help-41

[amber wasp]

@rocky fjord Has your question been resolved?

[rocky fjord]

.close

[amber wasp]

Channel closed

Closed by @rocky fjord

Use .reopen if this was a mistake.

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[keen quartz]

someone please give me the answer to this question

[keen quartz]

anyone 😭

[amber wasp]

@keen quartz Has your question been resolved?

[sinful sapphire]

oof that's hard to do without paper

[keen quartz]

thjank yto

[sinful sapphire]

8sin(12t/pi − 9) maybe

[keen quartz]

someone has finally responded 😭

lemme try that

is there any vertical shift or no

[sinful sapphire]

oh yeah

• 47

[keen quartz]

like this

[sinful sapphire]

no wait that's not right

+55

that looks right

maybe

could it be upside down?

no that's worse

[sinful sapphire]

this but 55

[keen quartz]

OH MY BAD

I DIDNT SEE YOUR MESSAGES

IM SORRY

is it +55 instead of 47

@sinful sapphire

IT WAS RIGHT

TYSM

[amber wasp]

@keen quartz Has your question been resolved?

Channel closed

Closed by @keen 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[manic spindle]

Bonus question help please

I literally tried but I couldn’t even make a system of equations

[amber wasp]

@manic spindle Has your question been resolved?

[mint nacelle]

if the sum of 2 numbers is 5.5, what is their mean?

[manic spindle]

(T1 + T1 + d)/2

[mint nacelle]

don't think of it as an arithmetic sequence

if I have two numbers a and b, what is their mean in terms of a and b?

[manic spindle]

(A+b)/2

[mint nacelle]

yes

and from the question, what must a + b equal?

[manic spindle]

5.5

[mint nacelle]

great, so the mean of the two numbers must be 5.5/2

[manic spindle]

Yes

[mint nacelle]

yeah and that is enough information to set up the linear equation actually

the "inserted" part is confusing I know

[manic spindle]

Wait

But the thing is there’s not only 1 arithmetic mean

There’s “k” amount of means

[mint nacelle]

yes, but all of those means are equal to 5.5/2

[manic spindle]

Liek the sum of them?

[mint nacelle]

wait, do you have the answer for the bonus question?

[manic spindle]

Yeah 12

[mint nacelle]

thank god I get that

ok so I am interpreting the question correctly

[manic spindle]

Wait so does (a+b)/2 give u the value of the sum of the means

[mint nacelle]

no, that just gives you one of the means

[manic spindle]

Oh

So how does that work

Cuz there could be more than 1 mean

[mint nacelle]

this

[mint nacelle]

no, all of the means are equal to 5.5/2

[manic spindle]

What do you mean all of them

Like the sum of them

[mint nacelle]

no

mean 1 = 5.5/2
mean 2 = 5.5/2
mean 3 = 5.5/2
....
mean k = 5.5/2

[manic spindle]

So all the means are just the same?

But isn’t it an arithmetic series so all the means have a common difference?

[mint nacelle]

no, you're overthinking it

it's just k * 5.5/2 - 21 = k

[manic spindle]

Yep I’m fried

Welp my test tmr and I needa sleep so thanks for helping

.close

[amber wasp]

Channel closed

Closed by @manic spindle

Use .reopen if this was a mistake.

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[mortal vault]

need help with this question, this is my attempt for the first direction and need help on how to approach the other

[amber wasp]

@mortal vault Has your question been resolved?

[amber wasp]

@mortal vault Has your question been resolved?

[amber wasp]

@mortal vault Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[unreal mirage]

Tw: business math 💀
How to get the total number of payments (n)

[unreal mirage]

Ive done the 4 × 10 since the time is 10 years and its quarterly

Since theres the word semi-annually will it be 4 × 10 × 2 😭

Or is it just 40

Am I overthinking it

[wide perch]

wait what do you mean by n?

isnt that just 40? There are 40 payments involved, the interest rate/compounding/etc is irreleavant

[wicked girder]

number of patments is just 40

the semi annually affects the interest not the numver of payments

[unreal mirage]

Thanks

[wicked girder]

👍

[unreal mirage]

.close

[amber wasp]

Channel closed

Closed by @unreal mirage

Use .reopen if this was a mistake.

[unreal mirage]

.reopen

[amber wasp]

✅

[unreal mirage]

Same problem

How do I get the interest per period

Its r/m

So it should be 2%/2 right

Or is there something im not seeing 😭

This wasnt explained properly by my teacher so I have a lot of questions 💀

[wicked girder]

i think so (its been a while since i did financial math)

[unreal mirage]

Thank you

Alright

Im finding the future value now

Is this correct

<@&286206848099549185>

[celest sun]

ano ba yan anteh?

[unreal mirage]

bakit poh

Business math

[celest sun]

wait madali lng yan may notes em

[unreal mirage]

English only fo

[unreal mirage]

Fatingin

[celest sun]

huhu sorry i misplaced my notes

[unreal mirage]

I have mine naman

[celest sun]

awh

[unreal mirage]

I was just confused on finding the total number of payments

@celest sun

What about the total number of payments here

[celest sun]

what's quarterly

[unreal mirage]

Is it 12 x 5

What

[unreal mirage]

Its where m=4

[unreal mirage]

Or is it 5 x 12 x 4

Or is it just 5 x 4

[wicked girder]

sorry i dont remember how to do that

[wicked girder]

yes

[unreal mirage]

Thanks

Oke i think i got it now

[wicked girder]

remember the compound annualy or quarterly or whatever only applies to interest, not number of payments

[unreal mirage]

If its compounded ____ it -

[unreal mirage]

YES

Thank you

[wicked girder]

sorry cant help with finding fv tho 😞

[wicked girder]

nwws

cant really remember nhow to do it

[unreal mirage]

So if its compounded whatever it will only apply to i and n where it is i/m and t(m) respectively

Confusioj #1 solved ig

Thank you kristy

[wicked girder]

ig so

[wicked girder]

hurray

[wicked girder]

🔥🔥

[celest sun]

like quarterly means 4 months

[unreal mirage]

Yea

Okay

Another

Applying last times

[floral raven]

This is investment,annuities and loans right

[unreal mirage]

Number of payments should be

7 x 12

[unreal mirage]

Yes

[unreal mirage]

HOL UP

If its 7 x 12

Then i ( interest rate per period ) should be?

idk anymore

[wicked girder]

mhmm

[floral raven]

Interest rate should just be divided by 12

[wicked girder]

what do u think semi annually means?

[wicked girder]

isnt it by 6

bc semi annually

[unreal mirage]

Whats the purpose of compounded semi anually then

[floral raven]

Oh ye

[unreal mirage]

😭😭😭😭

[floral raven]

I was only doing 12 cause he did 7 x 12

[unreal mirage]

Wait so

[wicked girder]

semi anually means its compudned every 6 months (aka half a year)

our qn says u make payments per MONTH

[unreal mirage]

In payments its per month and in interest its different

[wicked girder]

so u wanna change this from per 6 months to per one month, thus u divde the 8.5 by 6

[unreal mirage]

Oh

[wicked girder]

the qn states were paying for 7 years right, and we make payments each month thus u get 7x12 payment installments

[unreal mirage]

Uhuh

[wicked girder]

the compounded semi anually basically indicates the kinda like extra accumative value u own per 6 months

[unreal mirage]

Oh

Wait lemme process

[wicked girder]

essentially ur interest from the qn tells us it accumates by an additional 8.5% per 6 months

but sicne were paying per one month

we want to change the compound interset from per 6 months to per one month

thus we divide 8.5 by 6

and rhats ur interst for ur qn

[unreal mirage]

Oh

Like

[wicked girder]

to solve and stuff

[unreal mirage]

Cus

[wicked girder]

u want everything to be in terms of only per one month

[unreal mirage]

Its monthly and then the semi annually

So its 8.5% / 6

Wait i got this let me process the information

OHHHH

[unreal mirage]

I get this now

Okay thank you again kristy

[wicked girder]

yussss

[wicked girder]

yayyyy

[wicked girder]

nwwws

[unreal mirage]

If it said quarterly instead then it will be every 3 months and we gonna do 8.5% / 3

Ig

Gonna close this now

.close

[amber wasp]

Channel closed

Closed by @unreal mirage

Use .reopen if this was a mistake.

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[clever sage]

Hey, i need help with probabilities calculations

[tulip tapir]

!da2a

[amber wasp]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[clever sage]

I have an urn with 13 black balls, and 7 white balls,
i draw them one by one and sort them in a line until i run out of balls in the urn.
A. what is the probabillity that the last 4 balls in the line are black, if its known the first 3 ones are white.
B. GIVEN that 4 black balls are last in line, and 3 white balls are first in line, what is the probabilty that the first 6 balls in line at White?

i have solved for Question A, but i am having trouble understanding B,
i have calculated in A where:
A = the time where 3 white balls are drawn first,
B = the time where 4 black balls are drawn last.

and then did P(B|A), which gave me the answer

but for question B, i am unsure on how to approach it, is it like this:
C = the occurence where first 6 balls are white ?

and then P(C|AB)

or just take the "Starting position" where i have only to sort 13 balls, where 4 of them are white and 13 of them are black, and i need the first 3 ones to be white

its my first time doing homework in Probability and i am unsure on how to approach this

[covert onyx]

Do you know how many way it could satisfy the arrangement for Question B?

[clever sage]

i can calculate it

there are 14 ways for that arrangement

out of 77520

[covert onyx]

How

[clever sage]

you are left with only 1 white ball, and 13 black balls

[covert onyx]

First six are fixed, you only have one more white ball going around other 9 balls

[clever sage]

there are only 14 ways to rearrange them in different ways

[covert onyx]

Last 4 is fixed to be black

[clever sage]

ohh thats for exclusvily 6 white balls

9 including the 4 fixed black balls

basically 10!/9!

[covert onyx]

Think 10 more second

[clever sage]

10 ways

[covert onyx]

Yup

And can you calculate the total combination for 3 white ball and 9 black?

[clever sage]

yeah, 12!/3!*9!

[covert onyx]

Yup!!

So you get it

[clever sage]

hmmm

is it, not P(A|B) in this situation?

since its a GIVEN state?

and not "if a then b?"

this is why i am confused, i am unsure of what to actually look for

[formal dome]

P(A|B) means probability of A happening, when we already know that B has happened

[clever sage]

i am still a bit confused

in question A they said if its known that, that implies A|B

but in B they explicitly said given

[covert onyx]

Here already give |AB

[clever sage]

so given the state the first 3 are white and last 4 are black

[formal dome]

i think you're confusing your A and B sets with the A and B questions

[clever sage]

shoulda used 1 and 2 for questions

is, is question 2, refering to P(C|AandB)

[formal dome]

Okay, what are you calling A, what are you calling B, and what are you calling C?

[clever sage]

A - 3 white balls at the beginning

B- 4 black balls at the end

C- 6 white balls at the start

[formal dome]

Okay. So you calculated the amount of arrangements that have A and B happening, correct?

[clever sage]

yeah

[formal dome]

can you please mark it for me?

[clever sage]

i have already calculated P(AandB)

the text is in hebrew, but essentially, this is what i did for the first question

writing is a bit funky, but i hope its enough to understand

[formal dome]

yeah that looks fine

so you're only missing the amount of arrangements C

you can work easier if you fix the balls at the start and end

[clever sage]

so for C its 14

like, 14/omega

[formal dome]

that does not sound right

[clever sage]

well, if given the first 6 ones are white

we have 1 white and 13 black remaining

so there are 14 ways to sort them

[formal dome]

yes, but you also have 4 black at the end

remember, you have the first 3 whites and the last 4 blacks fixed

[clever sage]

so should my C be 6 white and 4 black at the end?

[formal dome]

so you can only move the 4 white and 9 blacks remaining

[covert onyx]

That is C|AB as you defined

[clever sage]

yeah, C|AB

[formal dome]

and out of those arrangements, only the ones that have 3 whites at the start (fixed) are "successes".
So the valid cases would be the arrangements of 1 white and 9 blacks, while your total arrangements would be the arrangements of 4 white and 9 blacks

and that would be your P(C|AandB) as defined

[clever sage]

so there are 13!/4!*9!

ways of doing so

[formal dome]

that would be the total

now you need the valid oens

[clever sage]

so starting point is AandB

3 white, 4 black

and what are teh chances to get from AB to C

essentially

[formal dome]

yeah, you can work with the probabilities of both, or you can work with the number of cases of both

usually, the number of cases is easier unless you already have the probs computed

so, how many arrangements of 1 white and 9 blacks do you have?

[clever sage]

10

10!/9!

[formal dome]

so your prob would be those 10, divided by the 13!/4!9!

[clever sage]

yeah,

and is that equal to P(C|AB)?

or are we calculating something different

i am just confused defentionally

[covert onyx]

It is

[clever sage]

i see

i think that i need to seperate my intuition from this

but thank you very much everyone!

much appriciated

[formal dome]

as you defined them, it is

[amber wasp]

@clever sage Has your question been resolved?

Channel closed

Closed by @clever sage

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[split sail]

!status

[amber wasp]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[cedar inlet]

3/4

[split sail]

I am only well acquainted with the disk method

So I can check that

However you could wait for someone to come along and help you with the shell method

[cedar inlet]

Well I was required to use online calculator for this for my project

But then the disk and shell method do not compute the same answers

[split sail]

Huh

That’s interesting

I’ll just let someone smarter come along and help you with this. I am really quite unaware of the shell method

[cedar inlet]

I even double checked with my friends the equation for the disk and shell and still isnt the same

[cedar inlet]

Do you know someone who can help?

[split sail]

@mint nacelle (Sorry for the ping senõr) is quite a smart fella. He may be able to help

He’s helped me multiple times before

[cedar inlet]

Thank you man :)

[mint nacelle]

can you not ping me for random questions

[split sail]

Noted. Sorry

I will not do that ever again

[cedar inlet]

Could you help me out with a disk and shell method question

[mint nacelle]

be active enough in help channels

[mint nacelle]

I'm working on it

okay so you have $x = \left(\frac{37}{10} y \right)^{1/3}$

[grizzled pagoda]

south, just south

[cedar inlet]

yeah

[mint nacelle]

the bottom horizontal line is y = 7.297 approximately

[cedar inlet]

Just as a background info( With this equation when revolving around Y axis creates a cup and I'm supposed to calculate the disk and shell method for it)

[mint nacelle]

,w integrate 2 pi (y - 7.297)(4 - (10/37 y)^(1/3) from y = 7.297 to y = 17.297

[grizzled pagoda]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by sooouth.

[mint nacelle]

jesus

[cedar inlet]

Shouldn't this be calculated using disk method?

[mint nacelle]

huh it's not working

[mint nacelle]

you did it using the disk method though right

[cedar inlet]

Yeah disk in terms of y

and shell in terms of x

Disk method gave me 397 with some decimal value

[mint nacelle]

wrong

[cedar inlet]

While shell method gave me 265 with some decimal value

[mint nacelle]

https://www.desmos.com/calculator/pc0gsvgdmm

check the calculations in this graph

[cedar inlet]

can you explain this?

[mint nacelle]

so each of these horizontal lines represents a shell

it has a radius, so that's the distance from y to the bottom horizontal line, y = 7.2973

[cedar inlet]

Also since its revolving around y axis, shouldn't disk method be in terms of y?

[mint nacelle]

it also has a length, so that's the distance between x on the function and x = 4

[mint nacelle]

no, the disk method revolves around the x axis

[cedar inlet]

But in the question I provided it revolves around y axis?

[cedar inlet]

.

[mint nacelle]

oh shit

[cedar inlet]

Yeah I did it again and I'm still getting different answers for both disk and shell

[mint nacelle]

ok give me more time

[mint nacelle]

what calculations did you do?

[cedar inlet]

For the disk method I put in terms of y with limits from 7.297 to 17.297

For shell I put the same equation *2pi x with limits from 3 to 4

[mint nacelle]

no, what integrals did you get exactly

[cedar inlet]

You mean the answer?

[mint nacelle]

no

what expressions did you get when you set up the integral

[cedar inlet]

How i set it up?

[mint nacelle]

yes

[cedar inlet]

give me a minute

[cedar inlet]

Yeah so

Disk method

shell method

@mint nacelle are they correct?

[mint nacelle]

no, this disk method is not correct

hold on

[cedar inlet]

Yeah I'm here

[mint nacelle]

wouldn't that just be $\pi\int_{7.2973}^{17.2973}\left(4-\left(\frac{37}{10}y\right)^{\frac{1}{3}}\right)^{2}\ dy$

[grizzled pagoda]

south, just south

[mint nacelle]

but that gives the volume as 9

[cedar inlet]

Why is it 4-the y equation?

[mint nacelle]

you want to find the horizontal distance between the curve and the vertical line x = 4

that's your "height"

but horizontal

[cedar inlet]

Isnt x=3 and 4 limits to use for x?

[mint nacelle]

no

you were correct originally

when you revolve around the y-axis using the disk method

the integral is in fact dy

[cedar inlet]

What does it mean if disk and shell method answers are different?

Like which one do I need to consider then

[mint nacelle]

they should be the same answer ofc

[cedar inlet]

But idk my equation isn't giving the same answers

[mint nacelle]

https://www.desmos.com/calculator/jj1xcvqmtc

okay now check this graph

this should be for the y-axis being the axis of revolution

[cedar inlet]

I thought you didnt need to put subtract 4 or 7.297 since they're just boundaries you need to calulate area for

[mint nacelle]

they are super important

please take a look at my annotations

[cedar inlet]

Oh damn

You literally solved what I was thought was unsolvable

Ty so much man

You have no idea how much you helped me

[mint nacelle]

no worries!

[mint nacelle]

also like 4 - x is also the height when you do it with the disk method

[cedar inlet]

I see

[mint nacelle]

the only difference is that we use $x = \left(\frac{37}{10}y\right)^{1/3}$

[grizzled pagoda]

south, just south

[cedar inlet]

You literally helped me so much

[mint nacelle]

and for the washer method, we use $y = \frac{10}{37} x^3$

yeah that's how it works

[mint nacelle]

alr no problemo!

[cedar inlet]

Ty so much once again

[mint nacelle]

.close

[amber wasp]

Channel closed

Closed by @mint nacelle

Use .reopen if this was a mistake.

[grizzled pagoda]

south, just south

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[trail panther]

Solve the following sets of equations by graphing them on a rectangular corridinate system. Check your answers by substituting them back into the original equations.y=x+4 and y= -x+2

[edgy sky]

go on desmos.com and graph those two equations

[amber wasp]

@trail panther Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[split sail]

Can someone help with the 3rd question

[split sail]

This is what I did (the one I have cut)

[amber wasp]

@split sail Has your question been resolved?

[split sail]

<@&286206848099549185>

[amber wasp]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[amber wasp]

@split sail Has your question been resolved?

[green swan]

do you still need help?

[green swan]

so you can actually find the smallest angle on the triangle arctan(32/75) and that angle will be an alternate angle

[split sail]

Hello

Why 32/75?

.close

[amber wasp]

Channel closed

Closed by @dusky cove

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[arctic oriole]

Can someone explain the annihilator method to me please?

[arctic oriole]

I don't feel like I understand it, factoring operators feels wrong and theres nothing intuitive about it

[pallid canopy]

do you have a problem you're working on?

[arctic oriole]

I can make a random one but its really just the concept I'm confused about

$9y'' - 4y' - 12y = x - 6$

[grizzled pagoda]

Nathan

[pallid canopy]

https://en.wikipedia.org/wiki/Annihilator_method#Example

[arctic oriole]

I'm looking for an explanation than examples

I just dont get the concept

[pallid canopy]

what line exactly

[arctic oriole]

Factoring the operators

It feels like an abuse of notation

[pallid canopy]

$\frac{d}{dx}\frac{d}{dx} = \frac{d^2}{dx^2}$

[grizzled pagoda]

riemann

[pallid canopy]

it's not more complicated than that

[arctic oriole]

How would you do $$(D^2 + 5D + 6)y = (D+2)(D+3)y$$ in normal notation though

[grizzled pagoda]

Nathan

[pallid canopy]

$D = \frac{d}{dx}$

[grizzled pagoda]

riemann

[arctic oriole]

Sure but I mean exanding it in that format and factoring

[pallid canopy]

use this 2-3 times

[arctic oriole]

but its saying that y'' + 5y' + 6y = (y'+2y)(y'+3y)

is it not?

$y' y' \nqt y''$

[grizzled pagoda]

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

[pallid canopy]

nope it's not saying this

[arctic oriole]

Whats it saying?

[pallid canopy]

plug this

into here

[arctic oriole]

$\left(\frac{d}{dx} + 2\right)\left(\frac{d}{dx}+3\right)y$

[grizzled pagoda]

Nathan

[arctic oriole]

yes?

Thats not any clearer to me

[pallid canopy]

keep expanding

until you get the left side

[arctic oriole]

$\left(\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}+6y\right)$

[grizzled pagoda]

Nathan

[arctic oriole]

Again this is no clearer to me

It didnt pass up the fact that its factoring operators

[pallid canopy]

no idea why ¯_(ツ)_/¯

don't know what you mean by "factoring operators"

[pallid canopy]

this?

[arctic oriole]

I'm quite literally factoring operators

[arctic oriole]

Yes

Its not multiplication though

[pallid canopy]

correct the derivative is not multiplication

[arctic oriole]

dy/dx * dy/dx is not d^2y/dx^2

[pallid canopy]

this isn't multiplication either

it's an operator acting on an operator

[arctic oriole]

yes I know

but its still having me write it as a binomial that is expanded through multiplication

or factored through division

its abuse

I cant say that $$5^2+5 = (^2 + 1)5$$

it makes no sense

[grizzled pagoda]

Nathan

[pallid canopy]

nobody writes it like that, but you can if $f(x) = x^2$ and $g(x) = 1 * x$ so that $(f + g)(5) = f(5) + g(5)$

[grizzled pagoda]

riemann

[arctic oriole]

so this is what a composite?

[pallid canopy]

If you understand that $\frac{d}{dx}$ is an operator, then you can understand that $\frac{d}{dx} + 3$ is also an operator with 3 being the function $g(x) = 3 \cdot x$

[grizzled pagoda]

riemann

[arctic oriole]

So can I say that $$ D^2 + D + 1 $$ is like $$ D^2(f) + D(f) + f $$ such that we can define it as $$L(f) = D^2(f) + D(f) + f$$ and so $$ L(y(x)) = \frac{d^2y}{dx^2} + \frac{dy}{dx} + y$$

[grizzled pagoda]

Nathan

[arctic oriole]

Is this right

[pallid canopy]

Yea

[arctic oriole]

Okay...

and so

$$ D^2 + 2D + 1 = (D+1)(D+1)$$ and if we put $$ L(y) = D^2(f) + 2D(f) + (f) $$ then we can say that it is the same as $$(D(f)+f)(D(f)+f)$$?

[grizzled pagoda]

Nathan

[arctic oriole]

But then that wouldnt make sense

because expanding that gives us a f^2

Also is D synonomous with y in that D(f) is synonymous with y(x) where the (x) is ommitted for simplicity?

[pallid canopy]

this is where you're making a mistake

[arctic oriole]

yeah thats where im confused too

[pallid canopy]

You did (operator 1)(operator2) f = [operator1(f)] * [operator2(f)]

operators do not distribute

operators act in sequence right to left

[pallid canopy]

$\frac{d}{dx}\frac{d}{dx}f \neq \frac{df}{dx}\cdot \frac{df}{dx}$

[grizzled pagoda]

riemann

[arctic oriole]

i agree

but how would I express that binomial otherwise

with the f included

[pallid canopy]

idk what you want

[arctic oriole]

I was expressing it as D(f)

[pallid canopy]

that's already fine

[arctic oriole]

Yeah sure but

you said it is equal to $$D^2(f)+2D(f)+f$$

[grizzled pagoda]

Nathan

[pallid canopy]

yea this is fine

[arctic oriole]

so how would I factor that

[pallid canopy]

you did here?

[arctic oriole]

Yeah if I omit the f

I'm saying what would it look like with the f included

[pallid canopy]

it's just this with f instead of y

[arctic oriole]

but thats like me saying y(x) + x = (y+1)x

[pallid canopy]

.

did you get that?

[arctic oriole]

yes

but it doesnt like up with what I said

D(f) is not D*f just like y(x) is not yx

[pallid canopy]

instead of 3, your example is just 1

$(f+g)(x)$ is very common notation for $f(x) + g(x)$

[grizzled pagoda]

riemann

[arctic oriole]

ohh

so (D^2+D+1)(x) if like (f+g+h)(x)

right?

[pallid canopy]

sure you can think of it that way

[arctic oriole]

okay so then if I say

f = x^2
g = x
h = 17

(f+g+h)(x) = x^2+x+17

and

i = d^2/dx^2
j = d/dx
k = 1

(i+j+k)(y) = (D^2 + D + 1)(y) = d^2y/dx^2 + dy/dx + y

But then wouldnt that mean that (f+g+h)(x) is x^2+x+17x if (i+j+k)(y) = d^2y/dx^2 + dy/dx + y

[amber wasp]

@arctic oriole Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[tepid widget]

when is $\log(z^n)=n\log(z)$ false in the complex numbers?

[grizzled pagoda]

UbuRoi

[tepid widget]

and can i always use that if i add 2kpi*i?

to solve equations like e^z=-1 for instance

[abstract canopy]

by the definition of the principle branch of the complex logarithm, $\log(re^{i\theta})=\ln(r)+i\theta$, so $\log(r^ne^{ni\theta})=n\ln(r) + in\theta$

[grizzled pagoda]

Bair

[abstract canopy]

err wait

well i guess it's because z^n might not be in the domain of the complex log

[tepid widget]

hmm

[abstract canopy]

if z=i and n=2 for example

but also, n theta might overcount the number of rotations

[tepid widget]

but like i CAN say in a equation like e^z=a then z=lna+2kpi*i, i can 'use' the property with the adjustment of adding the rotations

right?

[abstract canopy]

yes

for some k

[tepid widget]

ok good cause i solved a lot of questions doing that i'd be really sad if i couldn't do that would have to redo all of it

it didn't occur to me the thought until i saw this fake proof

[abstract canopy]

ye, it's because e^ix is not injective

[tepid widget]

so the mistake here is on step two already yeah?

[abstract canopy]

right, you would need to account for the rotation

[tepid widget]

alright thanks!

.close

[amber wasp]

Channel closed

Closed by @tepid widget

Use .reopen if this was a mistake.

[amber wasp]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sinful breach]

Need help

[amber wasp]

Please don't occupy multiple help channels.

[sinful breach]

Is my proof for this limit correct?

[amber wasp]

It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.

[pallid canopy]

this is too small to read

[sinful breach]

Here you go the pdf

[pallid canopy]

why can you just l'hopital here but not in the very beginning ?

[sinful breach]

No I am proving the limit

[pallid canopy]

but also you don't need l'hopital to prove that limit

[vast scaffold]

Think she has to use delta epsilon proof

[pallid canopy]

delta epsilon rarely ever invokes l'hopital

[sinful breach]

So I just verify the limit holds as I did substitution

Because it’s undefined when I finished substitution

So I had to verify and I didn’t have scratch paper with me so I used LH there

[pallid canopy]

doesn't mean you can use l'hopital

[sinful breach]

I used LH to verify if my substitution holds not to prove the limit

[pallid canopy]

wat

[sinful breach]

u Goes to 1 is not defined for the fraction

I have to mention or its indeterminate

I have to show that it tends something then I prove the limit by incorporating delta - epsilon notation

[vast scaffold]

I don’t see where lh is used

Didn’t u jsut do u sub

And then divide numerator and denom by u-1

[pallid canopy]

yea but that doesn't mean you can use l'hopital

if you can use it at all, you can just use it in the very beginning

[sinful breach]

Proof is different than showing value

[runic kraken]

when you do delta epsilon you can't use l'hopital from what i know

[vast scaffold]

Ye

[runic kraken]

you replace the x in the limit by a sequence

and the limit of that sequence should be the value for which the initial limit goes to

[pallid canopy]

using l'hopital at all is supporting your proof

[runic kraken]

in this case 0

[pallid canopy]

either you can use it in the beginning before the subsitution or you can't use it at all

[sinful breach]

Yes that’s true kinda…

Yes

You’re right 😭😭

I forgot that part

Then still this limit is actually only solvable by Taylor expansion

[pallid canopy]

you don't need l'hopital to prove this limit is correct

[sinful breach]

Can I claim the limit to be 1/3 then prove it using delta epsilon?

I actually never used substitution for this kind of proof

[runic kraken]

i don't think you usually use substitution for proving limits

[sinful breach]

I couldn’t find articles so

[runic kraken]

you just say that any sequence for which the limit when k -> infinity = 0 in this case

[sinful breach]

Yes but k is defined

[runic kraken]

this is a proof that i did

much simpler than your example but it should be the same method

hopefully my handwriting isn't horrible

[sinful breach]

Why can’t I use substitution if I may ask? 😭

[runic kraken]

i got no clue 💀

you may be able to

but i don't know

[sinful breach]

I think it can, I just need to isolate x at one point

Other wise that limit is probably only provable by Taylor in term of basic method

[runic kraken]

maybe

you probably are learning more advance proofs than i am

becasue i never had to prove anything like what you have

[sinful breach]

This limit I think is quite textbook styled

[runic kraken]

apparently yes

i looked it up

[sinful breach]

Can you guys verify another solution

Bar{number) is equivalent classes in the modulo

Please help me with this divisibility proof <@&286206848099549185>

This should hold right?

Another question

[runic kraken]

iono

[sinful breach]

Is the method rigorous?

[runic kraken]

try looking up this book: Mathematical Proofs- A Transition to Advanced Mathematics

it might have some answers to your questions

[amber wasp]

@sinful breach Has your question been resolved?

[sinful breach]

<@&286206848099549185>

[amber wasp]

@sinful breach Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sinful breach]

Guys is this method rigorous help me please ☺️☺️☺️

No please help me 😭😭

It’s actually quite some multiplicative groups and subgroups and some quotient rings

[patent raptor]

is this Algebra?

[sinful breach]

I basically rewrote my high school number theory using ring theory

Literally

It looks very fancy (knowledge points are fancy) but it was actually my youth ☺️☺️🤭🤭

[patent raptor]

damn taking Algebra rn but havent gone through ring theory yet

[sinful breach]

Ring theory, and majority is group theory though

This is effectively making a high schooler’s homework equivalent to fancy stuff however it is still just basic modular arithmetics

[patent raptor]

What are you trying to prove?

[sinful breach]

And it’s fun to see people’s reactions on those notions

[sinful breach]

10 | n

[patent raptor]

😂

[sinful breach]

n is that huge number

I used cyclicity of multiplicative subgroup to prove it

Involving Lagrange theorem

Subgroup

Basic property of rings

Blablabla

[patent raptor]

,w 3^(14102019)+3 mod 10

[sinful breach]

Basically for modular arithmetics

[patent raptor]

nice

ok let me see

[sinful breach]

Some basic group is actually quite advantageous for these problems especially if you draw Cayley s table

But high schooler group theory 🫠🫠

[patent raptor]

how would you figure -3

[sinful breach]

All calculations are based on equivalent classes instead of basic arithmetics

Because of the quotient ring and some basic property of equivalent classes

Basically it is isomorphic to bar(10-3)

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by adoniszgks

[sinful breach]

Is it very strict to call it isomorphic since it’s really structured at this point

But this is still basic modular arithmetics

[patent raptor]

Ok I would have explained it more in the proof, at least for me it's not obvious

[sinful breach]

Yes, this is a very fancy revisit of that definition which is in modular arithmetics

Being decorated within algebraic structure 🤭🤭

One of my mischievous game 🤭

In essence these elements are subgroups so they are cyclic

In a order (cardinality of the group) raised to phi(10)

By Lagrange theorem the order of subgroup must divide the order of the multiplicative group

[patent raptor]

ok i understood lol

i was lost for a moment

[sinful breach]

Though I must say using cyclicity makes things a lot easier

[patent raptor]

yup

[sinful breach]

Though notation can be a bit too rigorous

But in high school especially EEA, misuse dan be common especially elementary number theory is quite abstract for high schooler

[patent raptor]

after that you defined the prime remainder class of Z_10 if I understand correctly?

[sinful breach]

Yes I think I just took subgroup <3> and analyse its cyclicity

See if it matches 7 for the cycle wise

It doesn’t have to be prime remainder though

Relative prime to 10 otherwise it’s an ideal (principle ideal) instead of a subgroup

You can’t have a principle ideal in multiplicative group

&\mathbb{Z}/10\mathbb{Z} \cong \mathbb{Z}/5\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}$

[sinful breach]

why won’t my latex work

[patent raptor]

I actually can make it even more trivialized but it would be even more abstract I can perform ring decomposition: \[ \mathbb{Z}_{10}\mathbb{Z} \conj \mathbb{Z}_{5}\mathbb{Z} \oplus \mathbb{Z}_{2}\mathbb{Z} \] by taking it into direct sum I can just do a lcm to verify it.

lmao

[sinful breach]

&\mathbb{Z}/10\mathbb{Z} \cong \mathbb{Z}/5\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}$

I got it wrong the directly of dividing/

&\mathbb{Z}/10\mathbb{Z} \cong \mathbb{Z}/5\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}$

Or not

[patent raptor]

imma behonest after the Let part I dont get the idea nor what you tried to do lol prob due to my lack of algebra knowledge

[patent raptor]

$ $ not & $

[sinful breach]

It’s CRT

Omg I am probably day dreaming 😭😭

$\mathbb{Z}/10\mathbb{Z} \cong \mathbb{Z}/5\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}$

[grizzled pagoda]

meow

[sinful breach]

Exactly this one

[patent raptor]

what does that even mean

[sinful breach]

Cong means isomorphic

[patent raptor]

ye

[sinful breach]

It means that LHS is isomorphic to the right hand side

With smaller n

In which case simpler

[patent raptor]

What does Z/10Z denote

[sinful breach]

However it’s just 10 so I don’t have to make it even simpler

It’s a quotient ring

[patent raptor]

ok

[sinful breach]

Fancier way of saying modulo though

[patent raptor]

hm

[sinful breach]

Though using decomposition is a thing probably not allowed for basic number theory

[patent raptor]

are you talking to yourself

[sinful breach]

No?

[patent raptor]

a crazy scientist

[sinful breach]

Well I study those stuff 😭😭

[patent raptor]

https://tenor.com/view/funny-discord-walter-white-breaking-bad-meme-gif-25095974

[patent raptor]

me too, teach me :)

[sinful breach]

Like undergraduate mathematics

I am only good with real analysis set theory and number theory

[patent raptor]

you probably have a doctor degree

[sinful breach]

I am yet to be a master student

[patent raptor]

damn me too

whats your favorite number

[sinful breach]

I just took some elective

Me? Probably pi*e

[patent raptor]

i see you like 🥧

[patent raptor]

shit that's like 10 = 5 + 2 but multiplied

[sinful breach]

Pi*e is very interesting number though

I might not be transcendent

It might not

[fair fjord]

so is e^pi i think a classic question is to compare which larger

[fair fjord]

then you're rational?

[sinful breach]

Is not only a classic question it’s a open question

Ignore me I am just daydreaming

Can’t type properly

[patent raptor]

see talking to yourself hahahaha

[sinful breach]

Direct sum is only called a sum though

That’s why 2+5 = 10

It means to sum the structure together

[patent raptor]

yea i see that's why you used the circ plus

oplus

[sinful breach]

If you study math then you know at the second year of math journey

[patent raptor]

well i do and i do know nothign

[sinful breach]

If you take algebraic structure then you know probably first off

[patent raptor]

tbh i dont like that algebra stuff as opposed to analysis or calculus

[sinful breach]

I got 6 for calculus

9 for real analysis

[patent raptor]

is that good or bad

[sinful breach]

Bad

For calculus I took result

[patent raptor]

how bad

[sinful breach]

Resit

10

[patent raptor]

wow really bad

you got a 9 in real ana

[sinful breach]

But I am very good with analysis on the other hand 😢

[patent raptor]

try harder next time

[sinful breach]

Which is why I felt weird

[patent raptor]

i see you are prob a theorist

[sinful breach]

Like failed cal for once while excelled in real analysis

Functional analysis I got a 3.7

Hahaha

Contradiction

[patent raptor]

what is the stuff you do in real analysis

[sinful breach]

Convergence analysis, different proofs, series blablabla

Delta-epsilon basically

[patent raptor]

ok i think i had that

[sinful breach]

And some axiomatic proofs

I am particularly good with axiomatic proofs they are fun

And delta epsilon too

[patent raptor]

i sometimes struggle delta epsilon

[sinful breach]

Ap is like high school right?😭

[patent raptor]

havent done that very often

sometimes i just dont get the logic

[sinful breach]

If you are good with axiomatic proof delta and epsilon would be much easier I think

[sinful breach]

Tbh real Analysis once you mastered delta epsilon notation everything will be fine I think

[patent raptor]

what are axiomatic proofs

[sinful breach]

Like using only most elementary axioms to proof higher stuff

[patent raptor]

achso

[sinful breach]

Assume no other theorem than axiom

[patent raptor]

this reminds me more of linear algebra then

[sinful breach]

I think real analysis actually relies on axioms a lot

But it makes it less abstract so introduced lemma’s

[patent raptor]

you are a math student right?

[sinful breach]

Like lower upper bound which you can construct using axiom of completeness instead of using definition derived lemma

How so?

[patent raptor]

you seem to be not only pretty good at it but also obsessed

oh no

are you

[sinful breach]

A bit

[patent raptor]

a cs student

[sinful breach]

Let me show you something the. You guess

[patent raptor]

a little crazy too

[sinful breach]

[
\begin{tikzcd}[column sep=5em, row sep=5em]
% Diagram F: J -> C
J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \
J_3 \arrow[r, "k"'] & J_4

% Limit Cone
& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] \arrow[dd, "u"', dashed] & \\
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] & & \\
& M \arrow[r, "m"'] & N

\end{tikzcd}
]
]

[grizzled pagoda]

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

[patent raptor]

real

[sinful breach]

\begin{tikzcd}[column sep=5em, row sep=5em]

J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \\
J_3 \arrow[r, "k"'] & J_4


& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] \arrow[dd, "u"', dashed] & \\
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] & & \\
& M \arrow[r, "m"'] & N

\end{tikzcd}

\end{document}

[grizzled pagoda]

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

[sinful breach]

\begin{tikzcd}[column sep=5em, row sep=5em]

J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \\
J_3 \arrow[r, "k"'] & J_4


& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] \arrow[dd, "u"', dashed] & \\
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] & & \\
& M \arrow[r, "m"'] & N

\end{tikzcd}

[grizzled pagoda]

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

[patent raptor]

if that's LaTeX it doesnt work always with TeXit

[sinful breach]

\begin{tikzcd}[column sep=4em, row sep=4em]
% Original Diagram F: J -> C
J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \
J_3 \arrow[r, "k"'] & J_4

% Limit Object L
\arrow[dashed, bend left=30, from=J_1, to=J_2]

% Additional Cone (K, φ_j)
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] \arrow[dd, "u"', dashed] & & \\
& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] & \\
M \arrow[r, "m"'] & N &

\end{tikzcd}

[grizzled pagoda]

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

[sinful breach]

Just a simple commutative diagram

begin{tikzcd}[column sep=4em, row sep=4em]
J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \
J_3 \arrow[r, "k"'] & J_4
\arrow[dashed, bend left=30, from=J_1, to=J_2]
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] \arrow[dd, "u"', dashed] & & \
& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] & \
M \arrow[r, "m"'] & N &
\end{tikzcd

begin{tikzcd}[column sep=4em, row sep=4em]
J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \
J_3 \arrow[r, "k"'] & J_4
\arrow[dashed, bend left=30, from=J_1, to=J_2]
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] \arrow[dd, "u"', dashed] & & \
& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] & \
M \arrow[r, "m"'] & N &
\end{tikzcd}

\begin{tikzcd}[column sep=4em, row sep=4em]
J_1 \arrow[r, "f"] \arrow[d, "g"'] & J_2 \arrow[d, "h"] \
J_3 \arrow[r, "k"'] & J_4
\arrow[dashed, bend left=30, from=J_1, to=J_2]
K \arrow[ur, "\phi_1"] \arrow[dr, "\phi_2"'] \arrow[dd, "u"', dashed] & & \
& L \arrow[ul, "\pi_1"'] \arrow[dl, "\pi_2"] & \
M \arrow[r, "m"'] & N &
\end{tikzcd}

[grizzled pagoda]

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

[sinful breach]

Here you go the formal definition of limit

Despite its not complete

[patent raptor]

i never understood these diagrams

[sinful breach]

The very doorstep of modern mathematics

Limit

[patent raptor]

well i guess i will never enter the room

[sinful breach]

You will

Category theory

[patent raptor]

I hate theories

[sinful breach]

It’s actually fun

[patent raptor]

ikr

now what you study

[sinful breach]

You may guess now

[patent raptor]

ok you know

you dont study

you play chess

that's your secret

[sinful breach]

I actually don’t play chess

[patent raptor]

see i am very awful at taking a guess

[sinful breach]

I’m studying theoretical mathematics

[patent raptor]

bruh

[sinful breach]

The kind of math that has nothing to do with any application

[patent raptor]

i was so close

i am the very opposite of you

[sinful breach]

Applied mathematics?

[patent raptor]

yes

[sinful breach]

Then after real analysis it’ll much easier

[patent raptor]

we are supposed to hate each other 🔥

[sinful breach]

Like for me after real analysis gig goes directly to hell

Yes

Like impurity of mathematics

[patent raptor]

haha

[sinful breach]

Impurifies the noble art of mathematics

[patent raptor]

you started it

[sinful breach]

Tbh I’m thinking taking stochastic process though

[patent raptor]

but i wonder

if you are good at the theory how you fail at the application

[sinful breach]

Make a bit more money before going to spend rest of my life in academia

Calculus? That thing is too dense in computation

Like integration is almost like too complex

[patent raptor]

why would you spend your life in academia, you wanna become a professor?

[sinful breach]

Like I remember one I failed is like the surface area of ellipsoid derivation

Which was like bizarre and I failed

[patent raptor]

exactly what i love

[sinful breach]

The computations too dense

I love complicated epsilon

[patent raptor]

we are the very opposite

[sinful breach]

Calculus I was expecting one for final which my professor didn’t give us one

Otherwise I would be passing it without resitting

Delta-epsilon proof

[patent raptor]

that's all you know and need

[sinful breach]

I can manipulate delta epsilon too a point to direct bound delta by using different inequalities though sometimes

For first year indeed

Delta epsilon is like my strongest weapon

[patent raptor]

hahaha

crushed by bernoulli l'hopital

[sinful breach]

Yes

Lhopital is horrific

Like 3 iteration of derivative

…

[split kraken]

this isn't uncommon fwiw

[patent raptor]

it saves lifes from what i hear

[split kraken]

specific applications can be hard

even when you know the theory well

[split kraken]

what math might that be?

these days, it seems hard to find any math that has zero application whatsoever

[sinful breach]

Like how the fuck can one do 3 iterations on such shit thing x^lnx/(lnx)^x

[patent raptor]

I am saying theoretical math is nothing without application. The same vice versa, applied math is nothing without some theory behind it.

[sinful breach]

No direct application

[split kraken]

I think calling either "nothing" without the other is too harsh

[patent raptor]

the world is harsh

[split kraken]

debilitated? probably

nothing? idk

[sinful breach]

x^lnx/(lnx)^x I still can’t do 3 iterations of derivative on this thing

[patent raptor]

unless you wanna become a professor, try to make some money just knowing pure maths

[sinful breach]

For pure math it’s actually easier I would say

[patent raptor]

but vice versa, if you only know to calculate stuff, and apply formulas, you are not much more than an AI

so both go hand in hand

[sinful breach]

Easy contracted job for faculty especially some rare abstract field these days

People went god digging

Even I wanted to do a bit of stochastic process study

[patent raptor]

in what year are you currently meow

[sinful breach]

For that sake

[patent raptor]

cake

[sinful breach]

Like academic life is much easier

Than actually working I felt

[patent raptor]

😂

[split kraken]

I think there is a distinction to be made between the fields and the practioners

the fields of study would likely be okay if a single individual didn't go down one or the other

[sinful breach]

The thing I hate the most during calculus is that one

[patent raptor]

this is indeed a modular cycle study the stuff only to teach it to others, that will also teach it to others and that cycle never stops

[split kraken]

any given person would be in a tougher spot

[sinful breach]

Lhopital Taylor’s and fancy integral

[split kraken]

wdym

[split kraken]

hm? why?

[sinful breach]

Dense in computation

I see one and then I’ll panic

[split kraken]

you must hate diff geo then

[sinful breach]

Yes

[patent raptor]

as Matplotlib said, becoming a professor as someone who studies math is your typical golden route

[split kraken]

[sinful breach]

That one is even more analysis and PDEs

Fuck PDEs

[patent raptor]

HAHA

[split kraken]

mhm

[patent raptor]

i loved diff geo

[sinful breach]

I hate hearing PDEs

[patent raptor]

ODEs

[split kraken]

wait, you know diff geo.

teach me some please

[patent raptor]

yea

[sinful breach]

ODEs actually saved my life for calculus

[patent raptor]

i dont think that will work

[sinful breach]

Otherwise I failed it twice

[split kraken]

why not

can I ask you questions?

[patent raptor]

i got lost when it came to tensors and einstein summation

[split kraken]

[patent raptor]

but i passed reasonably well

[split kraken]

I see

[patent raptor]

i understood like 70 % maybe but the very deep theory was too much for me to bear

[patent raptor]

i can try 😄

[split kraken]

70% is probably better than what I'm doing rn

[sinful breach]

$otimes$

[grizzled pagoda]

meow

[split kraken]

,, \otimes

[grizzled pagoda]

higher!

[sinful breach]

$\otimes$

[grizzled pagoda]

meow

[sinful breach]

Tensor product

[patent raptor]

but you are like studying math and me applied math so that might make a difference e.g. be more difficult for you

[sinful breach]

Remember the property of tensor product? For its determinant

[split kraken]

meh, someone who knows DG is someone who knows DG

I don't care if they do applied math or not

I don't discriminate

I'm not a fan of the holier than thou attitude that a few people exhibit sometimes

[patent raptor]

i honestly dont care hahah

nobody is holier than the other we all will die

[sinful breach]

I remember I had a la exam which had a very weird matrix like no one solved it but I did, find diagonalizer for \begin{bmatrix}
0 & A \
A & 0
\end{bmatrix}

Can you actually guess how did I find the diagonalizer in just one or two steps 🤭🤭🤭🤭

Though I dare not write the process on exam paper bcs I used something in LA 2

So I basically said set the unknowns to be blablabla haha

[patent raptor]

The things I covered tho were like mathematical basics with introduction to vector analysis and tensor calculation, space curves, areas/surfaces iirc and "special surfaces"

[split kraken]

icic, so focused on curves and surfaces

[patent raptor]

yes

[split kraken]

cool!

I'll learn some in the future

[sinful breach]

Master?

Btw any of you figured out how to find diagonalizer for that one in a simple way