violet wind]

wtf

[carmine veldt]

was there any additional info

[ionic harness]

everybody post your ideas so that I can compile all the work that's done in this channel and publish it as my own

[violet wind]

thats actually crazy

[carmine veldt]

like the schedule being cyclic or smn

[violet wind]

i dont think so

idk if they came up with it themselves

do i have to learn about hypergraphs now

[carmine veldt]

even if u do you gotta be the first person to solve this one

goodluck 🙏

[violet wind]

wait so

i'm guessing its always possible then?

for n=7

[finite briar]

@violet wind does this not suggest otherwise

[alpine python]

i just meant you can't complete it if you start it like that

[arctic field]

that just means you can't complete those subjects

but you can choose other subjects to miss

[finite briar]

ah good point

[carmine veldt]

that one's doable

[violet wind]

oh ok

[carmine veldt]

1765432 works

[violet wind]

so its not always possible to complete

well

ig that means the unsolved problem isn't easy

[carmine veldt]

for 7x7 it is

[violet wind]

well like a partial one isn't always completable

7x7 is always possible then?

[carmine veldt]

yeah yeah

and nxn where n is odd and 11>=n its doable

[violet wind]

hmm 11 is open

is even always impossible?

[carmine veldt]

not always

but it isn't guaranteed for all possible arrangements in an even graph

consider 2x2 where first row is (1,2) and second row is (2,1)

[violet wind]

these are like the only two 4x4s right

[carmine veldt]

that's impossible

[violet wind]

neither of those seem to work

[carmine veldt]

nah there's more

[alpine python]

https://www.youtube.com/watch?v=Kx2OiHVi0Mw at 3:09 she said the cayley tables of Z/(2k)Z don't have full transversals

if i understand correctly

[carmine veldt]

what is a cayley table

[violet wind]

addition table mod 2k

in this case

in general a table for a groups binary operation

then you can add 1 to every element if you want indexes to start at 1

Ok well she definitely seems to know what she's talking about and that's a version of the problem I can comprehend

So ig it is unsolved

What even Latin square, if any, has a full transversal and why doesn't the cayley table mod 2k have one

This is like placing 2n queens that don't attack each other but the board is a torus and the queens only move on one of the diagonals

that doesn't seem too helpful

[arctic field]

[violet wind]

Ohhhh lol

||A transversal has to contain one of each number||

||so the sum has to be 0+1+...+(2n-1) = n mod 2n||

||But it needs to also appear in each column and row once. Since we're looking at an addition table, its a sum involving each number twice!||

||2(0+1+...+(2n-1)) = 0 mod 2n||

This is such a sick problem that I'll spoiler it so other people can try too

Cayley table for S_3 also has no transversals

Ig 8x8 can work though

Maybe latin squares are too pathological to analyze in generality like this and it only holds heuristically

I can't think of another in-reach problem so thanks everyone for the help

.close

[devout snow]

Channel closed

Closed by @violet wind

Use .reopen if this was a mistake.

[violet wind]

Oh cayley table of Z2 × Z2 has a transversal too lol

ok

[devout snow]

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[tight peak]

can $GL_2(\mathbb{R})$ act transitively on $\mathbb{R}^2$

[woven radish]

ginny

[tight peak]

for it to do so, the orbit of any element in R^2 has to be all of R^2

[tight peak]

I am supposed to show if this is true or false

if it is true, I must have a homomorphism between the group and Aut(R2)

moreover this homomorphism should be injective I think? as the stabilizers need to be singleton (cardinality of R^2 and GL_2(R)) is the same

but idk what to do with all this

[void fox]

hint what is the orbit of 0

[tight peak]

under what action

[void fox]

is the question like

"is the canonical action of GL2(R) on R2 given by left multiplication transitive"

or is it asking does there exist a transitive action of GL2R on R2

[tight peak]

this

[tight peak]

This is false I think

like no that action isn't transitive

[devout snow]

@tight peak Has your question been resolved?

[arctic field]

you just want GL_2(R) -> Aut(R^2) to be a group hom?

what kind of object are you viewing R^2 as?

vector space? abelian group?

[tight peak]

anything is fine

vector space is stronger, so that maybe for now

[arctic field]

so GL_2(R) -> GL_2(R)

i mean in this case you're just looking at some subgroup of GL_2(R) acting by the canonical action

so 0 is fixed as plantianus said earlier

[tight peak]

how do you come to this, I had R2 and not this

GL_2 is not isomorphic to R2

[arctic field]

but like what is Aut(R^2)

if you want vector space automorphisms, that's GL_2(R)

[tight peak]

okay yes

[tight peak]

it is not anymore

the identity in GL_2 is the identity matrix

which of all the things is not fixed?

[arctic field]

?

the identity matrix acts on R^2

it fixes everything

[tight peak]

identity matrix fixes everything yes

it itself is not fixed I meant?

[tight peak]

wdym here

[arctic field]

but we're looking at an action on R^2

let's say as a vector space as you said earlier

so an action on it must go through GL_2(R)

because the action of a group G on R^2 is defined as a group homomorphism G -> GL_2(R)

so for some g, i get a matrix M which acts on R^2 by left multiplication

M0 = 0 always for any matrix M

[tight peak]

but why does the action have to be left multiplication?

[arctic field]

well, that's what an automorphism of R^2 is as a vector space

[tight peak]

even when both the groups are the same we know there are actions defined by conjugation etc'

[arctic field]

it's a linear transformation R^2 -> R^2 which is an isomorphism

and it's a theorem of linear algebra that all such transformations are represented by matrices multiplying column vectors on the left

[tight peak]

ah

does it change anything if I say R2 is just the set R2?

[arctic field]

well in that case you sort of lose all structure

as a set, R^2 is a just some collection of points with cardinality the continuum

im sure you can find some action on it that's transitive

[tight peak]

Because we weren't told to view it as a vector space, I thought the answer is invariant of that.

[arctic field]

wdym by invariant of that

what kind of structure you view R^2 as will change the kind of automorphisms that are allowed

let's say we view R^2 as a metric space

and we allow only distance preserving bijections

then the allowed automorphisms of R^2 are usually called the euclidean group

this includes translation as well as multiplication by orthogonal matrices

[tight peak]

I see.

[arctic field]

you might be able to find a transitive action by somehow finding a copy of R^2 inside of GL_2(R^2)

and then acting by translation

[tight peak]

I'll try to work this out and see where that gets me

thanks

.close

[devout snow]

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[arctic field]

[devout snow]

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[timid obsidian]

Where did I go wrong?

[timid obsidian]

This is number theory arithmetic progressions

On the top right corner are the variables given

[winter patrol]

do you have a pic of the original question?

[rain summit]

$a_n = a + (n-1)d$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

interesting indeed 😭

[winter patrol]

is that
$$a_n = 4$$
$$d = 2$$
with the goal of finding $n$? \
what else are you told about this A.P.

[woven radish]

ραμOmeganato5

[timid obsidian]

SN=-14
d=2
aN=4
Find a and d

[timid obsidian]

That Sn=-14

[mystic scarab]

I can't read your handwriting, honestly.
Can you send a photo of the original question, please?

[timid obsidian]

Sure

[winter patrol]

where's coming from

[timid obsidian]

-14=(n/2)(2a+d(n-1))
2a+d(n-1)=a+a+d(n-1)
a+d(n-1)=aN
-14=(n/2)(a+aN)
holy shit you're right
Wait this looks like a quadratic but a bunch of variables

[winter patrol]

you only have two unknowns,
a and n
d and a_n are given

[timid obsidian]

Yes

-14=n/2(a+aN(
-7=n(a+aN)
aN=4
-7=na+4n

[winter patrol]

you're not manipulating that equation correctly

how did you end up with -7 on the left

[timid obsidian]

Divide by 2

[winter patrol]

why divide by 2 though

[timid obsidian]

Look that n/2 there

[winter patrol]

yes

and to rid yourself of the fraction, you'd want to use the inverse operation
multiplying both sides by 2

[timid obsidian]

Ok

Forgot about that

But where do we go from here now?

-28=n(a+a_n)?

[winter patrol]

you've yet to use
a_n = 4 and
a+d(n-1)=a_n (with 2 for the value of d)

[timid obsidian]

-28=na+4n

Now?

We have removed all known variables

[winter patrol]

like actually use

a+d(n-1)=a_n (with 2 for the value of d, and a_n = 4)

to get a separate equation

[timid obsidian]

-28=n(a+4)
4=2d
-28=n(a+2d)
-28=n(a3)
That's also good to know

[winter patrol]

one sec, what are you doing

why are you trying to bring a_3 into this

[timid obsidian]

Nvm it's useless

[winter patrol]

like actually use
a+d(n-1)=a_n (with 2 for the value of d, and a_n = 4)
replace those values, do nothing else

[timid obsidian]

Ok

We get to n(10-2n)

[winter patrol]

where's that coming form

[timid obsidian]

a=6-2n
(Just solve it)
-28=n(a+4)
-28=n(4+6-2n)

-28=n(10-2n)

[winter patrol]

jumped ahead but ok,
write the full equation next time

[timid obsidian]

Ok

[winter patrol]

as i was surprised how an equation turned into an expression
and you didn't respond with what i requested

anyway seems ok so far atm

[timid obsidian]

This becomes a quadratic
10n-2n²=-28
-2n²+10n+28=0
2n²-10n-28=0
Divide by 2
n²-5n+14=0
x=14
+=-5

after solving this we get (n-7)(n+2)
n=7
n=-2
N is equal to 7

This was a hard question

[winter patrol]

you overcomplicated a few things

[timid obsidian]

Yeah ik

And a bunch of silly mistakes

[winter patrol]

use definitions/formula where given info can be applied directly

and go from there,

[timid obsidian]

Will do that next time

.close

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[devout snow]

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[sterile owl]

hi there

[sterile owl]

i need help with this im stucl

stuck

[lunar harbor]

(In the future, please make the first message you send the actual question since that's what the bot pins. This saves us the effort of having to change the pin manually.)

you're missing the binomial coefficient part on the left

[sterile owl]

ohh

[lunar harbor]

$a^7 (2x)^0 \binom{7}{0}$, $a^6 (2x)^1 \binom{7}{1}$, etc.

[woven radish]

Civil Service Pigeon

[sterile owl]

7 choose 4?

[lunar harbor]

mhm

which is 35 iirc

that's where the 35 came from

[sterile owl]

yhh i got it

[lunar harbor]

[devout snow]

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

[sterile owl]

.close

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[sterile owl]

im stuck

this is the question

[devout snow]

@sterile owl Has your question been resolved?

[toxic rain]

what are u stuck on?

what to do or how to start?

[winter patrol]

you've made multiple algebraic mistakes when attempting to simplify the fraction

trying simplifying this again

[devout snow]

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[hardy marlin]

I'm doing some math in a game for fun and im kinda stuck because I dont really know % all that well, maths never been my thing and I need help to put the math behind the calculations into a simple formula that I can simple put in the % numbers to get a final number, it's basically only % and no flat numbers (forgot the name for this, learnt mathematics in a different language) Is there someone that could help with this?

[wicked turtle]

can you show an example problem that illustrates what you're talking about?

[hardy marlin]

Basically there's an item that makes it so that if you don't get a % critical roll. Let's say for example 50%

If you don't get the 50% critical roll it doubles into 100% and if you get the 50% critical roll it doesn't double. What would that average out to into an increase in procent. And how can I easily calculate this. Sorry if it isnt clear enough I really suck at math 😭

I'm assuming it averages out to 66% but idk how to calculate with any other number above or below 50%

[topaz axle]

so if initial is 20% what happens?

[hardy marlin]

If you don't get that 20% roll it doubles into 40%. Dont get that 40% it doubles into 80%

[violet wind]

And when you get it it resets?

[hardy marlin]

Yes

[violet wind]

You want to know over a really long run, how frequently you can expect to get crits?

[hardy marlin]

What the average increase in crit % is

In my headmath if I have a starting value of 20% and it double every time and resets when I crit

Thats like a 25% on average increase

But I could be very wrong

[violet wind]

So take this and then find the percent increase from the base crit%?

[hardy marlin]

Yes

So 50% doubled results in 66% which is a 16% increase. I know that for sure

[violet wind]

The % increase part will be easy, that's just (new value - old value)/(old value) × 100

oh wait

absolute increase

not relative

ok

[violet wind]

So this is like from 20% to 45% if theres a 25% increase

[hardy marlin]

Or would that be too hard to calculate without some sort of program. Cuz if it is i could program a code that runs tests over and over

[violet wind]

Theres a loop that will calculate it

iirc this is just the expected value of the length of a run

well, 1/that

[hardy marlin]

I know how I would program that. But would take a while since I'm sorta new at programing

[violet wind]

20% as an example

[uncut crow]

i’m confused what the change is between each fail

[violet wind]

doubles success chance I think

[hardy marlin]

Success = resets to base value
Fail = doubles base value

[violet wind]

Doubles current value*

[hardy marlin]

Oh yeah sorry

[violet wind]

No worries

[uncut crow]

so if 50%, fail once, next one is success guaranteed?

[hardy marlin]

Yes since its 100%

[violet wind]

A run of non-crits, followed by a crit has a 20% chance of having length 1

[hardy marlin]

So a 66% chance on average across multiple successive tries

Meaning a 16% increase on average

[violet wind]

a .8*.4 = 32% chance of having length 2

A .8×.6×.8 = 38.4% chance of having length 3

and a .8×.6×.2 = 9.6% chance of length 4

[hardy marlin]

Oh!

[violet wind]

,calc .2 * 1+.32 * 2+.384 * 3+.096 * 4

[hardy marlin]

That gave me a eureka moment!

I know EXACTLY how to program a code that will spit out the correct numbers

[woven radish]

Result:

2.376

[violet wind]

oh nice

ok

[hardy marlin]

Thanks! I'll try it out and if it doesn't work I'll come back. Thanks a ton for the help

[violet wind]

,calc 100/2.376

[woven radish]

Result:

42.087542087542

[violet wind]

no problem