help-0

[north grail]

is it correct or not

just tell me

[red nacelle]

yes

[north grail]

aight

z – 19 + 19xy – xyz

[toxic verge]

Where you at rn

[north grail]

so

[twin nimbus]

one sec

sorry

[north grail]

what i did was

i took z – 19 + 19xy – xyz

and formed it into

(19+19xy).(z-xyz)

then i took the common factor of

19 and wrote

[twin nimbus]

that's not quite correct.

[north grail]

then??

[twin nimbus]

if . is supposed to mean multiplication

[north grail]

i have to factorize

[twin nimbus]

\begin{align*}
z - 19 + 19xy - xyz &= z - 19 + 19 (xy) - z (xy) \
&= z - 19 + (19 - z)(xy) \
&= z - 19 + (-1)(-19 + z)(xy) \
&= z - 19 - (z - 19)(xy) \
&= (z - 19)(1) - (z - 19)(xy) \
&= (z - 19)(1 - xy)
\end{align*}

[ocean seal]

OmnipotentEntity

[twin nimbus]

@north grail I tried to make this as slow and explicit as possible. Let me know if you have a question about a particular step, and if I have underestimated your fluency please forgive me.

[north grail]

i cant understand bro im dumb ash

i was in the hospital and missed all my classes

i know nothing about factorization

[twin nimbus]

ok which step did I lose you

[north grail]

first

[twin nimbus]

so in the first line, I explicitly factored term by term and isolated the xy

in each term

[north grail]

ok

[twin nimbus]

so 19xy became 19(xy)

this is just a difference in notation

to highlight the fact that I'm now focusing on the xy

[north grail]

can i send an image of my working after im done attempting it once?

[twin nimbus]

well, follow along with my work first.

then hide my work

and try to redo it from scratch

[north grail]

okok

[twin nimbus]

let me know if you have any other doubts or stopping points

please ping (just me, not mods in general) I'll be looking at other things

[north grail]

wait omg i just did it

[twin nimbus]

yo!

[north grail]

is this it??

i sent the image

[twin nimbus]

I don't see the image in this channel

[north grail]

this

[twin nimbus]

oh, be careful now

[north grail]

why

[twin nimbus]

you're off by a factor of -1

[north grail]

wdym

[twin nimbus]

line 2 to line 3 you screw up a sign

then again line 3 to 4

[north grail]

whaa

which sign

[twin nimbus]

actually sorry, the mistakes are 2 in the transition from 2 to 3, and none from 3 to 4

You have:

\begin{align*}
&z - xyz - 19 + 19xy \
&z(xy - 1) - 19(xy - 1)
\end{align*}

[ocean seal]

OmnipotentEntity

[twin nimbus]

when you should have:

\begin{align*}
&z - xyz - 19 + 19xy \
&z(1 - xy) - 19(1 - xy)
\end{align*}

[ocean seal]

OmnipotentEntity

[north grail]

does that change anything???

[twin nimbus]

it does

4 - 3 is not 3 - 4

[north grail]

oh yea

so i should always keep the 1 infront of the variable??

[twin nimbus]

no, you should just be careful of preserving the order of things

[north grail]

so then what??

[twin nimbus]

if you see ax - bx this is (a-b)x not (b-a)x

[north grail]

for like what reason is the 1 infront

[twin nimbus]

you just need to be careful about the order.

[north grail]

how do i keep the order

[twin nimbus]

x - bx = 1x - bx = (1-b)x

bx - x = bx - 1x = (b-1)x

[north grail]

im asking like in the future

how should i know where to keep the 1 in the equatio

[twin nimbus]

are my examples above not enough?

[twin nimbus]

these

[north grail]

phhh

mb mb

sorry

thanks!

.close

[lone heart]

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[lone heart]

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[ember zenith]

Doing math with my girlfriend, we're stuck on LCD. She has the question (2/x)+(3/x^2)

[ember zenith]

LCD should be X because both sides are divisible by it? But google and answer both say answer is x^2

why am i being stupid??

What am I doing wrong

[minor needle]

Imagine it's 2/5 + 3/25

for example

[ember zenith]

Yeah, LCD is 5, not 25

[minor needle]

What would you do in this case?

How would you add 2/5 and 3/25

[ember zenith]

multiply 2/5 by 5(/5)

(you know what i mean

[minor needle]

Yes and you do it because...?

[ember zenith]

AH right, i see now

ty

i thought LCD was the factor, not the result

the LCD here is x^2 because thats what we're trying to get, we multiply by X

What's X called in this case, then?

the Least common Factor?

[north rover]

I guess we can find it from the defintion of GCF and LCM?

Wait LCD means least common divisor, right?

[ember zenith]

yeah

LEast common divisor/denominator

[keen idol]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[ember zenith]

.closed

.close

[lone heart]

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[rustic coral]

<@&268886789983436800> ^

[vale wigeon]

<@&268886789983436800> advertisement

[clever folio]

Don't advertise here

[toxic verge]

fiverr link for animations ah yes

[lone heart]

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[ember briar]

sorry 😦

[lone heart]

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[scenic stream]

How the hell do I go about solving this assignment? I have no clue what the kernel of f is when I have no vectors with numbers given

Were given a linear mapping f: R3 → R3. The arranged base π = (e1, e2, e3) of the vector space R^3 is such that the vector e1 belongs to the core ker f (kernel of f) and is f(e2) = e3 and f(e3) = -e2. Write a matrix, which is in a ordered (pretty sure its ordered, translated from slovenian, thats why I'm not sure, maybe sorted?) base π, covered by f.

[forest marsh]

Ordered is the word

f(e1) = ?

[scenic stream]

this is in slovenian

maybe it will help

ker f is the kernel

[forest marsh]

I do not speak Slovenian unfortunately

[scenic stream]

I know

[forest marsh]

How so kekw

Anyway

[scenic stream]

f(e1) is somehow the kernel

of f

[forest marsh]

e1 is in ker(f)

So f(e1) = ?

[scenic stream]

I have no clue

[toxic verge]

Bro boutta break out fluent slovenian

[forest marsh]

Ker f := {x in R³, f(x) = 0}

See

So if e1 is in it

f(e1) = ?

[scenic stream]

then its 0 0 0?

[forest marsh]

Yeah

Can say just 0

[scenic stream]

ok, thank you : )

[forest marsh]

answer is now straight forward

[scenic stream]

my bad

.close

[lone heart]

Channel closed

Closed by @scenic stream

Use .reopen if this was a mistake.

[scenic stream]

.reopen

[lone heart]

✅

[scenic stream]

wait

[scenic stream]

how do we know e2 and e3 though?

does the arranged/sorted base π = (e1, e2, e3) mean its the standard base?

[forest marsh]

f(e2) and f(e3) are given

[scenic stream]

?

except for e1

[forest marsh]

I think the use of e1,e2,e3 is induced as standard basis

[vale crag]

no, it doesn't even matter what basis you have for the purposes of this question

[forest marsh]

No idea what ordered basis is

[scenic stream]

ig that when in doubt, standard base is it

[vale crag]

but sure think standard basis here if you want

[scenic stream]

it does since I have to give an answer

the answer being this

[forest marsh]

Yeah so you express f(ei) in terms of the ei

First column for e1 and first line for e1

And so on

[vale crag]

so what, I'm saying the answer doesn't depend on the basis at all here

[scenic stream]

ig I get it

thanks again

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[scenic stream]

Assignment:
f: R^2 -> R^2 is a linear mapping, where f(x,y)=(3x+4y, 2x-5y).
Find a matrix, which belongs to the mapping f based on the sorted base ((1,2),(2,3)).

My question:
Why does my solution work? I dont understand it and would like to.

EDIT: Is it because Ax=y so were solving for x? Thats how I interpret it currently.

[lone heart]

@scenic stream Has your question been resolved?

[scenic stream]

<@&286206848099549185>

[patent vale]

is it Ax=y?

[scenic stream]

I just figured out its not

but what is it then?

is it that we're deriving the matrix from the column matrix and its corresponding vectors? that the only thing I can think of

idk

[onyx swallow]

you are finding out the matrix, $M$ where $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}M=\begin{bmatrix}11 & 18\ 8 & -11\end{bmatrix}$

[ocean seal]

qwertytrewq

[scenic stream]

I semi understand this, but I still dont understand why these steps work

also what even is this matrix? why do we write the vectors left to right and not top down

[onyx swallow]

Why is this? because you are mimicking row operation on both sides, and row operations are multiplication on the left by elementary matrices: so essentially you have
$$E_1\cdots E_k \begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}M=E_1\cdots E_k \begin{bmatrix}11 & 18\8 & -11\end{bmatrix}$$
and you have shown that after this row operations, $E_1\cdots E_k \begin{bmatrix} 1 & 2\2& 3\end{bmatrix}=\mathrm{Id}$

[ocean seal]

qwertytrewq

[scenic stream]

an elementary matrix is I right?

[onyx swallow]

no, elementary matrix correspond to single row operation

[scenic stream]

why did you then write E_k * the matrix [1,2;2,3] if elementary matrices correspond to single row operations? whilst the matrix [1,2;2,3] has two rows

or are E_1...E_k single line matrices?

[onyx swallow]

E_1,...,E_k are the row operations you have done

listed one by one

[scenic stream]

this?

[onyx swallow]

you did three elementary row operations, subtract 2 of the first row from the seconf row, invert second row, and subtract 2 of second row to first row

[scenic stream]

ok

[onyx swallow]

for example, subtracting 2 of row one from row 2 is the same as multiplying on the left by
$$\begin{bmatrix} 1 & 0 \ -2 & 1\end{bmatrix}##

[ocean seal]

qwertytrewq
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[scenic stream]

oohh ok

[onyx swallow]

And you can check: $\begin{bmatrix} 1 & 0 \ -2 & 1\end{bmatrix}\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}=\begin{bmatrix} 1 & 2\ 0& -1\end{bmatrix}$

[ocean seal]

qwertytrewq

[scenic stream]

what do you mean by the fact that I have shown that after this row operations, $E_1\cdots E_k \begin{bmatrix} 1 & 2\2& 3\end{bmatrix}=\mathrm{Id}$ ?

[ocean seal]

N1cK
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[onyx swallow]

because you did some row operations and got the identity matrix

that means that $E_1E_2E_3\begin{bmatrix} 1 & 0 \ -2 & 1\end{bmatrix}$ gives you the identity matrix, where $E_3$ is your first row operation, $E_2$ is your second, and $E_1$ is your third

[ocean seal]

qwertytrewq

[scenic stream]

but I didnt get it, an identity matrix is in the 1. screenshot whilst I got the 2. screenshot

[onyx swallow]

you didn't specify your latter two row operation

but you did them right there

[scenic stream]

oh

[onyx swallow]

like these row operations corresponds to the row operations making $\begin{bmatrix} 1 & 2\ 0 & -1\end{bmatrix}$ into $\begin{bmatrix} 1 & 0\ 0 & 1\end{bmatrix}$

[scenic stream]

ok I get this part now

[ocean seal]

qwertytrewq

[onyx swallow]

you just didn't write it out properly

[scenic stream]

but I dont understand this one

why is this true that when I do row operations I get the corresponding matrix for the given base on the right side?

[onyx swallow]

let your row operations be $E_3$, $E_2$, $E_1$, so what you computed is $E_1E_2E_3\begin{bmatrix}11 & 18\8 & -11\end{bmatrix}$

[ocean seal]

qwertytrewq

[onyx swallow]

But let is suppose that there is a matrix $M$ such that $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}M=\begin{bmatrix}11 & 18\8 & -11\end{bmatrix}$

[ocean seal]

qwertytrewq

[onyx swallow]

show that $M$ is the matrix you computed (hint: left multiply both side by $E_1E_2E_3$)

[ocean seal]

qwertytrewq

[scenic stream]

ok, but I still dont get where the getting the identity matrix on the left side means that we gont M on the right side part comes in play here

[onyx swallow]

multiply both side by E_1E_2E_3, simplify, and youll get M=the thing you computed

on the left you get Id *M which is just M

[scenic stream]

so matrix M is the matrix that belongs to f when the base is (1,3),(2,5) right?

in this example

[onyx swallow]

wdym

i havent shown that M is the matrix yet

im just telling u essentially what you got

it turns out M is the matrix you want

[scenic stream]

no I'm saying, the answer that I got in my example is the matrix that belongs to f when the base is ((1,3),(2,5))

[scenic stream]

yea, I'm just asking what that matrix is exactly so that I can clarify it for myself

[onyx swallow]

idk what "mattix belongs to f" is and where ((1,3),(2,5) came from

[scenic stream]

Find a matrix, which belongs to the mapping f based on the sorted base ((1,2),(2,3)).

this is the assignment

so I'm guessing waht I found is the matrix that belongs to the mapping f based on the sorted base ((1,2),(2,3)), no?

I mean it is since its written in the solutions, I just want to tie it back to your explanation

[onyx swallow]

yeah but not (1,3,(2,5

[scenic stream]

in your explanation this would be the matrix M right?

oh my bad

wrong assignment I was looking at

base ((1, 3),(2, 5)) is what I meant

where the solution is

[scenic stream]

and in your explenation this would be matrix M?

[scenic stream]

this one

[onyx swallow]

yeah M is the matrix you want

[scenic stream]

please say yes because if so then I have understood

lets gooo

thank you for the help, much appreciated : )

[onyx swallow]

well we havent shown that M indeed is the matrix yet

[scenic stream]

what is missing?

[scenic stream]

you mean in your explanation or in my solving?

[onyx swallow]

do you know why $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}M=\begin{bmatrix}11 & 18\8 & -11\end{bmatrix}$ implies $M$ is the matrix for $f$ in the given base?

[ocean seal]

qwertytrewq

[scenic stream]

no I have no clue why this implies M is the matrix for f in the given basis

[onyx swallow]

then theres more work to be done

we have to show that M is precisely what we want

all we know rn is that we have this radom matrix that satisfy a random equality

[scenic stream]

ok, how do we show this

[onyx swallow]

Let $N$ be the matrix of $f$ in the given base, we wish to show that $N=M$

[ocean seal]

qwertytrewq

[scenic stream]

also why are you not giving me te full explanation directly? I'm guessing I'm too dumb to understand it right away?

[scenic stream]

ok so you just changed the label from M to N?

oh nevermind

theyre 2 sepperat things ok

[onyx swallow]

i think the purpose of this channel is to not give the solution right away and making sure pppl understand every step

[scenic stream]

thanks for taking the time

[onyx swallow]

yeah what do we want N to satisfy?

What should $N\begin{bmatrix}1\ 0\end{bmatrix}$ spit out?

[ocean seal]

qwertytrewq

[scenic stream]

being the same or same to the linear combination of vectors in M?

[onyx swallow]

i wasnt too specific, can you answer the second question instead?

[onyx swallow]

^this one

[scenic stream]

it should spit out $\begin{bmatrix} 1 & 2\ end{bmatrix}$

hahhahahah

[scenic stream]

it should spit out the matrix [1,2]^T?

[onyx swallow]

no

[scenic stream]

are we not multiplying it with this base?

[onyx swallow]

1,0 reposent the basis vector 1*(1,2)^T+0*(2,3)^T

it really means that we have 1 part of the first basis, and two part of the second basis

[scenic stream]

yea exactly, so you would get the vector (1,2)^T

(1+0,2+0)^T, I dont get where I'm wrong here

[onyx swallow]

no N applies the transformation f

so N(1,0)^T should really output (11,-8), but written in your new basis

[scenic stream]

did you mean N*[1,0]^T here or N = [1,0]^T?

[onyx swallow]

i didnt write =, so yeah the former

[scenic stream]

yea I have no clue what N is

thought I did, but I dont

[onyx swallow]

^

N just applies the transformation of f but in your new basis

[scenic stream]

I mean if its this matrix, shouldnt you have written that N ∼ M here?

[onyx swallow]

input how many part (1,2) you have, and how many part (2,3) you have, it outputs how many part (1,2) you have and how many part (2,3) you have after the transformation og f

[onyx swallow]

what does N~M mean?

im trying to show that N and M are the same matrix

[scenic stream]

Im lost with this N matrix

I dont understand the perpouse of it

[onyx swallow]

we are setting N to be the answer to the question

and showing M=N

[scenic stream]

ok

[onyx swallow]

an indirect approach but easier to explain

[onyx swallow]

so lets go back to this question

If N is the answer what do we expect this product to be?

[scenic stream]

how should it spit out (11,-8) when [(1,2),(2,3)]*[1,0]^T is not = to (11,-8)

[onyx swallow]

it shouldnt spit out (11,-8)

it should spit how (11,-8) is written in the new basis (1,2),(2,3)

[scenic stream]

no I'm talking about this

oh wait youre right

[onyx swallow]

and you can verify, -49(1,2)+30(2,3)=(18,-11)

Anyways notice that this is exactly saying that $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}N\begin{bmatrix}1\0\end{bmatrix}=\begin{bmatrix}11\-8\end{bmatrix}$

[ocean seal]

qwertytrewq

[scenic stream]

ok

[onyx swallow]

try and verify it if u want

$\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}N\begin{bmatrix}0\1\end{bmatrix}=\begin{bmatrix}18\-11\end{bmatrix}$

[ocean seal]

qwertytrewq

[onyx swallow]

by a similar argument

[scenic stream]

I get (-147, 150) wth

[onyx swallow]

might be a computation mistake?

multiplying by this 1 2 2 3 matrix is just recovering from the basis (1,2)(2,3) to the normal basis (1,0),(0,1)

[scenic stream]

so what I should compute is (-49)*1+39*2?

[scenic stream]

for this

[onyx swallow]

wait a sec

[scenic stream]

wait mb I get 11

but still, its not 18

[onyx swallow]

yeah thats a typo it should be (11,-8)

[scenic stream]

oh it should be (11, -8)

ye

[onyx swallow]

as tou originally wrote

[scenic stream]

ok, I verified it

[onyx swallow]

where (1,2) maps to

[onyx swallow]

and you can check this true

[scenic stream]

it is yea

[onyx swallow]

intuitively it makes sense because you are just recovering the actual mapping

[scenic stream]

so what have we proven?

it still doesnt though in my head

[onyx swallow]

this will show that $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}N=\begin{bmatrix}11 & 18\-8 & -11\end{bmatrix}$

[ocean seal]

qwertytrewq

[onyx swallow]

So since $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}$ is invertible, $M=N$

[ocean seal]

qwertytrewq

[scenic stream]

so basically if I understand it correctly, since we know how to do the mapping with normal i, j, k... vectors, but when we have some different base, we dont, we then have to traverse the transfomation matrix via the process that you are proving to me?

[onyx swallow]

yeah

[scenic stream]

fok mey backwords

[onyx swallow]

it outputs "how many part (1,2) you have, and how many part (2,3) you have"

but by multiplying by the matrix $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}$ you get its value

[ocean seal]

qwertytrewq

[scenic stream]

is the process that you were proving basically this?

[onyx swallow]

yeah

[scenic stream]

not exactly but similar?

ooooh

but where did we use teh SAS^1 matrix in this process?

or in other words why didnt we use it?

[onyx swallow]

$N=\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}^{-1}\begin{bmatrix} 11&18\-8&-11\end{bmatrix}$ if you want

[ocean seal]

qwertytrewq

[scenic stream]

huh

[onyx swallow]

and $\begin{bmatrix} 11&18\-8&-11\end{bmatrix}$ is really $\begin{bmatrix}3&4\2&-5\end{bmatrix}\begin{bmatrix} 1& 2\ 2&3\end{bmatrix}$

[ocean seal]

qwertytrewq

[onyx swallow]

So you get your $N=\begin{bmatrix} 1& 2\ 2&3\end{bmatrix}^{-1}\begin{bmatrix}3&4\2&-5\end{bmatrix}\begin{bmatrix} 1& 2\ 2&3\end{bmatrix}$

[ocean seal]

qwertytrewq

[scenic stream]

Ill try to solve it using SAS^1

[scenic stream]

also I didnt understand this part

why is it being invertible important here?

[onyx swallow]

If $A$ is not invetible, then $AM=AN$ would not imply $M=N$

[ocean seal]

qwertytrewq

[proven leaf]

Also, $\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}N=\begin{bmatrix}11 & 18\-8 & -11\end{bmatrix}\implies \begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}^{-1}N=IN=N=\begin{bmatrix} 1 & 2\ 2& 3\end{bmatrix}^{-1}\begin{bmatrix}11 & 18\-8 & -11\end{bmatrix}$

[ocean seal]

PajamaMamaLlama

[proven leaf]

where I is the 2x2 identity matrix

[scenic stream]

Wth why did I get the wrong answer

[onyx swallow]

S^{-1}AS i think

[scenic stream]

youre right

also why do we get (1,2)(2,3) and not just (1,2) or just (2,3)

do we have to have 2 base vectors in a R^2 space?

[lone heart]

@scenic stream Has your question been resolved?

[scenic stream]

.close

[lone heart]

Channel closed

Closed by @scenic stream

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• 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.

[mystic steeple]

@patent vale

[peak juniper]

Mb

I aint see

[mystic steeple]

How did u get that line

[peak juniper]

Huh

[mystic steeple]

Not u

[patent vale]

thats just what the W function does

if you feed it something in the form xe^x it will return x

just like how e^x if you use ln it returns x

[lone heart]

@mystic steeple Has your question been resolved?

[mystic steeple]

How

[patent vale]

its just how it works

its a non standard function though so there is no way on a regular calculator to calculate it

[mystic steeple]

Is it e^z = 1/Wk ?

[patent vale]

I dont think so

[grizzled mauve]

did you learn about how

under certain assumptions

an equation with x and y in it has y define a function of x locally even if you can't solve for y

[mystic steeple]

Am watching a YouTube video

To get a clear insight

[grizzled mauve]

this is usually presented to students when they learn implicit differentiation

informally

and formally in calc 3

like if I write

y^4 + 3xy -y^2 +yx^2 - 5 = 0

,w plot y^4 + 3xy -y^2 +yx^2 - 5 = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by gfauxpas

[grizzled mauve]

then this LOCALLY defines y as a function of x

did you learn that

[mystic steeple]

What my brain is not braining rn

[grizzled mauve]

did you take calc i

[mystic steeple]

Nah am taking alg2

[grizzled mauve]

oh so that's why you havent heard of it lol

take a look at the graph of y^4 + 3xy -y^2 +yx^2 - 5 = 0

[mystic steeple]

But I do know a bit of differentiation

[grizzled mauve]

no need, it's actually not needed, one moment

[mystic steeple]

Glad to hear that

[grizzled mauve]

this is a graph of this equation

you will notice that y is not a function of x in general BUT

if you zoom in to a small enough area, and ignore the rest of the graph

then IN THAT AREA y is a function of x, does that make sense?

in this particular example, the top curve defines y as a function of x, and the bottom curve also defines y as a function of x, so as long a you consider them one at a time

then y is a function of x, but you can't say y is a function of x everywhere at once

does that make sense

[mystic steeple]

Wait

Lemme think a bit more

[grizzled mauve]

[mystic steeple]

Oh yeah I get that

[grizzled mauve]

okay so

the equation

$ye^y = x$

[ocean seal]

gfauxpas

[grizzled mauve]

also defines y as a function of x LOCALLY

in a particular area

but you can't solve for y uniquely for all of x at once, because the curve is not a function everywhere at once

just like the above curve becomes two functions

this curve also becomes two functions

the blue one is called $W_0$ and the red one is called $W_{-1}$

[ocean seal]

gfauxpas

[grizzled mauve]

either way we use the letter "W"

and the definition of this W, called Lambert W, are the TWO functions given by

$We^W =x$

[ocean seal]

gfauxpas

[mystic steeple]

For the red one does x=0 provide the same y value? It kinda looks like it does

[grizzled mauve]

that point is not x=0 but x=-1/e

there is where they agree

[mystic steeple]

No at 0

[grizzled mauve]

so in your original problem you have, let me look at your notes again

no at zero the blue curve and red curve are different

they are ONLY the same at -1/e

$ze^z = \text{thing}$

[ocean seal]

gfauxpas

[grizzled mauve]

this is from your notes right

[mystic steeple]

No I mean I am talking about the red graph solely

At x=0 does it give same y value

[grizzled mauve]

wdym it's a function

W(0) = a single number

[mystic steeple]

Oh yeah right my bad

[grizzled mauve]

it's confusing!

because

the whole thing is two functions at once

anyway in your notes you have

$ze^z = \text{thing}$

[ocean seal]

gfauxpas

[grizzled mauve]

how do you solve for z?

well that's what lambert w is for

$z= W(\text{thing})$

[ocean seal]

gfauxpas

[mystic steeple]

So at that line its not a function

[grizzled mauve]

and if you write it without a number "0" or "-1" then this isnt function right

it means this equation has two values

but

when the note writes $W_k$

[ocean seal]

gfauxpas

[grizzled mauve]

it means, for a particular choice of W, to be a function

these choices are called branches

for real numbers there are only two branches, if you allow z to be complex there's one branch for each integer

so infinitely many branches

but when the author writes W_k here they mean "for a particular choice of branch one at a time"

hth

[mystic steeple]

Does it need to be 0 or -1 specifically or it could be any value u want?

[grizzled mauve]

it has to do with the shape of the curve when you use complex numbers

good question

-1 corresponds to looping around once clockwise

0 corresponds to looping 0 times

in complex numbers looping counterclockwise is called positive and clockwise is called negative

[mystic steeple]

What about real numbers

[grizzled mauve]

then there arre only two choices, W0 and W-1

[mystic steeple]

When to use what

[grizzled mauve]

thats a good question that i don't know the answer to

[mystic steeple]

Oh ok
Thank you so much for your help!

[grizzled mauve]

bo

np*

[mystic steeple]

@patent vale

When do we use 0 and -1 for k.
You have used both here 👇🏻

[patent vale]

bit late response but you use the -1 branch whenever the number in the lambert W function is between -1/e to 0

so -0.37 to 0 approximately

and the value inside the lambert W function here is around -0.00005 which is within the range

[lone heart]

@mystic steeple Has your question been resolved?

[lone heart]

@mystic steeple Has your question been resolved?

[lone heart]

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[alpine sable]

Hey is 0 raised to the power 0 equal to 1 or 0?

[unique dune]

Undefined

[alpine sable]

My teacher said its both 0 and 1 depending on the contex5

Context*

[unique dune]

Ye

[alpine sable]

So how do I know the context?

[modern sedge]

I'd say don't worry about it for now. If it's useful to define 0^0 to be either 0 or 1 in some specific context, your teachers should tell you

[alpine sable]

Oh ok 👍
Thank you

.close

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[crimson crow]

hey, I'm having trouble expanding this quadratic, here is the question.

[crimson crow]

(5x − 3)(x + 2√2)

[vale wigeon]

ok, and what's troubling you?

you're gonna have some radicals in your final answer. if that's what was tripping you up, this is perfectly normal

[crimson crow]

yeah, exactly. my answer was 5x^2+10√2x-3x-6√2

but negative square roots are imaginary (my first time learning this).

[vale wigeon]

there are no square roots of negative numbers in here

the only number that appears under a square root sign here is 2 and that's positive as can be

[crimson crow]

what about -6√2

[vale wigeon]

$-6 \sqrt{2}$ means $(-6) \times \sqrt{2}$.

[ocean seal]

Ann

[vale wigeon]

the minus sign is not under the root.

[crimson crow]

oh ok

[vale wigeon]

the phrasing "negative square roots" is confusing and bad for exactly this reason

[crimson crow]

ok, interesting

im going to send you another questions regarding this one second

i dont understand how they got to the third step, could you explain

[vale wigeon]

they just collected the two x terms together

$-ax - bx = -(a+b)x$

[ocean seal]

Ann

[crimson crow]

right, yeah i see now. thank you. This is to simplify right?

[vale wigeon]

yeah sure

[crimson crow]

ok, thanks again, apreciate it

[vale wigeon]

!done

[lone heart]

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

[crimson crow]

.close

[lone heart]

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[somber dagger]

what does it mean by series has a finite sum

[vale wigeon]

it means that the sequence of partial sums of the series is convergent

[somber dagger]

so sum to infinity exists if the series has finite sum?

[vale wigeon]

yes

[somber dagger]

oh alr tysm! if series has infinite sum means divergent right?

[vale wigeon]

"divergent" could mean that the sum is ±∞ or that it doesn't even exist at all

[somber dagger]

ohh got it tysm for ur time

.close

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[devout cypress]

what am i doing wrong here? in integrating via horizontal strips

[livid sage]

judging from what you did, the error is you didn't multiply the integral of sqrt(y) dy by 2

if you accounted for that, then there's an algebra error somewhere down

[lone heart]

@devout cypress Has your question been resolved?

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[halcyon yarrow]

I jsut don’t even know where to start like I already struggle on this topic of quadratics and figuring out the stuff on the graph

[halcyon yarrow]

If someone could like show me some steps to help me do it

[rigid tree]

Do you know the formula to find what x value yields the maximum y value for a parabola?

[lone heart]

@halcyon yarrow Has your question been resolved?

[lone heart]

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[nocturne prism]

Is the 6/(x-1) = X+4/4 correct

This is a practice exam so some help if it's correct twould be 👍

It's kind of a bad pic as I ran out of room lol

[lone thicket]

3rd to 4th line: -x+4x = +3x not -3x

[nocturne prism]

Yep U are right

[lone thicket]

Oh, there is an error even before that.

[nocturne prism]

Its just 7 and -4

[lone thicket]

24 = (x+4)*(x-1) <=> 24 - (x+4) (x-1) = 0 <=> 24 - [ x^2 - x + 4x - 4] = 0

[nocturne prism]

Does the =0 matter

[lone thicket]

Of course it matters. It is an equation.

[nocturne prism]

Ok I will re do the question

.close

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[nocturne marsh]

A pulley system has a 3 kg object on one side and a 5 kg object on the other. The 5 kg object is held at a height of 4 meters above the ground, while the 3 kg object is resting on the ground. The system is initially at rest. If the 5 kg object is released, what height from the ground will the 3 kg object reach? (Take g=10)

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[keen idol]

can u draw a diagram?

[nocturne marsh]

ok

[keen idol]

thats awesome!

now can u use newtons second law on each body?

[nocturne marsh]

Yeah, first we need to find the acceleration, right?

[keen idol]

mhm

notice how their accelerations r the same in magnitude?

just that one is going up and the other is going down

[nocturne marsh]

ame

[keen idol]

so try writing f=ma for body 1 and f=ma for body 2

[nocturne marsh]

same

i got a =20/8ms-2

[keen idol]

correct!

so the 3kg mass accelerates upwards with 2.5 ms^-2

now use the kinematics equation for motion

v^2=u^2+2as

[nocturne marsh]

for which body?

[keen idol]

the one that the question asks

the 3kg object

[nocturne marsh]

but i dont knowthe initial velocity

[keen idol]

"while the 3 kg object is resting on the ground."

[nocturne marsh]

so u=0?

[keen idol]

yes

[nocturne marsh]

but it dont make any sense. then i got the answer for V

[keen idol]

yeah

then u find max height

wait let me see again

oh yes

whatever distance the 5kg pulley moves

that distance is moved upward by the 3kg pulley

so we use v^2=u^2+2a(4)

first can u find v?

ill tell u what to do next

[nocturne marsh]

v=root(20)

[keen idol]

okay before we proceed, do u understand this logic?

try visualizing the 5kg pulley moving down

and seeing what happens to the 3kg pulley

[nocturne marsh]

do u mean the distance move by 5kg same to distance move by3kg in a given time?

[keen idol]

yes

but then when the 5kg block hits the floor

[nocturne marsh]

so is it 4m

[keen idol]

the 3kg block becomes a projectile because it has an initial velocity which we calculated here

so now we need to find the max height achieved

we r basically shifting the problem to a new projectile that is launched with an initial velocity √20 directly upwards

can u find the max height for that?

[nocturne marsh]

isn't it final velcoity?u said initil; velocity is 0

[keen idol]

that was for first part of the problem

v represents the velocity exactly when the 5kg block hits the ground

once the 5kg block hits the ground, the 3kg block is going to move up for a bit with velocity v then fall back down to some height due to gravity

[nocturne marsh]

but imagine when one sideof the pully is go down the same distance move by other side as the two bodies hangon same thread so answer is 4m?

[keen idol]

final answer is not 4m

[nocturne marsh]

why

[keen idol]

yes the 3kg block travels 4 meters up

then it travels a bit more

because it has a nonzero velocity at that point

[nocturne marsh]

how?

[keen idol]

this is a nonzero velocity

for 3kg object

[nocturne marsh]

whatis that?

[keen idol]

the 3kg object will keep travelling up for a bit even though the 5kg object is on the ground now

[nocturne marsh]

ahh ok

[keen idol]

okay so now we change the problem a bit

[nocturne marsh]

bcz theres is a velocity root(20) and that go up until become zero

[keen idol]

what we have now:

a 3 kg block is at height 4 meters with an upward velocity of √20 ms^-1

do u agree?

[nocturne marsh]

ok

yes

remain part go under gravity?

[keen idol]

now we transform the problem to a standard free fall problem:

a 3kg block is thrown directly upwards with a velocity of √20 ms^-1 and gravity acts on it downwards. what is the max height it achieves?

[nocturne marsh]

1m

[keen idol]

correct!

so it travels 4 meters PLUS 1 meter

[nocturne marsh]

then final ans 5m?

[keen idol]

yes

[toxic verge]

Why do you still have the shiny role

[nocturne marsh]

You're super helpful, thank you!

[keen idol]

no worries

u may type .close

[nocturne marsh]

.close

[lone heart]

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[rapid python]

!help

[lone heart]

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

[rapid python]

Which symbol is used in this set-builder form?

!help

[lone heart]

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

[vale wigeon]

that command only prints the factoid

it doesn't do anything else and it doesn't make helpers magically come to you

anyway that symbol looks broken

we can't tell what it is

best guess is that they meant ≠, but the encoding went kaput

[toxic verge]

x is such that x ladder x

Totally

[rapid python]

So what does that question means? What's the answer? The question is awkward

[rapid python]

What?

[toxic verge]

Nothing

[modern sedge]

the symbol is broken, try solving it like if it was
{x : x ≠ x}
and report it to your teacher later

nothing better you can do

[rapid python]

It's not teacher's I was practicing SETS on website: Self study

[modern sedge]

I see, then just move on

[rapid python]

Can't that question be solved

[modern sedge]

the symbol is broken

that ladder-like symbol has no meaning

it's a computer issue, not math issue

you could try reloading the page

[rapid python]

And what about this question? Does not (B-C)' = (B' union C')

[modern sedge]

nope, that's (B ∩ C)' = (B' union C')

(B-C)' is different

you can write B - C as B ∩ C', and then apply the same rule

[rapid python]

Oh yeah

But how did you write intersection symbol in your keyboard?

[modern sedge]

i copied it from net

[rapid python]

But how will I solve that question

[modern sedge]

this one?

[rapid python]

Is (B - C) = (B intersection C')' = B' union C

[rapid python]

Yeah

[rapid python]

Am I right?

[modern sedge]

Yes

[rapid python]

How can I solve question further

[modern sedge]

oh actually you just forgot '

(B - C)' = (B intersection C')' = B' union C

and now its fine

[modern sedge]

now compute B' union C

[rapid python]

This is what I do as well

But what will be "B' " - ?

Bruh what's going on🤯. I am going to gpt

[modern sedge]

B' is just complement of B

[vale wigeon]

!nogpt

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[modern sedge]

B' includes everything which is in the universal set, but not in B

[rapid python]

Then what should I do? No one is helping me

[rapid python]

Ok

I am not using

[vale wigeon]

that's kinda rude to say when @modern sedge is literally guiding you

[rapid python]

I know that but in this case that will not gonna make me answer

[modern sedge]

It will

we are trying to find (B - C)'

we already figured out that it's equal to
B' union C

so we just have to find out what B' union C is

so start by finding B' and then take the union of it with C

so.. if you still need help, have you found out what B' is? If so, can you just list its elements here?

[rapid python]

#Questions -

Universal set = {a,b,c,d,e,f,g,h}
A = {b,c,d,e,f}
B = {a,b,c,g,h}
C = {c,d,e,f,g}

                          Find (B - C)'

My Solution:
(B - C) = (B intersection C')' = B' union C

So, B' = {a,b,c,d,e,f,g,h}

= B' union C
= {a,b,c,d,e,f,g,h} union {c,d,e,f,g}
= {a,b,c,d,e,f,g,h}

---

Am i correct?

[modern sedge]

So, B' = {a,b,c,d,e,f,g,h}

this isnt right

[alpine obsidian]

Hi

I have a problem

[modern sedge]

B' means "set of everything that is in universal set, but not in B itself"

[rapid python]

So I will not be using elements of B

Let me do again

[modern sedge]

Please claim another channel

[rapid python]

#Questions -

Universal set = {a,b,c,d,e,f,g,h}
A = {b,c,d,e,f}
B = {a,b,c,g,h}
C = {c,d,e,f,g}

                          Find (B - C)'

My Solution:
(B - C) = (B intersection C')' = B' union C

So, B' = {a,b,c,d,e,f,g,h}

= B' union C
= {d,e,f} union {c,d,e,f,g}
= {c,d,e,f,g}

---

Done?

[modern sedge]

Seems good now

[rapid python]

Yeah the answer is correct as well

[modern sedge]

(B - C) = (B intersection C')' = B' union C

So, B' = {a,b,c,d,e,f,g,h}

This should just be

(B - C)' = (B intersection C')' = B' union C

So, B' = {d, e, f}

but i think you just forgot to change that

[rapid python]

Oh yeah

[lone heart]

@rapid python Has your question been resolved?

[rapid python]

Yes

[stone orchid]

put .close

[lone heart]

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[mystic steeple]

@grizzled mauve

[grizzled mauve]

[mystic steeple]

He has answered this question. U can check it out if u want

[grizzled mauve]

but they overlap

so if the area you want is only one of them i know how to pick

but in the overlapping area [-1/e, 0] i dont know which to pick

[proud obsidian]

i did not know banana stealer helped people

[grizzled mauve]

he steels bananas

but he also helps people

[mystic steeple]

Oh yeah he does

[toxic verge]

Fr

[mystic steeple]

He picked both right?

For the overlapping area you're talking about

[grizzled mauve]

idk i told you i dont know the answer to this lol

i dont understand how he answered in the case where they overlap

<@&286206848099549185> M wants to know, when to use the -1 branch of Lambert-W and when to use the 0-branch? I have no idea

on the interval where they overlap

[mystic steeple]

What am saying is in the picture it says u can use both

[grizzled mauve]

it could be there really isn't a reason to use one over the other unless you're doing some applied math problem where one answer makes more sense

maybe you want the answer closer to the line y=x or something because that's the type of computer you're building

or maybe you want the answer with the smaller absolute value

[lone heart]

@mystic steeple Has your question been resolved?

[lone heart]

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[turbid ice]

$\int \left( \frac{1}{\sqrt{b\ln{(ax+b)}-b+ax\ln{\left(\frac{ax+b}{ax}\right)}-cx}} \right) dx$

[ocean seal]

Aditya

[turbid ice]

how do i approach this? any idea?

[red nacelle]

what the fuck is that

[red nacelle]

try reordering the terms

[woeful zenith]

sometimes you must use the force of your mind to push through hard problems for optimum learning. At other times, you must use wolfram alpha

this is one of the latter

[red nacelle]

you can get ln(ax + b) + ln(ax + b/ax)

meaning you can multiply them together

js brute force ts

[wheat isle]

vro is ts elementary 💔

[turbid ice]

coeefficients are different

[red nacelle]

yeah but you can drag them

(ax + b)^b

((ax + b)/ax)^ax

[turbid ice]

i can take ln (ax + b) common so we get (ax + b)*ln(ax+b)

and i get ax*ln(ax)

and -cx and -b

i know there is something called euler substitution

but it requires something like ax^2 + bx + c

[wheat isle]

ever heard of the wolfram alpha substitution

u plug ts into wolfram

💔

[red nacelle]

ok i only noticed the dx just now

[lone heart]

@turbid ice Has your question been resolved?

[lone heart]

@turbid ice Has your question been resolved?

[turbid ice]

oh well

i don't think its resolvable

i'll just tick so others can use the channel

[lone heart]

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[alpine sable]

I need to ask the generalization of some results

[cerulean orchid]

I’m a cyber monkey

[alpine sable]

In linear algebra

For infinite dimensions or infinite collection and how to think abr them

Like the way we define

Linear sum of subspaces and direct sum ...those are for finite number of subspaces

What if there are infinite number countable or uncountable

Similarly we define dependency and independency on finite number of vectors

Whatif infinite?

[maiden glen]

for linear/direct sums over infinite collections, you take the collection of finite linear combinations of vectors drawn from the component spaces

$$\bigoplus_{i\in I}U_i:=\left{\sum_{i\in J}u_i;\middle|;J\subseteq I \text{ finite}, u_i\in U_i\right}$$

[ocean seal]

Desync

[maiden glen]

the definition of linear independence also extends similarly

you still only look at finite sums

[mortal trellis]

equivalently, infinitely many terms but only finitely many nonzero. thats also a version you will see

[alpine sable]

Why can't we define infinite sum?

[maiden glen]

you might see things like "finite support" in this context a lot

[mortal trellis]

for infinite sums you need convergence

[alpine sable]

And it's pretty vague to me that we are considering, sets for finite sums

[mortal trellis]

you dont have that in a general vector space

[maiden glen]

and a vector space in general does not have a topology for convergence

[alpine sable]

But convergence of what? Here it could be any vector .. abstract then?

[alpine sable]

🥺🥲 topology...still I haven't studied ..m in first yr 🥲

Sorryyyyy🥲

[maiden glen]

iterating your operations infinitely many times might not yield an element of the vector space without convergence results

vector addition is VxV->V and scalar multiplication KxV->V

are only defined for one or two inputs at once

by induction, they're defined for finitely many inputs

but there's no general notion of infinitely many inputs for a general vector space

like, if you add 1+1+1+... in R, you don't get a R-vector

[alpine sable]

True

[maiden glen]

ignoring topology and convergence, allowing infinite sums also makes the theory much more involved

[alpine sable]

Isn't there should be union?

[maiden glen]

like, we have that the cardinality of a basis determines the vector space up to isomorphism

[alpine sable]

Of all the sets of finite sums

[maiden glen]

that's implicit from the set comprehension

by taking J as a subset of I, we're taking the union of all finite sums over each fixed cardinality of J

[alpine sable]

Mm makes sense

[maiden glen]

you could write it as $$\bigoplus_{i\in I}Ui:=\bigcup_{n\in\mathbb{N}}\left{\sum_{i\in J}u_i;\middle|;J\subseteq I,|J|=n, u_i\in U_i\right}$$

to make it explicit

[alpine sable]

Hmm ...got it

And what about some results ..like
For finite dimensions

[ocean seal]

Desync

[alpine sable]

Like if V is a finite dim space

And U is a subspace then there exists another subspace W such that V = U direct sum W

Whatif V is infinite dimensional

I am just not able to generalise

And most of the texts cover finite dimensions

[maiden glen]

I think that statement is true, if you assume the axiom of choice

infinite dimensional linear algebra is more commonly covered in/called functional analysis

it qualitatively behaves very differently

[alpine sable]

Ohhhhhh ...when will I be learning that?

[maiden glen]

so it doesn't really make sense to cover them in the same textbook

[alpine sable]

Like in undergraduate??

[alpine sable]

Hmm

[maiden glen]

it was an optional module in the second/third year of my undergraduate

I'm not an analyst, so I don't have much experience with it

but it needs some point-set topology and measure theory as prerequisites, and maybe some ring/module theory depending on approach

[alpine sable]

Hmm..for now I am learning linear, abstract and real analysis ..
Linear from axler, abstract from gallian and artin and analysis from Tao

I will learn topology once I am done with this

#chess-go-shogi

Thankssssssssss @maiden glen @mortal trellis both of youuuuu

.close

[lone heart]

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[maiden glen]

nw, good luck with your studies

[lone heart]

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[versed spindle]

Number 8

I dont understand if the answer is 32% or 21%

is the extra info at the end about 18 junk info, or is it an additional parameter we are filtering the dataset with before random selection

[lone heart]

@versed spindle Has your question been resolved?

[toxic verge]

,w 21/(21+22+23) * 100

[ocean seal]

Results provided by WolframAlpha

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

Requested by executor.1011

[toxic verge]

@versed spindle

[lone heart]

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[toxic verge]

.reopen

[lone heart]

✅

[toxic verge]

[lone heart]

@versed spindle Has your question been resolved?

[lone heart]

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[alpine sable]

Help

[alpine sable]

I have the answers to these two graph questions but I’m not sure if they are correct

Concave down is (-4,0)

(-4,-1),(3,inf)

The other is this

Lmk if it’s correct pls and thx and asap

[unique dune]

Is this

Interval

Or point

Wait

Nvm

[toxic verge]

'k'

[unique dune]

Reconsider

The first one

[alpine sable]

(-4,0)?

[unique dune]

The graph is f’

[alpine sable]

Concave down question right?

[unique dune]

Concave down is f’’ < 0

[red nacelle]

did they give you a function

or just the graph

[alpine sable]

Just the graph

What I sent is the question itself

[red nacelle]

immaculate

[alpine sable]

Wait if it’s not (4,0) then what is it

-4*

[red nacelle]

you need the second derivative to test for concavity

[unique dune]

Look at the slope

[red nacelle]

solve for critical points then see which of the factors lead to negative or positive

[unique dune]

Should be pointing down

[unique dune]

Only graph is given..

[alpine sable]

Is the other one correct tho?

Just not the (-4,0) one

[unique dune]

Seems to be ye

[alpine sable]

Can u tell me the answer pls

[alpine sable]

https://tenor.com/view/rdc-mark-rdcworld-rdcworld1-mark-phillips-gif-9981396256126751443

Yo bless a brudda up..

Yo.. PLEASE MAN

(-4,-2) (0,inf)? @unique dune

https://tenor.com/view/praying-crying-downfall-sad-tears-praying-gif-7785197299162436598

[toxic verge]

Could you stop shitposting

[alpine sable]

Sorry

Is that right tho

[toxic verge]

Which question

[alpine sable]

He said it was wrong

I first had (-4,0)

[minor needle]

You can try to sketch a rough graph of f''

Then see where f'' < 0

[alpine sable]

How I do that

(-4,-2) (0,inf) is wrong then?

[minor needle]

Use some properties of the derivative

critical points and monotonicity (i.e. if f'(x) > 0 -> increasing, f'(x) < 0 -> decreasing)

[alpine sable]

(-inf,-4) U(-2,-1)?

@minor needle

[minor needle]

Almost

[alpine sable]

Bro can u just tell me

This is like 30% of my grade I can’t get it wrong

I’m exaggerating but still

It’s important pls tell me I’m so close man

[minor needle]

Why do you think the interval should end at -1?

Why did you decide to take (-inf, -4)?

[alpine sable]

Does it at at 0

Idek anymore dawg

[minor needle]

You're looking for f'' and you know f', we know that if f'' < 0 then f' is decreasing and if f'' > 0 then f' is increasing

Look for example at (-inf, -4)

What's the behaviour of f'?

Is it increasing or decreasing?

Yes, this is your f'

or f'(x)

[toxic verge]

r\whoosh

[hallow zephyr]

the aswer is (-inf,-4) U (-2, 0) no?

When the function is concave down, the derivate is decreasing

And the graph show the derivate of the function

sooo

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[alpine sable]

What is the answer if it’s wrong

[toxic verge]

<@&268886789983436800>

[alpine sable]

@minor needle

[clever folio]

Don't spam other peoples channels with troll garbage.

Oh somebody deleted the post as I was replying.

Nvm lmao

[sly mantle]

me lol

@gilded sparrow what he said. take a day off

[minor needle]

Did you separate the intervals with comma as they suggested?

Don't use union

[alpine sable]

Oh no I used used Union

[minor needle]

First step is always to read the question carefully.

[alpine sable]

Oh besides that is it right?

[minor needle]

Should work

[alpine sable]

.close

[lone heart]

Channel closed

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[alpine sable]

Tysm for ur help

[lone heart]

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[marble knot]

I think that I have proved it for k = 1, but I'm a bit lost on how to prove it for k = m and k = m + 1.

[minor needle]

It refers to the Fibonacci sequence, right?