help-36

[umbral hamlet]

are you sure you don't mean that V is over R or C

[whole halo]

Im starting to see the issue here

its only ever over R or C, V is not R or C itself, whoops

[umbral hamlet]

right, that would be really boring inner products otherwise

[whole halo]

now thats really strange

I specify V to be C itself and the inner product isnt always defined to have [1, 1] = [i, i]

but I leave V open and its possible to get around any additional requirements

unrelated: requirements (a) and (d) have been corrected, and I may be stuck on (c)

[umbral hamlet]

[1 + i, i - 1] = 0, [1, i] = 0, and [i, 1] = 0 using the [x, ix] = 0 property with some conjugates and scaling

but from linearity, [1 + i, i - 1] = [1, i] - [1, 1] + [i, i] - [i, 1]

using our 0s, we get

0 - [1, 1] + [i, i] - 0 = 0 -> [i, i] = [1, 1]

oh i made a typo one sec

[whole halo]

youre writing -conj as taking the conjugate? is that conventional?

[umbral hamlet]

not really, i just made it up

[whole halo]

amazing

I sort of never want to see it written like that again

alternatively it can be really funny if it looks worse than that

this was the kind of argument I was looking for, I wasnt sure where to start on proving they were the same

what I did was think that if [1, 1] ≠ [i, i], the inner product looking very similar to the dot product of R^2 would suggest I could find a counterexample in R^2 with [a, b] * [x, y] = ax + 2by
but I couldnt find one, so I was stuck

[umbral hamlet]

okay fixed

(and linearity in the second entry can be proved by linearity in first entry + conjugate symmetry)

[whole halo]

and youve made it nicer too, great

I dont see it being any nicer than
0 = [i + 1, i(i + 1)]
= [i + 1, i - 1]
= [i, i] + [i, -1] + [1, i] + [1, -1]
= [i, i] + 0 + 0 - [1, 1]
= [i, i] - [1, 1]

clean, now for the bigger problem of doing (b) and (c) properly

.cloes reopening the problem with doing (b) and (c) properly then

.close lol

[final saddle]

Channel closed

Closed by @whole halo

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[minor quartz]

I’m stuck on task 5 trying to finish a packet rn

[tranquil pine]

hard to make out what the given equations are supposed to be

[minor quartz]

So the one fraction that is in the box I use as my m

And I pick a coordinate to plug it in slope intercept form

For this one?

[tranquil pine]

no i mean these

what are these supposed to be

[minor quartz]

Oh that’s just example I wrote in y= mx+b cause it told me to fill it out

But the problems I actually have to do only ask for the point

[tranquil pine]

oh wait-

uh

ok so one interesting thing you can do is multiply both sides by 11 for each

[tranquil pine]

so in this example you get 11y=-4x-6 and 11y=-8x+174

and there's just an 11y on one side of both, meaning the other sides are equal

so -4x - 6 = -8x + 174

[minor quartz]

Okay

[tranquil pine]

i think you got that one right actually, everything checks out

[minor quartz]

Yea I did that with help but now I’m on my own trying it

So I’m just like confused in some parts

[tranquil pine]

ohh

[minor quartz]

Can I plug in zero to find my b ?

[tranquil pine]

yeah

so if that's (0,0) and (6,15) then the y-intercept is just gonna be (0,0)

[minor quartz]

Ye

[tranquil pine]

because you need it to intersect that point, yeah?

[minor quartz]

I just suggested using it to make the problem easier

[tranquil pine]

oh ok

also quick question, why are you inverting the fractions?

oh nvm

[minor quartz]

Which one

Are you saying when I got rid of them ?

[tranquil pine]

well for most of them, you get an answer like 11/-4 and flip it around to be -4/11

[minor quartz]

Oh yea I messed up

[tranquil pine]

for example

[minor quartz]

But corrected it

[tranquil pine]

okay

so like change in x ÷ change in y instead of the other way around, gotcha gotcha

[minor quartz]

Yea 👍

[tranquil pine]

ok ok

what else do you need help with

[minor quartz]

I need help with online homework as well

Ima send a ss

[tranquil pine]

alr

[minor quartz]

Don’t mind the dirty screen

[tranquil pine]

uhh

man this was the kind of thing i was never good at

[mighty apex]

What terms do u think u should grouo

[minor quartz]

A

S

[mighty apex]

Huh

U have four terms

U need to group any 2 together

[minor quartz]

I mean there all different

[mighty apex]

Which terms should u grouo

Yea but see if u group the first two, what do u get common

6st+8t

Whats common in it?

[minor quartz]

Hmm 2

[mighty apex]

And also t

2t is common

[minor quartz]

Oh

[mighty apex]

Yea now u should be able to solve it

Make the two groups

[minor quartz]

Okay I’m making them

[mighty apex]

Tell me if u get stuck somewhere

[minor quartz]

Did I do something wrong

[mighty apex]

Uh when u take 2t common

From 6st+8t

You get 3s+4

Take gcf of only 6st+8t

Ur not grouping

[minor quartz]

Ok

[mighty apex]

This is how u group

[tranquil pine]

oh interesting

i thought it was like "factor the equation into like 2 or 3 terms" or whatever maybe im just a little slow

[mighty apex]

Lol no worries

@minor quartz did u do the question??

[minor quartz]

I’m cooked

Help me

[mighty apex]

Alright

Did u get the grouping thing??

[mighty apex]

This

[minor quartz]

This is all I have

[mighty apex]

Alr8ght

[mighty apex]

Complete the whole equation

Do u see anything common to takr??

[minor quartz]

St?

[mighty apex]

Nope 9nly t

2t not s

[minor quartz]

Okay

[mighty apex]

U have taken 2t as common

Qhen u take 2t common from 6st u get 3s

6st = 2x3xst = 2t(3s)

And when u take 2t common from 8t, u get 4

[minor quartz]

Hmm

[minor quartz]

What this?

[mighty apex]

When u take common 2t from 6st

U get 3s

[minor quartz]

I’m so confused

[mighty apex]

Do u know how tp take common??

Wait

[minor quartz]

You’re saying that’s the gcf?

[mighty apex]

Gcf is 2t

[minor quartz]

Yea

[minor quartz]

Okay I get that

[mighty apex]

Yea

[mighty apex]

This is splitting the middle term

Have u been taught that

[minor quartz]

Hmm

[mighty apex]

What are all the methods u are taught

[minor quartz]

Like my notes

[mighty apex]

Yea

[minor quartz]

I can show you my notes currently

[mighty apex]

Alr

[minor quartz]

All I have down at the moment

[mighty apex]

Use the method u have used in this

Do u remeber how u did it??

[minor quartz]

Which image is that ?

The first one?

[mighty apex]

Sorry its loading

The third one

Top question

[minor quartz]

It’s so long…

[mighty apex]

Lol but ur taught that

But its gonna make maths a lotta easier in future

[mighty apex]

So u mutikply 6 and 24 then make its factors till u find the sum/diff 11

[minor quartz]

6 and 24?

[mighty apex]

Sprry

6 and 4

😭😭

[minor quartz]

Ohh

Ohh

[minor quartz]

Mmm

[mighty apex]

I gtg now, im om vacation so network is sooo frekin trash ! U can ping helpers tho :((

[minor quartz]

Okayy thank you so much!!

Have a good vacation ❤️

[final saddle]

@minor quartz Has your question been resolved?

Channel closed

Closed by @minor quartz

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tall vector]

How do I simplify the equation from -3(cos^2x-sin^2x) to -3cos(2x)? And I'm stuck solving cos(2x)=0

[untold wagon]

it's called the double angle identity

[odd seal]

How do I simplify the equation from -3(cos^2x-sin^2x) to -3cos(2x)
cos^2(x)-sin^2(x) is exactly the same as cos(2x). Its an identity, which you can derive if you use the formula for cos(A+B)

[untold wagon]

for cos(2x) = 0, what angles of cos make 0

[odd seal]

As for solving

cos(2x)=0
try to recall when is the value of cosine is 0

[untold wagon]

2x = pi/2 + kpi

[final saddle]

@tall vector Has your question been resolved?

[tall vector]

.close

[final saddle]

Channel closed

Closed by @tall vector

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dire rivet]

can someoe help me here please

im a tad lost on how exactly the distances are ot be calcualted

[hallow hound]

physics correct?

: P

i have no clue what im saying

best of luck man

I wanna kms from all these hard quesitons

[dire rivet]

yea

dont do that

[hallow hound]

inshallah

[dire rivet]

they may be hard but there si always more to life

[hallow hound]

I picked chemistry

tru

[dire rivet]

chemistry? ur gonna give me flashbacks

[hallow hound]

dw

im kinda

kinda

gudat it ig

at the basics at least

[jagged hornet]

is the answer value exact?

[dire rivet]

make su better than me

[hallow hound]

nont rly

[dire rivet]

what do u mean?

[hallow hound]

my school not that gud 🙁

[jagged hornet]

or in terms of trig functions?

[hallow hound]

trig also applies to physics?

[jagged hornet]

yes, in mechanics it does

[hallow hound]

hmm

wait

what does medical or nurses need?

as courses?

[dire rivet]

ooh if u mean if its a one number yea it is

[hallow hound]

hopefully I get that at least

[dire rivet]

yea trig is everywhere sadly

[hallow hound]

sadly but its still useful I suppose

if u apply it to real life situations

perfect ones though

[dire rivet]

still i don wan do trig

[hallow hound]

same 🙁

[dire rivet]

i have everyhting i need i just need to find the distances . part of em thinks i can use the ones given but i dont know if thats right

[jagged hornet]

i mean

have you tried the distances?

[dire rivet]

i have

[jagged hornet]

and you didnt get the correct answer?

what value did you get?

[dire rivet]

but this one doest have an answer thing

so i cant work backwards

[dire rivet]

with just the direct distances?

[jagged hornet]

yep

[dire rivet]

744.14

[jagged hornet]

and whats the answer?

[dire rivet]

thats the thing i dont know

i know the answer for the x and y comp

563.82 for x and 205.21 for y

usually id js aks whatever teacher gave me the test to go over the questions with me after its graded

but this one doesnt do that

who doesnt give out the answers after a test to see why ur wrong

[jagged hornet]

real

uh

i think the answer is cos((4/9)pi) * 5 ft

[dire rivet]

wha

[jagged hornet]

this value multiplied by F

probably

ill combute it just a sec

man

idk the imperial units

ill just get the number

[dire rivet]

units dont really matter

ill js use the ones given

[jagged hornet]

434.12?

[dire rivet]

hm

[jagged hornet]

Idk that dont seem right

Wait

I got the values a lil wrong

Wait you got 563 originally?

[dire rivet]

for the vaule

i got 744.14

when i used the raw distacnes

[jagged hornet]

Uh

Show calculations?

If possible

[dire rivet]

sure

i dont knwo how to sue this servers plugin tho

but

(f1 * d1)-(f2 * d2)

where

f1=600 sin 20

f2= 600 cos 20

d1 = 5

and d2 = 0.5

f1 = 1026.06

f2 = 281.90

we are taking clockwise moments as positve

so f1 becomes -1026

and f2 becoms -281.90

[dire rivet]

i js realsied i amde a mistake here

to get 1307

well 1307.907

[dire rivet]

turns out i made a mistake with 744

[jagged hornet]

Damn

A lack of an answer key hurts my soul

[dire rivet]

yes

[jagged hornet]

Well i got the answers in radicals and such but exact computational answer is not something im gonna do

Too long

[dire rivet]

whats worse is this teacher has a nasty habbit of teaching us the exeptions and not the rules

[dire rivet]

thats ok u helped alot already

[jagged hornet]

So its all sorted then?

Ill close the channel if so

[dire rivet]

not yet

but im not sure if anyone will be able to help in a reasonable timeframe

so feel free to close it

[jagged hornet]

Hmm maybe someone will

Ill just leave it open

[dire rivet]

kk

[jagged hornet]

Can you explain how you got this?

[dire rivet]

ooh thats js the formula were suppsoed to use

[jagged hornet]

I mean

[dire rivet]

cant use the top one cause it specifcally asks for the differing distances

[jagged hornet]

Oh i see what you did

Makes sense

But

There is a mistake

F1 and F2 are not F sin 20 and F cos 20

Look closely

@dire rivet

[dire rivet]

hm

[dire rivet]

u mean in the formula?

fy and fx stand for the y and x compnets of the force

[jagged hornet]

And you have taken that wrong

20 degrees isnt taken from the surface of the beam, but from the horizontal

F2 is Fcos50

[dire rivet]

ooh no

[jagged hornet]

F1 is Fsin50

[dire rivet]

if this were trusses or vectors i think so yea

but in this case the compnets of F are treated as thier own little pocket thing

besides those 2 i got correct the thing i had wrong was distances

[jagged hornet]

They are , but that would require the components of F to be correct in the first place

If you are using the d1 and d2 as 0.5 and 5, you need to take components along the beam

[dire rivet]

then 0.5 and 5 are incorrect

which js leaves me more confused really

[jagged hornet]

Just do the same calculation

But instead of 20 degrees use 50

Das it

Everything else is correct

[dire rivet]

the calcualtions for the componets are known

those i got correct

[jagged hornet]

No?

[dire rivet]

yea

[jagged hornet]

Wait ill draw a proper diagram when i get to my pc

[jagged hornet]

I didnt know that you were calculating seperately

I thought we were still on the total moment

Lol

[jagged hornet]

I got confused by this

[dire rivet]

so am i

[jagged hornet]

The Fx and Fy that you answered and were correct would not look like those

That you drew

[dire rivet]

howso?

[jagged hornet]

Just a sec

[dire rivet]

oohou mean this?

[jagged hornet]

Yea

[dire rivet]

no no this includes the multiplication of the 5 and 0.5 respectfively

so the numbers are bigger / smaller

[jagged hornet]

Yea, i thought you were implying F1 = Fx and F2 = Fy

[dire rivet]

yea

[jagged hornet]

Didnt know you needed fx and fy for a separate question

[dire rivet]

so this question i used f1 and fs instead of fx and fy to avoid confusion

[dire rivet]

but f1 does equal fy these are technically f1xd1 and such my mistake

[jagged hornet]

welp

as long as you get the final torque correct

[dire rivet]

yop

[final saddle]

@dire rivet Has your question been resolved?

Channel closed

Closed by @dire rivet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[woeful sable]

I need an explanation to this statement

[warm python]

,rccw

[final saddle]

@woeful sable Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vague anchor]

,rccw

[vague anchor]

.close

[final saddle]

Channel closed

Closed by @vague anchor

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[empty plume]

how many numbers less then 1000 are perfect squares which are also 3 times an odd number

[empty plume]

whats a good way to do this without like brute force?

like not just writing down every perfect square number

and then checking one by one

js like a method to narrow it down a lot

[desert mantle]

so we are looking for numbers of the form k^2

with k<=31

[worldly mesa]

and k^2=3m for m odd

[desert mantle]

from the conditions what do we know about the prime factors of k^2

and then what do we know about the prime factors of k

[empty plume]

wut

[empty plume]

ye i found this out but then wut

doesnt rly narrow it much

[desert mantle]

what wut

[empty plume]

divisible by uhhhh 3

then idk

[worldly mesa]

Yes, then k^2 is divisible by 9

[desert mantle]

ok so 3 is a prime factor of k^2

there is one more prime number we can say something about

[empty plume]

wait huh y?

i thought its js k^2 is divisible by 3

[empty plume]

uhhhhhh k^2 is an odd number?

since its 3 x odd number making it an odd number

[worldly mesa]

But 3 is prime so it divides k

Ans if 3 divides k then 9 divides k^2

[empty plume]

wait what why can 3 divide k?

._.\

lowkey confused

[worldly mesa]

Thats a property of prime numbers, if a prime p divides ab then it divides one of a,b

[desert mantle]

given that k^2 is an odd number, what number is not one of its factors?

[empty plume]

idk even numbers?

[empty plume]

lowkey lemme go js look into it online rq

gimme a sec

[desert mantle]

what is "the" even number

given that we used the word prime a lot

[empty plume]

uhh why is the number which we cant use prime specifically?

[empty plume]

oh alright i understand this now

[verbal viper]

K must have 3 in its prime factors

theirfore a multiple of 3

[desert mantle]

being even/odd is about having/not having 2 as a prime factor

so 3 is a prime factor of k^2 and 2 is not a prime factor of k^2

so that means 3 is a prime factor of k and 2 is not a prime factor of k

[empty plume]

okok

wait can i ask

like since k^2 is divisible by 3 so k is also divisible by 3 right

so we can make it so K^2 = 3m
k = 3t since its also divisible by 3 so that means k^2 = 9t^2

then 9t^2 < 1000

t^2 < 111.11111

then t < 10 ( cus it has to be an interger)

then as u said it cant be an even number ( have 2 in it )

[agile yew]

First find the smallest number whose square goes above 1000 which might be like 36 something. I dont understand the 2nd part are you talking about the square being the 3 times of the odd number or the number being 3 times the odd

[empty plume]

so then 1,3,5,7,9 works no?

[desert mantle]

t=1,3,5,7,9, yes

[empty plume]

making the answer like 9,81,225,441,729

this correct?

[worldly mesa]

Looks correct

[empty plume]

alright alright

thanks yall

for helping me

.close

[final saddle]

Channel closed

Closed by @empty plume

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[zenith cedar]

How do I do this without differentiation

[final saddle]

Please don't occupy multiple help channels.

[zenith cedar]

.close

[final saddle]

Channel closed

Closed by @zenith cedar

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[worldly mesa]

looks fine

generally this follows from that lim n-->inf (1/2 + 1/n) = 1/2

[tiny gorge]

small hitch: what if 1/V is not an integer?

yep that's fine

there exists n, i think you meant

but yep that's correct

1/2 is clearly in all of the intervals so it's in their intersection

loosely speaking yes, but talking about sets "approaching" things is a bit vague

unlike for sequences of real numbers and despite the notation B_n (downarrow) A, there's not really any limiting process involved here

the intersection is the set {1/2}

the argument is fine, the wording could be more precise

probably you have proved something about continuity of probability measures?

something along these lines

that can be applied here

you can also just do it using monotonicity

${1/2} \subseteq B_n$ , so $P({1/2}) \leq P(B_n)$

and this holds for every n

[soft zealot]

Bungo

[tiny gorge]

why is it undefined?

it's in the sigma algebra

because {1/2} can be expressed as the intersection of countably many open intervals
also, as shown in part (a), it can be expressed as the intersection of countably many half-open intervals

yep that's probably the simplest way

yep and i'm not sure of the context, but presumably you know how to compute P([1/2, 1/2 + 1/n))?

or tbh, you could just not use the result of (a) and instead say that {1/2} is a subset of (1/2 - 1/n, 1/2 + 1/n), and you do know the probability of that since it's an open interval

yep, once you know P({1/2}) you can do that, but it would be circular since you're asked to compute it

well you could say:
$(1/2 + \epsilon, 1/2 +1/n) \subseteq [1/2, 1/2 + 1/n) \subseteq (1/2 - \epsilon, 1/2 + 1/n)$ if $\epsilon$ is small enough for these intervals to make sense
and so
$1/n - \epsilon \leq P([1/2, 1/2 + 1/n)) \leq 1/n + \epsilon$

and since that holds for any small epsilon, you conclude that $P([1/2, 1/2 + 1/n))$ indeed equals $1/n$

[soft zealot]

Bungo

Bungo

[tiny gorge]

texit output got reversed because i fixed a typo in the first one

not 1/n...

{1/2} is just a point, what is n here?

yea it's <= 1/n for all n, so it's 0

and yes, once you have that, you can find the probability of [1/2, 1/2 + 1/n) as the probability of (1/2, 1/2 + 1/n) plus the probability of {1/2}

yw

[final saddle]

Channel closed

Closed by @vital kelp

Use .reopen if this was a mistake.

[tiny gorge]

cheers

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[soft pewter]

f6(x) = (f3 + f4)(x)

[soft pewter]

f3(x) = 2|x-5| + 4

f4(x) = 2 sqrt x-8 + 3

how do i do this

[vital crag]

what is the question?

what's "do this" mean

[soft pewter]

how do i do f3 +f4

[vital crag]

you add them and simplify like terms

4 + 3 = 7

|x-5| + sqrt(x-8) generally can't be simplified further

[soft pewter]

2|x-5| + 4 + 2 sqrt x-8 + 3

4 + 3?

[vital crag]

.

[soft pewter]

where do i put the 7

and how do i add 2|x-5| + sqrt x-8

[vital crag]

.

[soft pewter]

so how do i answer to this

thats helpful

.close

[final saddle]

Channel closed

Closed by @soft pewter

Use .reopen if this was a mistake.

[vital crag]

you did here already

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wraith peak]

Can anyone explain how to calculate the area of a sector or just basically everything recapped about a sector

[gritty drift]

how would you calculate the area of an annulus?

[wraith peak]

whats is the annulus?

[wraith peak]

ohh

i dont

i dont know to calculayte to area of the annulus

[gritty drift]

Well start with a circle then

You know how to calculate the area of a circle, right?

[wraith peak]

pi x r squared

?

[gritty drift]

yes.

Now what if we had a sector that was only 90 degrees

Which is a quarter circle (90/360)

[wraith peak]

uhm u calculate the whole area of a circle then divide by 4?

[gritty drift]

yeah exactly

what if the sector was 100 degrees instead?

[wraith peak]

u divide it by 100/360?

[gritty drift]

yep

does that give you an idea on how to go from full shape -> sector of it? at least for stuff that looks like a circle?

[wraith peak]

yeah what would be the formula? to put in a calculator

[gritty drift]

what do you think it would be?

[wraith peak]

A= pi x r squared divided by 100/360?

[gritty drift]

Yeah, that's only for a sector of 100 degrees though

if you had a sector of 80 degrees, it would be A*80/300

So the general formula is [area of circular shape] * angle/360

Now you just need to find the area of the full circular shape in your problem, then you can get the area of its sector

[wraith peak]

that makes sense

how do u find the radius of a sector if u had the area and arc length ?

i learnt it but im still unfamiliar and confused

[gritty drift]

jsyk this is a different question, you know that, right?

[wraith peak]

yeah

[gritty drift]

alright then. the angle is related to 360 degrees (the angle of a full circle)

the arc length is related to circumference

That should give you a hint on how to solve that type of problem

The process is very similar to the general formula we derived

[wraith peak]

so wouldnt the formula be r= 2A/arc length ?

[gritty drift]

give it in terms of [area of circular shape] times something

[wraith peak]

how would that work out?

so raidus equals 2 times [ area of circular shape]divided by *Angle/360

[final saddle]

@wraith peak Has your question been resolved?

Channel closed

Closed by @wraith peak

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tranquil pine]

hey guys! i have a very interesting probability question i need some guidance on:

background information: we have a stall with a fun carnival game. the player must pay 2 tokens to play.

what we need to find: the win/loss percentage for the player (tieing aka getting back what you paid aka 2 tokens counts as a loss).

let c be 0 for now.

steps to the game:

1. the player will roll a 6 sided die. if they get 1, 2, 3, c will be set to 1. if they get a 4, 5, 6, c will be set to 2.

2. based on the variable c, they will choose that number of chips from a jar of chips. the current ratios are as followed:

6 chips: 2 tokens
4 chips: 1 token
1 chip: set c to 2, go back to step 2 and choose again
7 chips: 3 tokens
3 chips: 4 tokens
15 chips: nothing

the total will be tallied from what they win.

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

<@&286206848099549185> heya! anyone available to take a look?

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

<@&286206848099549185> please, if anyone could take a quick look at this i would really appreciate it 🙏

[vagrant vector]

what do u do for c=2

[tranquil pine]

repeat this step c times (step 2)

based on the variable c, they will choose that number of chips from a jar of chips.

[vagrant vector]

give one iteration of what is meant to happen because i absolutely do not understand your phrasing

[deft terrace]

um whats the use of c here

[tranquil pine]

i have a jar with chips in it and a 6 sided die. first the player will roll the die, if they get 1, 2, or 3 then they will pick 1 chip from the jar. if they get 4, 5, or 6 they will pick 2 chips from the jar.

this is the initial values in the jar

4 chips: 1 token
1 chip: pick 2 more
7 chips: 3 tokens
3 chips: 4 tokens
15 chips: nothing```

if they get that one special chip, then they need to pick 2 more chips from the jar, without replacement

[deft terrace]

ohh is it like 6 chips have the values of 2 tokens or like 2$

per chip

hmmm

[tranquil pine]

yeah

[vagrant vector]

1. why are u using a 6 sided die

[tranquil pine]

but im really confused how to take into account the 1 special chip. since i need to find the win-loss percentage

[vagrant vector]

this is like mathematically equivalent to a coin flip

then after that

[vagrant vector]

^i still dont know what this means

give one iteration

i assume you made the question

[tranquil pine]

ill replace the die with a coin toss.

player tosses the coin. gets a head (count this as 1 pick from the jar)

player picks one chip from the jar, turns out to be that one special chip

player picks 2 chips: 1 chip with value 1 token, 2nd chip with value nothing.

player looses the game, resulting outcome is less than what they paid to play (2 tokens)

[deft terrace]

the chips arent getting replaced right so find the probability of the special chip seperatly

[vagrant vector]

oh

if you want you could lowk just create a probability tree lmao

i think you'll see the pattern quite quickly if you do

[tranquil pine]

one of the requirements is to include a hypergeometric distribution in the solution though.

should i first make a probability tree and go from there or is there a different starting point?

[vagrant vector]

???

why

[tranquil pine]

its just one of the criteria ¯_(ツ)_/¯

[vagrant vector]

weird

ok anyway once you do a probability tree you'll notice something

you can get an infinite sum for every other thing

also

are the chips getting replaced

[tranquil pine]

no they arent

[vagrant vector]

oh

then isnt it like

[deft terrace]

[vagrant vector]

the only way for you to get 4 is either 1 token 3 times, 2 tokens twice or more, you get 3 tokens at least once, or 4 tokens at least once or a combination of them

[deft terrace]

it's just where you show the soln in combinatorics right?

[tranquil pine]

yeah that sounds right

[deft terrace]

well you can do it case wise

[vagrant vector]

case wise wld be my first thought tbh

[deft terrace]

or go through each point possibilty like cat

[deft terrace]

it's the best way to avoid any mistakes

[vagrant vector]

theres definitely some simpler way

[tranquil pine]

my main worry is if im not able to integrate a hypergeometric anywhere

[deft terrace]

why do you want to integrate it tho..

[vagrant vector]

you will definitely use it when you consider ways to hit the 3 lmao

[tranquil pine]

its one of the requirements

[tranquil pine]

oh ok

[deft terrace]

[vagrant vector]

i have never seen any course that made you use that either lol

[tranquil pine]

alr, thanks for the help! i should be good to go now

[deft terrace]

bye bye gl

[tranquil pine]

Calculations are complex by necessity and require the use of binomial or hypergeometric distributions and/or multiple steps to determine overall probability

¯_(ツ)_/¯

[vagrant vector]

and or multiple steps

💀

ok

[tranquil pine]

alr

.close

[final saddle]

Channel closed

Closed by @fervent reef

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[open heart]

I’ve already done the first part of the question now it says I need to find the differences between Klo and Chang in 10 years and 30 years I believe I’m on the percent change part here

[open heart]

I figured it out for this one

Need help figuring out how I structure this in the calculator i use to find the answer

This is the formula I was given to solve the equation

[final saddle]

@open heart Has your question been resolved?

[final saddle]

@open heart Has your question been resolved?

Channel closed

Closed by @open heart

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tranquil pine]

yo

[tranquil pine]

can i get help

it says “after n years” btw

[brisk haven]

is this compound interest

[tranquil pine]

Its to do with reccurence relations

[brisk haven]

you lost me

[rocky tusk]

whats confusing here?

[tranquil pine]

no problem

[tranquil pine]

i don’t understand anything

how do i relate this into a recurring sequence

whats the logic

[rocky tusk]

how about this, what would m_1 be

where m_0 = 5000

[tranquil pine]

well why are we doing this?

like what are we trying to do anyway

[rocky tusk]

can you answer my question?

[rocky tusk]

youll see the pattern eventually

a good strategy is to test some early cases if you cant immediately understand whats going on

[tranquil pine]

m_n = m_n-1 increased by 9%

[rocky tusk]

what?

where is m_{n - 1} coming from here

there is no n yet

[tranquil pine]

Fixed

[tranquil pine]

this would he m_1 = m_0 increased by 9%?

[rocky tusk]

ok but what does that mean in math terms

or just give me a number for m_1

[tranquil pine]

well idk

idk how to increase something by a percentage

m_1= m_0 + m_0 * 9% ?

idek

[rocky tusk]

ok if i have 100 dollars and next year that accumulates to 110 what is the percent increase for the year?

[tranquil pine]

10%?

[rocky tusk]

yes

so if my money m_0 increases by p percent then i have m_0(1 + p/100)

[tranquil pine]

can you please explain this expression

[rocky tusk]

the percent increase is $p = \frac{m_n - m_{n - 1}}{m_{n-1}}$

[soft zealot]

knief

[rocky tusk]

do you agree with this

[tranquil pine]

its more confusing tbh

[rocky tusk]

🤔

the top is the amount i made in the nth year

do you agree with that

[tranquil pine]

Yes

[rocky tusk]

ok then dividing by the amount i had at the beginning tells me the percent it increased

it tells me what the ratio is of the amount i made to the amount i had before

[tranquil pine]

why does it work that way?

[rocky tusk]

maybe an example will help you

lets use the 100 -> 110 example

i made 110 - 100 = 10

then i ask, how much is this 10 dollars relative to what i had at the start of the year

well, its 10/100 = 10%

so i gained 10% of the money i had from the start of the year

[tranquil pine]

oh i see, why do we use division specifically?

[rocky tusk]

im afraid i cant make it much simpler than i already have sir

[rocky tusk]

^

what do you propose instead?

[tranquil pine]

not that i would know

maybe 110-10

Idk

[rocky tusk]

but that just gives me what i had at the beginning of the year

doesnt tell me anything about the relative change

we care about this relative change because for example a 10% increase on 100 dollars is far less significant than say on 1,000,000 dollars no?

[tranquil pine]

wdym by relative change

[rocky tusk]

how much did it change as a percentage of what i had originally

[tranquil pine]

wouldn’t you be dividing by a 100 then

[rocky tusk]

yes

[rocky tusk]

^

[tranquil pine]

But youre dividing by m_n-1

[rocky tusk]

$m_{n - 1} \neq m_n - 1$

[soft zealot]

knief

[rocky tusk]

its a subscript

[tranquil pine]

Yeah i meant thay

[rocky tusk]

so whats confusing

in our example $m_{n - 1} = 100$

[soft zealot]

knief

[tranquil pine]

Why arent you just dividing by a 100 constant

[tranquil pine]

@rocky tusk bro i was right

bruh

[rocky tusk]

sure

[tranquil pine]

nahhh sure is crazy

😂

[rocky tusk]

🤔

[tranquil pine]

why do you say that

im not offended or anything

just curious

[rocky tusk]

tbh i didn't read that as you wrote it

i read $m_1 = m_0 + 0.09$

[soft zealot]

knief

[rocky tusk]

i didn't realize you multiplied it by m_0 as well

its clearer if you write $m_1 = m_0(1 + 0.09)$

[soft zealot]

knief

[tranquil pine]

i see

no problem then

[final saddle]

@tranquil pine Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vague anchor]

10th I don't know where to begin

[zealous storm]

do you know what an arithmetic mean is?

[vague anchor]

Yes

[zealous storm]

then it makes sense to first wrote out what the arithmetic mean would be

for {1,2,...,n}

and equate it accordingly with the arithmetic mean of the same set with {k, k + 1} missing

[vague anchor]

Wait

[vague anchor]

It's (n+1)/2

[zealous storm]

no

S_n = 1 + 2 + .... + n
S_n = n + (n - 1) + ... + 1

add those

2S_n = (n + 1) * n

so S_n = (n + 1)/2 * n

[vague anchor]

Yea

[vague anchor]

It's AM

[zealous storm]

Yes, AM is $\frac{\sum x_i}{n}$, and you know $\sum x_i = \frac{n (n + 1)}{2}$

[soft zealot]

mmmm7

[vague anchor]

Yea

[zealous storm]

anyway okay the AM for {1, 2 , ...n} is (n + 1)/2 sure

What about the AM for {1,2,..., n} when you remove k and k + 1

use the definition

[vague anchor]

[{n(n+1)/2 } - 2k-1]/(n-2)

[zealous storm]

yes

,, \frac{n(n + 1) - 4k - 2}{2(n - 2)} = \frac{\frac{n(n + 1)}{2}}{n} - 1 =\frac{n (n + 1) - 2n}{2n}

[soft zealot]

mmmm7

[vague anchor]

Wait
n-k=1

[zealous storm]

yes

looks like it

[vague anchor]

Thank You so much
@zealous storm
I appreciate ur efforts
.close

.close

[final saddle]

Channel closed

Closed by @vague anchor

Use .reopen if this was a mistake.

[zealous storm]

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[autumn osprey]

Got 0,67

So wanted to see if i was right

[versed crater]

Question is missing something

What’s the chance Harry will hit?

[autumn osprey]

0,5

Or 50%

[versed crater]

How did you get here

[autumn osprey]

Honestly i just want to see how you guys would do it

[proper dagger]

insufficient info

[versed crater]

They added

[autumn osprey]

But i used sum to infinity

[versed crater]

I’d probably try an infinite series

[proper dagger]

hang on

"Gienda also has a 50% chance..."
show the entire question, maybe?

the wording seems like Harry's chances were discussed earlier

[versed crater]

1/2 + (1/2)³ + (1/2)⁵ + …

[proper dagger]

ah ok so it's 50/50 for both archers

[versed crater]

“Also 50%” implies that but they added it here as well

[proper dagger]

ah

[autumn osprey]

Are you a mod?

[proper dagger]

no

[autumn osprey]

Hmmm...

[proper dagger]

you can check my roles list, but why ask anyway

[autumn osprey]

You helped me in a few of my problems so yeah

[proper dagger]

didn't know I have to be a mod to do that, but anyway

[autumn osprey]

Was just interested

[proper dagger]

also, I'm not sure if this is legal, but if P is the probability of the first archer winning, then either the first shot wins, or both miss with probability 0.25, so we're back to the start with probability P again

then we can model this as a recursive equation with P = 0.5 + 0.25P

you'll end up getting the same result though

[autumn osprey]

Thank you

[versed crater]

Yeah that’s the way to do it via markov chains

[proper dagger]

I see

[versed crater]

This is obviously also arⁿ with a = 1/2 and r = 1/4

The formula for a geometric series gives you the same solution

[autumn osprey]

Thank you and Hanako

.close

[final saddle]

Channel closed

Closed by @autumn osprey

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cedar obsidian]

How to solve (c) of problem 2nd

$ x = 5sin[(π) t + π/6]

[tiny kraken]

Mate your cropping skill sucks

Nah I'm kidding

[cedar obsidian]

I didn't crop

Its raw picture

[tiny kraken]

Okayyy

[tiny kraken]

So you get this

Or this is given

[cedar obsidian]

I solved the first two parts from that I came to know that w = 20 and A=5

So v_max is 100

[tiny kraken]

Great now I highly suggest you change it to function of cosin

cuz I hate sin function

[cedar obsidian]

100 = 100cos(20t + π/3)

[tiny kraken]

And it makes more sense how unit circle works

[cedar obsidian]

CorrectM

?

[cedar obsidian]

Why

[tiny kraken]

I dunno, I'll assume it is

[tiny kraken]

Good point gimme a min for a diagram

[cedar obsidian]

Is this clear

[tiny kraken]

Oh wait

Is that v or x

[tiny kraken]

this

[serene breach]

Question 3 right?

[cedar obsidian]

dx/dt = v

[tiny kraken]

v=100cos(20t+pi/3) righ?

[cedar obsidian]

Yes

[tiny kraken]

Okay now gimme a min

[cedar obsidian]

Yes

[tiny kraken]

This is the initial position of velocity

[cedar obsidian]

yes

_A' at t=0 is initial position? _

[tiny kraken]

It will circle counter clockwise

[tiny kraken]

Yeah

[cedar obsidian]

Okay

[tiny kraken]

cuz 20t+pi/3 when t=0 is pi/3 or 60 degree

[cedar obsidian]

Yes clear

[tiny kraken]

Now the motion start and it goes to C

Which is where it get maximum speed

And it circles an angle of 2pi/3

Okay I basically gave 80% of the sols

[cedar obsidian]

2π/3 = 20t +π/3

[tiny kraken]

Nahhh

It circles 2pi/3

It's pi at C

[cedar obsidian]

At its it π

Why 2π/3

[tiny kraken]

It start at pi/3

[cedar obsidian]

Do you mean it bypasses 2π/3

[tiny kraken]

Well yeah, it went a 2pi/3 angle

[cedar obsidian]

180-60 = 120

2π/3

[tiny kraken]

so it's at C which is pi rn

$\omega t$

[soft zealot]

Fionna The Unemployed

[tiny kraken]

Represent the angle it passed

so 20t=2pi/3 here

[cedar obsidian]

Everything was clear till here

I didn't understand after that

[tiny kraken]

C is where it has maximum speed

Do you why?

[cedar obsidian]

No

[tiny kraken]

ehhhh

Cuz cos()=-1

So abs(cos())=1

[cedar obsidian]

okay it's maxima for. Cosine

Okay got it

[tiny kraken]

Yeah only the thing inside the cos vary

So it went a 2pi/3 angle

Angular velocity is omega

So $\theta= \omega t$

[soft zealot]

Fionna The Unemployed

[cedar obsidian]

There are other angles from where it can went and as it starts ie π/3 to π (pt C) why do you pick 2π/3 f

[tiny kraken]

okay let say you are 2m from me and you go 5m further, with velocity = 1

Does that 2m involved when you calculate the time>

[cedar obsidian]

Yes

[tiny kraken]

No right? cuz you only go 5m

It's the same here

[cedar obsidian]

Oh yes

[tiny kraken]

so you can get the time

2pi/3 = 20 t

[cedar obsidian]

Well I didn't still get why you. Select 2π/3

[tiny kraken]

CUZ

It goes from A' to C

the angle between is 2pi/3

[cedar obsidian]

Oh

that is theta and it is 2π/3 = wt

Got it

T = π/30

[tiny kraken]

Yeah

[cedar obsidian]

very confusing sometime

[tiny kraken]

the second time it get maximum speed is A

And it goes a pi+ 2pi/3 angle

And the reason I told you to work with cos is...

$v=A\sin(\omega t + \alpha)$

[soft zealot]

Fionna The Unemployed

[tiny kraken]

Phi would be that angle alpha which is soooooo annoying to work with

[cedar obsidian]

Isn't alpha 90-60

[tiny kraken]

well yeah lol

[cedar obsidian]

Then how annoying

[tiny kraken]

Cuz it's hard to keep track of the angle when it moving

The angle it makes is with Oy

Not Ox

Isn't like how we are taught to use the unit circle

[cedar obsidian]

Yes

Like it should align with s equation

Shm*

[tiny kraken]

Okay that shouls be all

For today LOL

SHM isn't so easy haha

[cedar obsidian]

It's all trig

Haha

.close

[final saddle]

Channel closed

Closed by @cedar obsidian

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[inner spoke]

can anyone explain how we get what phi is equal to

im unsure abt the notation used

[rare girder]

$\phi=\begin{pmatrix}1&2&3\3&1&2\end{pmatrix}$ is the function $\phi:{1,2,3}\to{1,2,3}$ with $\phi(1)=3,\phi(2)=1,\phi(3)=2$.

[soft zealot]

Flip

[rare girder]

uh, but replace my example with the one that's actually used lol

[inner spoke]

so it means 3 1 2?

[rare girder]

what's 3 1 2?

[inner spoke]

a permutation

[rare girder]

which permutation?

[inner spoke]

like does (123 312) mean 312?

[rare girder]

what is 312?

[inner spoke]

the permutation of {1,2,3}

one of the permutations*

[rare girder]

ok but be explicit, what does this permutation map everything to

[inner spoke]

im not sure

[rare girder]

are you trying to use cycle notation?

[inner spoke]

is the top row like index, and bottom row the values?

[inner spoke]

not sure, wasnt told anything

[rare girder]

top row of inputs, bottom row of outputs

saying phi = 312 to say that phi(1)=3, phi(2)=1, phi(3)=2 is never used

[inner spoke]

lol okay

[rare girder]

and it'll be confusing to start using it when you use cycle notation

[inner spoke]

okay so what is it supposed to mean

is this cycle notation?

[rare girder]

$\phi=\begin{pmatrix}1&2&3\3&1&2\end{pmatrix}$ is not cycle notation

[soft zealot]

Flip

[rare girder]

I forget the term used for this explicit notation, maybe tabular or something blah

[inner spoke]

okay

but what does this notation mean exactly

[rare girder]

precisely this

for each input i in the top row, the entry directly below it is phi(i)

[inner spoke]

i see, but then wouldnt it make sense to keep the top row constant

and find the n! permutations

[rare girder]

I think the top row is usually written in the canonical way (1,2,3,...) yes

[inner spoke]

hmm i see

okay i think i sort of get it now

[rare girder]

oh but it's not a problem if the top row isn't in that order

also these are your notes right?

[inner spoke]

not "mine"

but im using them to study

[rare girder]

ok sure

that last $\phi$ needs angle brackets, $\langle\phi\rangle$ to denote the group generated by $\phi$

[soft zealot]

Flip

[rare girder]

$\phi$ is the permutation, $\langle\phi\rangle$ is the group

[soft zealot]

Flip

[inner spoke]

this one?

[rare girder]

ye

[inner spoke]

okay thanks

one question tho

why does it not matter if we change the order of inputs

[rare girder]

well, it doesn't because even if the top row is permuted, it still conveys all of the information needed to characterize the permutation

actually, I'm sorry, let me check again

I change my mind, I hate it

[rare girder]

I think you should disregard what I just said lmao

that's how I thought it'd work

but rereading it with the mindset I just had, all of the entries in the group looked the same

normally you'd still keep the top row fixed, so that the differences between any two permutations was still obvious

[inner spoke]

i see

also i think cycle notation is abt to come up

[rare girder]

$\phi^2=\begin{pmatrix}1&2&3\2&3&1\3&1&2\end{pmatrix}\to\begin{pmatrix}1&2&3\3&1&2\end{pmatrix}$

[soft zealot]

Flip

[rare girder]

1 goes to 2 and 2 goes to 3 by phi, so two applications of phi send 1 to 3

cycle notation is much less cumbersome to work with lol

[inner spoke]

right what you say makes sense

could you help me understand how cycle notation works?

[rare girder]

sure

so for a nontrivial example, consider the permutation $\phi=\begin{pmatrix}1&2&3&4&5&6\3&4&1&5&2&6\end{pmatrix}\in S_6$

[soft zealot]

Flip

[rare girder]

instead of reading the data of phi left-to-right via just the entries in the top row, subject to an arbitrary ordering, we instead consider cycles

we see that 1 goes to 3, and if we skip ahead, 3 goes to 1