help-39

[sharp karma]

so if it's the reciprocal, then what is cotangent?

not particularly

oh

you mean your answer?

[kindred kernel]

a/h?

[sharp karma]

like final answer?

[kindred kernel]

I think

[sharp karma]

yes the cotangent of 5pi/2 is in fact 0

because we know cotangent = cosine / sine

[kindred kernel]

yes

[sharp karma]

and here cosine = 0, sine = 1

[kindred kernel]

Thats right

[sharp karma]

so cosine / sine = 0 / 1 = 0

good job

👍

[kindred kernel]

So what do i do further

[sharp karma]

what do you mean?

your question was to find the cotangent of 5pi/2 was it not?

is there another part?

[kindred kernel]

So cosine comes first

Sorry I got a bit confued

[sharp karma]

in cotangent yes

[sharp karma]

that is fine

trig is quite hard

[kindred kernel]

Really is

[kindred kernel]

It is

[kindred kernel]

No, I think I got it

Thank u

[sharp karma]

oh okay

if you need help just ask

good job though

[kindred kernel]

yes sure i will, is it okay if i add you? if i have any questions is it fine to dm?

[sharp karma]

yes it's fine

feel free

[kindred kernel]

Okay Tysm!

[kindred kernel]

Im getting 1

😭

[sharp karma]

as the answer?

[kindred kernel]

Yes

[sharp karma]

from whom?

the textbook?

[kindred kernel]

like i solved it

and im getting 1

[sharp karma]

I'm confused

so you solved it

a different way?

[kindred kernel]

i thought u find the degree first which is 450 and then the reference angle is 90 so u graph it then u find cos and sin and then u divide them by eachother and thats why i got 1

[sharp karma]

okay

yes

the reference is 90

and we know the cosine of 90 is 0

correct?

[kindred kernel]

yup

[sharp karma]

and the sine of 90 is 1

[kindred kernel]

yup

[sharp karma]

and cotangent

is cosine / sine

be very careful

[kindred kernel]

yes

[sharp karma]

so

0 / 1

is 0

yeah?

[kindred kernel]

Ohhh

YES THEN ITS 0

[sharp karma]

$\dfrac{\cos(90)}{\sin(90)}=\dfrac{0}{1}=0$

[jolly parrot]

Oreo

[sharp karma]

yes

[kindred kernel]

waiy

[kindred kernel]

dont we have tofind the cos and sin of the degree 450
not 90

[sharp karma]

so

here's the thing about trig

if it goes over 2 pi

it is the same

$\cos(\theta-2\pi)=\cos(\theta)$

[jolly parrot]

Oreo

[primal stump]

Real

[sharp karma]

yeah

trig is funny (why radians maaan)

[primal stump]

@kindred kernel 2pi rad is just 360

[primal stump]

Ong

[primal stump]

So it doesnt really matter and you can deduct that

5/2pi is just a fancier way of saying pi/2

Which is also a fancier way of saying 90 degrees

[kindred kernel]

i dont get it

😭

[kindred kernel]

huh

😭

Im so confused atm

[primal stump]

Ok ok

Do you know why we’re using pi hete

*here

[kindred kernel]

No

[primal stump]

In the question

[kindred kernel]

I dont

[primal stump]

Oh ok then

When you see an angle notated using pu

*pi

[kindred kernel]

yeah

[primal stump]

It is very likely using what’s called “radians”

[kindred kernel]

Yes

[primal stump]

Radians is an alternative to degrees

Pi radians = 180 degrees

[kindred kernel]

Yeah

[primal stump]

Thus pi/2 radians = 90 degrees

And 2pi = 360 degrees

And 360 degrees is just 0 degrees

Because we go a full circle

[kindred kernel]

Yes

[primal stump]

So there is no angle eventually

So we can remove that to make this easier to see

[kindred kernel]

Ohh so liek it goes to infinity?

[primal stump]

No, no

It goes to 0

[kindred kernel]

How can it be 0 tho

[primal stump]

Hmm

Hold on

[kindred kernel]

Okay

[primal stump]

Here

There is the line (d)

And on (d) I place 3 points: A, B, C

[kindred kernel]

Yes

Okay

[primal stump]

What is the angle BAC?

[kindred kernel]

Its 180

or 0?

[primal stump]

No, no, that would be ABC

[primal stump]

Yeah

[kindred kernel]

Okay so its 0 degrees BAC

[primal stump]

Imagine a circle with its center being the point A

[primal stump]

Yes

Actually wait

No no

Theres a sinpler way

Stand up for me

[kindred kernel]

What is it

[primal stump]

Now face a certain direction, or face any object you want

[kindred kernel]

Alright

[kindred kernel]

Okay

[primal stump]

I want you to turn exactly 360 degrees

And tell me what you end up facing

[kindred kernel]

I did i came exactly back at same spot

[primal stump]

Exactly

Thats it

So now, here we have 5pi/2

Which is pi/2 + 2pi, right?

[kindred kernel]

Yes it is

[primal stump]

So we can remove that 2pi, because its 360 degrees which is 0 degrees

We’re left with pi/2

[kindred kernel]

Ohhh

[primal stump]

Yess

[kindred kernel]

I THINK I GET IT NOW

TYS

TYSM

[sharp karma]

I love this example

stand up and spin

[primal stump]

Lmaoo

[pearl pond]

@kindred kernel Has your question been resolved?

[kindred kernel]

but

how

tho

how does 360

[sharp karma]

huh?

[kindred kernel]

become 0

💀

[sharp karma]

since we end up at the same point at the end

like how you spun 360 degrees

[kindred kernel]

AHH SO THEY MATCH UP

?

[sharp karma]

yes

it is the same position

just named differently

[kindred kernel]

OHH okay i get it now

Ty

Tysm

[sharp karma]

np

[kindred kernel]

can u pls explain how u get -2 here

[sharp karma]

okay

let's start wiht what is our reference angle?

[kindred kernel]

90?

or 135?

[sharp karma]

so

from the x axis

what is our angle (in radians so we can convert later)

[kindred kernel]

135?

[sharp karma]

no

oh

do youi mean -135?

or +135?

[kindred kernel]

Yes -135?

[sharp karma]

yes

correct

so

let's convert that to positive

what is the positive equivalent of -135 degrees?

[sharp karma]

actually

no

it's not -135

sorry

[kindred kernel]

+135

[sharp karma]

it is negative in this case

but its' not 135

okay

[kindred kernel]

90?

[sharp karma]

$-\dfrac{8\pi}{3}=?$

[jolly parrot]

Oreo

[sharp karma]

like

let's convert to degrees

we know pi radians is 180 degrees

so

$\frac{-8\pi}{3}\cdot\frac{180\text{ degrees}}{\pi\text{ radians}}$

[jolly parrot]

Oreo

[kindred kernel]

YEAH

[sharp karma]

use a calculator and simplify

[kindred kernel]

I THINK I GOT IT NVM

[sharp karma]

okay

[kindred kernel]

THANK U

[sharp karma]

so what do you think the answer is?

[kindred kernel]

-2

i got -2 too

[sharp karma]

NICE

LETS GOO

[pearl pond]

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.

[vast mason]

How would you solve for this?

[gilded temple]

venn diagram best way

[pearl pond]

@vast mason Has your question been resolved?

[pearl pond]

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.

[midnight haven]

so reciprocal of 3 so we got 3: 3/1 which got the power of 3^1/1 yeh? and then its reciprocal gonna be like, 1/3^-1?

[midnight haven]

i mean ik that doesnt happen

but like why not

this is the reciprocal's symbol: n^-1

im just confused about the symbol tbh

[pseudo cobalt]

yes, n^-1 would be 1/n

[midnight haven]

im so confused about the symbol

like the minus part

its gthrowing meoff

like no number is like that unless its put in a certain situation to be like that

n^-1?

2^-1

1/2

[pseudo cobalt]

anything raised to -1 is just the reciprocal

[pseudo cobalt]

yes thats correct

[midnight haven]

yea but like no numbers naturally is like that yk? what situation does it have to be in to be like: n^-1

[pseudo cobalt]

usually when the question is asking you to simplify the expression

you might come across ones like n^-1

[midnight haven]

ah so like in questions

only

@pseudo cobalt ye?\

[pseudo cobalt]

im not too sure about tht, sorry

[midnight haven]

hello

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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.

[marble obsidian]

how do I start on this?

[warm current]

f must be continuous at x=0, and the derivatives of both equations must be the same at x=0

[marble obsidian]

yeah ik that

[warm current]

then I do not know where you are stuck

[marble obsidian]

but what do I do with that info

[plush bramble]

Do you know the definition of continuous at 0

[marble obsidian]

for it to be continuous, the lhs limit and rhs limit has to equal no?

[plush bramble]

Yes so find them

[marble obsidian]

but I don't know a and b

or is that fine

[plush bramble]

You're solving for them

Just treat them like numbers

[pearl pond]

@marble obsidian Has your question been resolved?

Channel closed

Closed by @marble obsidian

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.

[gilded bramble]

having trouble with boolean algebra. im not sure how to get ffrom step 2 to 3. here is my attempt but i dont think its in the right direction

[pearl pond]

@gilded bramble Has your question been resolved?

[pearl pond]

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.

[midnight haven]

mb lil bro

[midnight haven]

How in gods name did my teacher get that for dy/dx?

Also why wasn't it multiplied by -2?

is that not the derivative of the inside of (16 - x^2)^0.5?

[last summit]

!noans

[pearl pond]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

@midnight haven Has your question been resolved?

[midnight haven]

Bruh

.close

[pearl pond]

Channel closed

Closed by @echo oar

Use .reopen if this was a mistake.

[pearl pond]

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.

[quartz jewel]

• Optimization problems are one of the real-life applications of Calculus I (Differential Calculus)

• Study how optimization problems work and how they are related to Calculus I

•Choose a field in STEM (Science, Technology, Engineering, and Mathematics), create an example of an optimization problem and explain it to the class

Steps in creating project

1. What are optimization problems in Calculus I?

2. How to solve optimization problems?

3. What is your field of focus?

4. Give a certain problem (with illustration)

5. Give and explain the solution

6. Explain the importance of the problem and the answer

[quartz jewel]

i would like the example to be video game coding for technology

[plush bramble]

wtf

do you have a more narrow question

or are you expecting someone to help do a whole project for you

[quartz jewel]

not really

not done with the question mb

[plush bramble]

so this

[quartz jewel]

i just want to have an idea or an example answer to it

i can not visualize a real life example to it

i was thinking somewhere in the lines of

imagine a 200x200 playing field, how many players can fit in it if each person is 2x2 and each of them require a 6x6 breathing area

but apparently (according to my maths prof) thats a bad example, and he said it without elaborating

In a 500x500 playing area where any number of players can be placed anywhere, compute for the maximum and minimum amount of players that can fit in it if each person is 2x2 and each of them require a breathing area that is equal to 36, and the minimum size a side can be is 3 ( 3x12 / 12x3 ). All breathing area is required to be the same shape

[pearl pond]

@quartz jewel Has your question been resolved?

[pearl pond]

@quartz jewel Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[iron oracle]

hi i cant seem to find the ans to this

[pearl pond]

@iron oracle Has your question been resolved?

[pearl pond]

@iron oracle Has your question been resolved?

[pearl pond]

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.

[livid bolt]

exfcuse me

[livid bolt]

how do i do this

like

thats what ive done so far

im not sure what to use to find the equation

wait

is rise 3.5

and run 7

[latent quail]

Question A?

[livid bolt]

yes

[latent quail]

Mistake

[livid bolt]

oh

0-0 is 0

so its 0

?

[latent quail]

no

You plugged the figures into the wrong place

[livid bolt]

oh wut

oh.

0-0 / -3.5

[latent quail]

No XD

[livid bolt]

i changed it to his

this

[latent quail]

yes

[livid bolt]

is that right

btw is question d correct to?

sry i dont have worked solutions

[latent quail]

You missed a negative

Wait

Let’s do it one by one

[livid bolt]

wow. it is right there

the negative isnt it

[latent quail]

Start from this question

[livid bolt]

wait is it wrong den

[latent quail]

The gradient is supposed to be -0.5

Not 0.5

[livid bolt]

oh

its negative tho?

[latent quail]

yes it is

[livid bolt]

wait

so is it wrong

[latent quail]

It is wrong

[livid bolt]

oh..

[latent quail]

This is correct

[livid bolt]

wait

thats what i had in my screenshot

though

i screenshotted that from my screenshot

[latent quail]

What in the circle is incorrect

No lol

[livid bolt]

oh yeah

i scrapped that

[latent quail]

That was a misunderstandings

[latent quail]

Alr

Do you have any more questions?

[livid bolt]

dis 1!!

is 1d correct?

oops

[latent quail]

D?

[livid bolt]

ya

[latent quail]

Correct

✅

[livid bolt]

omg :OOOOOOOOOOOOOOOOOO

i have one more if thats ok

[latent quail]

Epic

Sure

Why not tho

[livid bolt]

so this is for the radius and coordinates of circle

i got this so far

what are the next steps?

i cant find the radius bc i cant square root a negative number

[light helm]

delete the last step

[livid bolt]

oh

how am i supposed to do this

[latent quail]

You are supposed to make it related to the formula you learnt

[light helm]

to convert to standard form, youd want to use the process of completing the square

[livid bolt]

its ok at least im not doing circle theorems and proofs

i thought the standard form was

uh

[livid bolt]

(x-h)^2 + (y-k)^2 = r^2

[latent quail]

You have to convert the below form to the above one

[light helm]

yes

[latent quail]

Epic

[livid bolt]

oh

I SEE I SEE

OK

[light helm]

that's what you want your equation in,
as in that form you'll be able to easily identify the centre (h,k) and radius r

[livid bolt]

uh..

how would i do this..

[light helm]

have you done completing the square before?

[latent quail]

What have you missed? Think of it

[livid bolt]

yes but my teachers way is very trash

[eternal tulip]

x^2+2ax+a^2

what is 'a'

[light helm]

,tex .cts

[livid bolt]

do u want to see my method of completing the square

[jolly parrot]

ℝαμΩℕωⅤ

[livid bolt]

?

give me an example

[latent quail]

Just think what have you loss, and try to make one

[livid bolt]

by rearranging it in this form is it correct?

[light helm]

(if you have an equation, instead of adding/subtracting the value
you can add the desired value to both sides of the equation)

[latent quail]

Nope, you have to try to make one

[livid bolt]

)::::::::::::::::::::::::::::::::::

[latent quail]

I think you missed b^2, right?

[livid bolt]

do i have to make it = 0?

[latent quail]

No

[livid bolt]

oh

this is a lil bit confusing

never learnt this in circles

[light helm]

lets focus on one component at a time

[latent quail]

You have these two stuff, just try to make a b^2 to make it a square root

[light helm]

starting with
x^2 + 6x
are you able to determine the value that when added will give you a perfect square trinomial

[livid bolt]

+9

[latent quail]

Epic

[light helm]

yes

[livid bolt]

I AM SO SMART

[latent quail]

INDEED

[light helm]

thus for your equation, you can add 9 to both sides for that
(and then express x^2 + 6x + 9 in the form (x-h)^2

similar idea for the part with y

[livid bolt]

what do u mean both sides

[latent quail]

If you add 9 at the left, just add an another 9 at the right

The equation remains in that way

[light helm]

left side of the equaiton = right side of the equation

[livid bolt]

x^2 +6x + 9 = 9?

[light helm]

no

from the equation you had

[livid bolt]

x^2 + 6x = 9.................................................?

[light helm]

from

[livid bolt]

oh WOW

THIS IS REVOLUTIONARY

law of conservation right now

[latent quail]

FR

yeah, just do it and you’ll be all good

[livid bolt]

WIAT

ok il ldo the next one

wait bruyh wth

[latent quail]

Is this your first time getting in touch with such thing?

[livid bolt]

its impossible

[latent quail]

How come?

[livid bolt]

well i completed the square but my teachers method is very weird

like it doesnt work logically

it just gets it into the form

[latent quail]

May I check it out?

[livid bolt]

hmm il try find the class notebook

wait

give me one

and ill do it for u

a complete the square question

[latent quail]

Sure

[livid bolt]

from quadratic

[latent quail]

Do you want the hard one or the easy one?

[livid bolt]

easy please

[latent quail]

x^2 + y^2 + 2x + 6y +9 = 0
Find its center

[livid bolt]

no.. A QUADRATIC PLS

[latent quail]

Oh

y=x^2 + 3x + 7
Find its vertex

[civic sorrel]

hiii i need help with my assignment and I'm very desperate

[latent quail]

!occupied

[pearl pond]

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).

[latent quail]

Sorry, it’s not available here

[latent quail]

@livid bolt

[livid bolt]

this is how i was taught

[latent quail]

yeah, it’s the conventional method

It’s good but I won’t suggest it

[livid bolt]

what really

its a bad way right it doesnt work logically

[latent quail]

We learn the x coordinate of vertex is -b/2a here

[livid bolt]

how does 3x just cancel out

how does (x^2 + (3/2)^2) turn into (x+3/2)^2

[latent quail]

No, it doesn’t

[livid bolt]

i wanna learn how to for real complete the square

but its too hard

[livid bolt]

what the frick

[livid bolt]

wait so now is it y^2 +25

and now i just need

y^2 + 10x + 25

(y+5)^2

[latent quail]

You wrote it wrong

[livid bolt]

i wrote dat the line below

wait bruh

did i just do it

[latent quail]

yeah, the one below the line is correct

[livid bolt]

x = -3 y=-5

[latent quail]

There are not supposed to appear non figure elements

[livid bolt]

i added 10y to both sides

[light helm]

you shouldn't be having variables on the right side

[livid bolt]

bruh.

BRUH

😭😭😭😭

[latent quail]

It ok, you will good

🍀

[livid bolt]

can u pls tell me the next steps..

i am sick and tired of math..

[latent quail]

Erase them

[light helm]

erase** all** steps you have here

[livid bolt]

im so sick im eating pumpkin soup for dinner

ok i will wait

[latent quail]

Looks delicious

[light helm]

and go back to the first step you originally had

from

[latent quail]

They are at the wrong spots

[livid bolt]

oh

[latent quail]

Decent

[livid bolt]

i was just writing the original equation down

[latent quail]

Now you can start

[livid bolt]

ok watch the MASTER MIND

OH

-10Y

-5X-5

ohhhh

i am a genius

pls pls pls pls

psl pls pls pls pls

pl spl spl sp l spl spl spl spl spl pls

guys

is this correct

[latent quail]

Decent

[livid bolt]

LETS GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

time to eat my pumpskin soup

[latent quail]

Fantabulous

Dismiss !

[livid bolt]

wait

I BASICALLY GOT 100% ON A 25 MINUTE TEST I DID IN 1 HOUR

[latent quail]

Cool

Good for you

[livid bolt]

thank u

now i need to use inverse proportion to do better

.close

[pearl pond]

Channel closed

Closed by @livid bolt

Use .reopen if this was a mistake.

[pearl pond]

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.

[west goblet]

Hiii can someone help me with a permutation problem? Robert borrowed 3 English books, 4 Mathematics books, and 2 Science books from the library. In how many ways can he arrange these between two bookends on his study table
a. if the books are arranged by subject matter?
b. if only the mathematics books should be next to each other?

[latent quail]

!status

[pearl pond]

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

[west goblet]

1

[west goblet]

Idk where to begin TT

[latent quail]

I see

Do you get any idea now?

[latent quail]

@west goblet

[west goblet]

Ohhh ok

[latent quail]

Your question seems identical to his

#help-1 message

Are you still there?

[west goblet]

Yup

[latent quail]

So ok

Permute the types first

There are three major categories

[west goblet]

I'm still confused a little srry TT

[latent quail]

Just see it as three vacancies

How many ways can you permute ABC?

[west goblet]

2?

[latent quail]

You sure?

[west goblet]

No

[latent quail]

Try again

[west goblet]

WAITT IT'S 3

3!

[latent quail]

Yep

[west goblet]

So do I multiply this?
4!x3!x3! ?

[civic sorrel]

that is wrongst

[west goblet]

Explain then:))

[civic sorrel]

use the permutation formula

P (3,3)

[west goblet]

Which rule?

[civic sorrel]

2nd rule

[west goblet]

So 3!/(3-3)! ?

[civic sorrel]

yeah

[west goblet]

So 6?

[civic sorrel]

there's your answer

[west goblet]

Ohhh ok thx!!

[pearl pond]

@west goblet Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[somber snow]

Prove this. I almost solved this but instead of ln2, I found - ln2

[west sapphire]

can you show your work?

[plush bramble]

,w sum n=2 to inf log(1-1/n^2)

[jolly parrot]

Results provided by WolframAlpha

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

Requested by rie.mann

[plush bramble]

your work is right. typo in the book's solution

[somber snow]

Ohh, okay, thankss

.close

[pearl pond]

Channel closed

Closed by @somber snow

Use .reopen if this was a mistake.

[pearl pond]

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.

[worthy grail]

what are roots?

[west sapphire]

if nothing else, you could try plugging in the options and see which work

[worthy grail]

i want to understand

it gets hard when problems like this come up

[cursive wraith]

Donc you have quadratic formula for roots?

[worthy grail]

no i’m kind of stupid

idrk what roots are

[cursive wraith]

Roots of 3x²-5x+1 are the x that verify 3x²-5x+1 = 0, the solutions of the equation "3x²-5x+1=0"

Like for example, 1 is a root of x²-1 because (1)² - 1 = 0

[worthy grail]

oookay

but plugging it in seems kind of counterproductive

is there an easier way than plugging in a super weird fraction

[cursive wraith]

You should have a formula

For solutions of ax² + bx + c = 0

Never seen the quadratic formula? Or Śrīdhara formula sometimes called?

[worthy grail]

nope

wait

yes

but not called that

[cursive wraith]

Ok

Then plug in the correct values of a,b,c

Like in 3x²-5x+1 = 0, find the values of a,b,c

And then use the formula

[worthy grail]

ohhh

but how do i get both x’s

[pearl pond]

@worthy grail Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[tall blade]

Let Γ be a circle with center A on which I have arbitrarily chosen points B, C. Let I be the center of the inscribed circle of triangle ABC. We denote by D the point of intersection of BI with the circle Γ, with M the middle of the segment DI, and D and E are diametrically opposite points. Show that EI = 2CM.

[pearl pond]

@tall blade Has your question been resolved?

[tall blade]

<@&286206848099549185>

[pearl pond]

@tall blade Has your question been resolved?

[edgy stone]

what have you tried

[pearl pond]

@tall blade Has your question been resolved?

[pearl pond]

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.

[velvet delta]

How do I do question 23

[velvet delta]

I just don’t get it😭

[keen rain]

can you express the question using four equations?

[velvet delta]

Huh

[keen rain]

for instance "the average of the first three integers is 32"

can you rewrite that mathematically

[velvet delta]

(a+b+c)/3 = 32

[keen rain]

yup

now attempt the other three equations

[velvet delta]

Sorry this is where I got stuck

[keen rain]

well you could write the second as
(a+b+d)/3 = 39

where d is the fourth integer

[velvet delta]

Yeah I guess

[keen rain]

if a,b,c,d are your initial integers you can see the possible groups of 3 as:
a,b,c
a,b,d
a,c,d
b,c,d

[velvet delta]

yeah

[keen rain]

which gives four equations like above

and with these four equations you can calculate the values of a, b, c & d

[velvet delta]

Wait is d the largest ?

[keen rain]

we don't know that yet

but yeah it is

once you have the three equations try solving for single variables and insert them into the other equations

or if you're familiar with solving a linear system of equations, the Gauß Algorithm would make it faster

[velvet delta]

yeah I’m not

[keen rain]

kk, then try it with insertion

[acoustic path]

symmetric structure of system is smth to be noted…

[keen rain]

yh you could also retrieve the differences of b, c, d to the first variable by looking at the difference in the average

which would probably be the fastest

[acoustic path]

(a + b + c)/3 = ?
(a + b + d)/3 = ?
(a + c + d)/3 = ?
(b + c + d)/3 = ?

add 4 equations,
a + b + c + d = ? + ? + ? + ?

can immediately solve for largest variable

[keen rain]

it would be [2]+[3]+[4]-2[1] to get the answer

[keen rain]

as this wouldn't yield values for a, b, c, d

[acoustic path]

“can immediately solve for largest variable”

[velvet delta]

.close

[pearl pond]

Channel closed

Closed by @velvet delta

Use .reopen if this was a mistake.

[pearl pond]

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.

[naive socket]

how can I find a and b values to take an integral?

[naive socket]

i did it myself and got the integral from pie/6 to pie/2 but somehow my teacher got it from 0 to pie

the way im doing it is

3cos(0*theta) = 0

cos(0*theta) = 0

cos(theta) = 0

theta = pie/2 and 2pie/3
then divide both by 3 (because of a three inside the cos)

and thats how I got my a and b values

[pearl pond]

@naive socket Has your question been resolved?

Channel closed

Closed by @naive socket

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.

[smoky saffron]

Is this the answer?

[fervent plank]

your missing a ^2

in the first line

[west sapphire]

in that last factor, you have -3x^2, but it should have been -3x^3

[smoky saffron]

ohh

[fervent plank]

why dont you distrbiute the 3 in?

ohhh

[smoky saffron]

Because

The ^4 i dont think it will let me idk

[west sapphire]

lazy grader 😁

[fervent plank]

I guess your teacher teaches different lol

Bungo can you check my work

in #help-4

[smoky saffron]

Guys do u understand this too

/c;pse

.close

[pearl pond]

Channel closed

Closed by @smoky saffron

Use .reopen if this was a mistake.

[pearl pond]

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.

[unkempt jay]

Would this be a function?

[plush bramble]

,rotate

[dire sky]

what do you think

[unkempt jay]

I think it’s a function

[dire sky]

reasoning>

?

why do you think so

just tell the reason

[unkempt jay]

Cause like on a graph the points were in a straight line

[dire sky]

Ok, so you are set

[unkempt jay]

It is a function?

[dire sky]

yeah of course

[unkempt jay]

Thanks

[dire sky]

where was the doubt

you did everything yourself

[unkempt jay]

Yippie

[pearl pond]

@unkempt jay Has your question been resolved?

[dire sky]

.close

click on the green tick @unkempt jay

[pearl pond]

Channel closed

Closed by @unkempt jay

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.

[quick yacht]

"If this sentence is true, then unicorns exist"

i know this is trivial, but i can't stop thinking about this, namely
this isn't like the liar's paradox, because there is no contradiction, there is no self-referential loop, this is just a true statement
i get that i can turn this into a liar's paradox "if this sentence is true, then this sentence is false" and i can readily reject this as it leads to a contradiction, but how do i reject the statement about unicorns?

Namely, how do we know if we can use self-reference

for example, godel uses self-reference in his incompleteness theorems, how can i trust his theorem knowing such a statement exists and is true

the same argument in sentential logic

1. X := (X -> Y) assumption
2. X -> X identity law
3. X -> (X -> Y) substitution 1,2
4. X -> Y contraction 3
5. X substitution 4, 1
6. Y modus ponens 5,4

[steep lion]

Wait, unicorns don't exist ??!!

[quick yacht]

:P

maybe they do, and this proves it

[pearl pond]

@quick yacht Has your question been resolved?

[tulip ore]

1. if this sentence is true, then unicorns exist
2. the first sentence is true
3. unicorns exist
4. [I know that] unicorns do not exist
   contradiction (3 and 4)
   which one is false? 3
   which one is false? 1 or 2
   which one is false? 2

if youre going to have sentences have weight in the real world, you also need to bring in real sentences like 4

otherwise its just fiction

[quick yacht]

im not sure what you mean

if unicorns exist, then this statement is true
well, clearly if that statement was true, then unicorns exist
so the statement must be true

[tulip ore]

and whats your problem with that?

[quick yacht]

i can derive an arbitrary proposition

regardless of whether its true or false

[tulip ore]

and whats your problem with that?

[quick yacht]

its not inherently false or contradictory

[tulip ore]

thats a shame isnt it

if only you were comparing it with something else to show that it has to be false

since youre doing a proof you have to exactly mention what is going against "unicorns exist"

you also need to consider that proofs dont connect with the real world at all

they're just mental gesturing

what you need to do to connect them to the real world is to use propositions that come from the real world

[quick yacht]

[tulip ore]

such as "unicorns do not exist"

you can consider a fictional world where unicorns do exist and then this statement would be true and there wouldnt be any issues

it would match up with that world

you can consider a fictional world where unicorns don't exist and then this statement would be true and there would be a contradiction

[quick yacht]

this transcends the real world, i am talking purely about formal systems, the point wasnt that unicorns exist, the point was that i can derive an arbitrary statement

[tulip ore]

then whats your problem with it?

why are you rejecting it?

[quick yacht]

fine
"if this statement is true, then false"

[tulip ore]

why is it false

cite your sources bro

what makes you say unicorns dont exist

[quick yacht]

i dont think you understand this at all

[tulip ore]

I dont think youre very good at making yourself clear

please rephrase this to answer what Im asking you, I dont get what the issue is with the system

theres a clear disconnect between the formal system and using that formal system in the real world
so far, it makes sense in both worlds that its "true by itself but doesnt mean anything" in the former and "false because of a proof by contradiction" in the latter

thats my stance sof ar

[quick yacht]

suppose: if this statement is true, then X
then, clearly, if the statement is true, X must follow, this proves the statement is true
but if the statement is true, then X must follow

so, then X follows arbitrarily

[tulip ore]

...thats not how statements work

you need to have a separate statement that says the first one is true

saying "if it rains, then use an umbrella" has to be combined with "it is raining" to be able to say "use an umbrella"

[quick yacht]

i know how modus ponens works

[tulip ore]

so when you begin with "if this statement is true,"...?

[quick yacht]

alright, ill be as clear as i possibly can be

[tulip ore]

have you considered if the statement is false?

then the statement would be flase

[quick yacht]

it cant be false

[tulip ore]

every statement is prepended with "if this statement is true and not false" bro

its a default assumption thats made when you use a system that only allows true or false

so it gets left out, but its always there

"if this statement is true, and if it rains, then use an umbrella"
"if this statement is true, it is raining"
=> "if the previous statements are true, then use an umbrella"

modus ponens lets you avoid having to declare "if this statement is true" and have it depend on the true/false of previous statements
pointing at a statement, making it true, then going "its true!!" is a tautology

[quick yacht]

Suppose:
"If this statement is true, then unicorns exist"
now, think about what it means if the statement were true, that would mean the statement "If this statement is true, then unicorns exist" is true. but that would mean if the statement was true, then unicorns exist
therefore, if the statement were true, then unicorns exist

that is what the statement is saying
therefore it is true that
"If this statement is true, then unicorns exist"

but that is the premise of the statement,
therefore unicorns must exist

it is a self-fulfilling statement, i am not defining it to be true, the statement just proves itself

[tulip ore]

how much weight does a true statement hold?

how much weight does a statement that is assumed to be true hold?

why the hell are you assigning different weights?

[quick yacht]

what are you talking about

i dont think you understand,
i am not saying it is true because i assumed it
i assumed it and proved it to be true, in a classical logical system

i proved the statement was true

[tulip ore]

how would just the statement "unicorns exist" fare under this?

wouldnt it also be just as bad because you begin with assuming its true and end with concluding that its true?

[quick yacht]

no

you misunderstand the proof

[tulip ore]

suppose you write it out with some more symbols than what Im seeing here, its not immediately clear what youre saying

math ought to clear this up

[quick yacht]

in classical sentential logic

1. X := (X -> Y)
2. X -> X identity law
3. X -> (X -> Y) substitution 1,2
4. X -> Y contraction 3
5. X substitution 4, 1
6. Y modus ponens 5,4

with the notation in mind, lets revisit the english version

"If this statement is true, then unicorns exist"
clearly if the statement is true, then unicorns must exist, so the statement must be true
but, if the statement was true, then unicorns exist
therefore, unicorns must exist

im really asking if there is a mechanical method to discern whether a self-referential statement is valid, i can only invalidate statements which cause a contradiction, arbitrarily invalidating self-referential statements isnt sound, because that would invalid godel's incompleteness theorem

since we still call it a theorem, there must be some way

[candid spire]

How does line 5 work here

Oh oh

[quick yacht]

X := X -> Y

[candid spire]

Yeah nvm

wtf that’s so weird

[tulip ore]

maybe dont use english next time

[quick yacht]

my biggest issue in general is that i can only prove X is true

X is clearly true

[tulip ore]

unless Y is false(?)

[quick yacht]

even if Y is false

we can substitute Y = false directly, and it still holds

[candid spire]

Wait wtf

[quick yacht]

this guy gets it

i cant cope with this, i need some method to check self-reference

[candid spire]

So basically, if you assume the following sentence is true:

if this sentence is true, then unicorns exist
Then you must necessarily conclude unicorns exist?

[quick yacht]

right

[candid spire]

So fucking weird lol

[tulip ore]

this doesnt even have a negation and its self-referential

I have a feeling it really cant be resolved but its easy to just not type the same letter as in the definition (which is why it isnt mentioned)

what if you chain it with more letters?

[quick yacht]

but that makes identity laws unwritable, i could never define x=x

[tulip ore]

you wrote X -> X

not X = X

X = X (and something else) would be the issue

however X only being equal to X unless proven or as the result of a proof(?) sounds disgusting

[quick yacht]

no, im saying if we cant have x in its own definition, the = identity rule cant hold, that is, we cannot have x=x, so this cant work to resolve the issue

[tulip ore]

Ive got an idea

say we try having some logic prover go over this

[candid spire]

Oh, if the sentence, that is, the conditional, is true, then it’s impossible to have simultaneously the hypothesis true and the conclusion false. So either the hypothesis is false or the conclusion is true. But we know the hypothesis is not false since the sentence was assumed to be true, and hence by or-reduction the conclusion must be true.

So weird

[tulip ore]

you can go over all the conditions though and a proof by contradiction is what enforces X to be true

[tulip ore]

not seeing an equals sign in this one https://logictools.org/prop.html

I have a feeling the equals sign is whats causing issues here like in russell's

[quick yacht]

<==>

in the binary logic, iff is equivalence

[tulip ore]

whoops I forgot about that

tried that then got a syntax error earleir

I think Im starting to get whats happening here

hear me out since this might be nonsense, but

what youre doing here is renaming "unicorns exist" to be another way of saying "this statement is true"

and this happens any time you say that X is equivalent to another statement

[quick yacht]

right

[tulip ore]

so that means "unicorns exist" is no different than just that initial "this statement is true"

now for having to look out for this

[tulip ore]

I dont immediately see a systematic way to catch self-references

[quick yacht]

but the big issue is that, i use only rules i can prove in the natural deduction, and by simply supposing a statement, i get an arbitrary statement must be true
but the natural deduction is based on the ability to suppose stuff arbitrarily
if there is no mechanical method to check for these issues, how can i trust natural deduction

[tulip ore]

theres no mechanical method against russell's paradox

[quick yacht]

zfc

[tulip ore]

thats not my point

[quick yacht]

restricted comprehension stops russels paradox

[tulip ore]

thats my point

[quick yacht]

well, i want a "restricted comprehension" for natural deduction

ig is the best way to put it

this simple trick allows me to prove anything in natural deduction

but its well known that natural deduction is sound-complete

that means logic falls apart

[tulip ore]

then again

[quick yacht]

the truth tables themselves show this

[tulip ore]

seeing a row of Ts does not necessarily mean you can say Y is true

[quick yacht]

no, that makes sense

the principal of explosion

[tulip ore]

and for that to be valid, you separate Y from false -> Y

[quick yacht]

suppose 0=1, then i can show 1=2, pretty trivally, i can also show 1=1 pretty trivially

[tulip ore]

I believe something similar is happening here

theres a catch in (X <-> (X -> Y)) -> Y

Y itself isnt necessarily true, but this deduction is

[quick yacht]

that is, i can show true and false statements from a false statement, this is different, this is me using well-founded rules to derive an arbitrary statement

[tulip ore]

wait

[quick yacht]

false and true is false, this doesnt mean much

[tulip ore]

it means the statement doesnt have to make Y be true

there's also

[quick yacht]

thats not the issue

[tulip ore]

I am so off right now

[quick yacht]

lets do the same proof, but this time say false
if this statement is true, then false
therefore false
so, t <==> f

[tulip ore]

for reference here's:

[quick yacht]

right, but we are taking it as a definition of this new X object

so, only consider the cases where it is true

as you can see, the only case is where y is true

[tulip ore]

and in the cases where its true, you are automatically assuming that both X and Y are true

therefore defining X to be X -> Y has an implicit assumption that X <-> (X -> Y)

and so you ignore the cases when this doesnt happen

that sounds like a solid answer to me

[quick yacht]

but i can suppose anything, even false statements

idk what to think about this anymore

[tulip ore]

I didnt suppose, I defined

[meager trellis]

the problem here is that self-referential definitions are invalid

[tulip ore]

there we go

[meager trellis]

which is because the justification of definitions doesn't work in the case of self-reference

[quick yacht]

right, i get that much, i just want some method to invalidate such a statement

it really hurts natural deduction for me

[meager trellis]

the reason that definitions work at all is that if you have a derivation of false that uses a defined symbol X, you can replace every instance of X with its definition and this is a valid derivation that doesn't use X

[meager trellis]

"self-reference isn't allowed therefore it's invalid"

[tulip ore]

I did mention this earlier but it was rejected

[quick yacht]

i have two things
a. what would precisely constitute self reference
b. that means the proof of godels incompleteness theorem is invalid

[meager trellis]

a. ok let's be more precise

we have the definition of introducing a definition: we can add a symbol X and the assumption "X <-> ..."

this has the condition that X must not appear in ...

if it does appear in ..., that is self-reference and is not a valid instance of adding a definition

[quick yacht]

what do we do about the identity laws, X <-> X

[tulip ore]

(that was the reason for the rejection)

[meager trellis]

well that's not an instance of introducing a definition

[tulip ore]

is it because those are axioms? nvm Idk what Im saying thats just true by default because T <-> T and F <-> F

[quick yacht]

how does the validity of a statement depend upon whether it is an axiom

[meager trellis]

i'm not saying that "X <-> ..." is always false if X is in ..., i'm just saying that the particular act of introducing definitions does not justify concluding "X <-> ..." if X is in ..., or if X is a symbol that we've already used

it's the difference between truth and provability

[quick yacht]

okay, so
X :-> (X -> Y) assumption
X :<- (X -> Y) assumption
X = (X -> Y) def =
X -> X identity law
X -> (X -> Y) substitution
X -> Y contraction
X substitution
Y modus ponens

[tulip ore]

you calling it an assumption makes this all-true deal reasonable again

[meager trellis]

well that's a valid argument to establish that if X -> (X -> Y) and (X -> Y) -> X then Y

[tulip ore]

...youve put an = sign in there now

[quick yacht]

right, it follows from X :-> (X -> Y) assumption, X :<- (X -> Y) assumption

[quick yacht]

but i prove the statement is true arbitrarily at step 5

[meager trellis]

if the "X :-> (X -> Y) assumption" line is supposed to be introduction of a definition and not introduction of a hypothesis, then again, the problem is that that's not a correct instance of introduction of a definition

[meager trellis]

?

[meager trellis]

it's the same problem as this argument
X -> X identity law
(X -> X) -> Y identity law
Y modus ponens

(X -> X) -> Y might happen to be true, but it isn't an instance of the identity law, so this is at a syntactic level an incorrect proof - the theorem being invoked doesn't match the statement we're trying to justify with it

[quick yacht]

ok, i get it i think, so why dont we like the original proof

[meager trellis]

...what is the original proof

[quick yacht]

X := (X -> Y) assumption
X -> X identity law
X -> (X -> Y) substitution 1,2
X -> Y contraction 3
X substitution 4, 1
Y modus ponens 5,4

[meager trellis]

i've somewhat lost track of what the question actually is

X := (X -> Y) assumption
this line isn't an instance of the introduction-of-definitions rule

[quick yacht]

the question is how can i make a mechanical method to invalidate self reference

wdym this line isn't an instance of the introduction-of-definitions rule

[meager trellis]

for "X := ..." to be a valid definition, X must be a new symbol, and must not appear in ...

"X := (X -> Y)" fails the second condition

[quick yacht]

is this an actual rule?

[meager trellis]

(it's the same kind of thing as: for "X -> Y" to be a valid instance of the identity law, X and Y must be the same)

[meager trellis]

yes
you need those two conditions for eliminating definitions to work

if X is a symbol that has already been used, then you can "prove" that X -> Y by just being like

Y := X assumption
X -> X identity law
X -> Y substitution

you can't define a symbol that already has a definition, a definition has to be of a new symbol

and with self-reference, well, we've seen what the problem is with that

whereas if that doesn't happen, if you have like

[tulip ore]

this (is what you get when you do self-reference)

[quick yacht]

what do we do about
X := Y
Y := X

[tulip ore]

• you didnt define Y
• you already defined X

[meager trellis]

prove that (X -> X) -> (X -> X)
Y := X -> X
Y -> Y identity law
(X -> X) -> (X -> X) substitution
we can eliminate definitions, replace each occurrence of Y with X -> X, and get
Y = X -> X reflexivity
Y -> Y identity law
(X -> X) -> (X -> X) substitution

[meager trellis]

if Y is a symbol that already existed, then Y := X is invalid, because it defines an existing symbol

if Y is a symbol that doesn't already exist, then X := Y is invalid, because Y doesn't mean anything at that point

[quick yacht]

hmm

what about the definition of provability

or any diagonal argument for that matter

[meager trellis]

you are correct, diagonalisation by pulling self-reference out of nowhere is invalid

the standard proof of godel's incompleteness theorem does not use self-referential definitions

[quick yacht]

it does tho

[meager trellis]

no it doesn't

that's not the definition of $G_F$

[jolly parrot]

bee [it/its]

[quick yacht]

what is the definition of gf

oh

im silly actually

gf is ->, diagonal argument shows <-

[meager trellis]

well... hm. there are multiple definitions that work, i don't know how exactly godel originally did it

[meager trellis]

(?)

[meager trellis]

but to give a rough sketch

[quick yacht]

idk how to type godel numbering in latex

[meager trellis]

the basic idea is that we form the statement "the statement you get when you substitute n into itself is not provable"

and then you substitute that statement into itself

[quick yacht]

let [a] be the godel numbering of a
F |- D -> A([D]) ===> F |- D <-> A([D])

thats the diagonal lemma

iirc

this should be how godel did it

[meager trellis]

hm
well, yep, you can use the diagonal lemma to construct G_F

[quick yacht]

okay, so, what do we do notationally to restrict ourselves from self-reference

[meager trellis]

.

[quick yacht]

notationally

[meager trellis]

uh
...idk what you mean by that then

[tulip ore]

you can simply choose to not do it

[quick yacht]

i can also simply choose not to make self-referential sets and not use set theory

the problem is that natural deduction seems to fall apart with this statement