help-27

[restive river]

but for vertical asymptotes?

[ionic belfry]

.close

[restive river]

tho

[ionic belfry]

oh

[ionic belfry]

its a number that makes the denominator = 0 but mustnt the numerator

what makes the denominator 0?

[restive river]

x

[ionic belfry]

what value of x?

it must be some number

[restive river]

0

[ionic belfry]

does substituting 0 in place of x in (x+3) give us 0?

[restive river]

no

3?

[ionic belfry]

its -3

this number is the VA

[restive river]

so only 1 va?

thats -3

[ionic belfry]

yes

[devout snow]

@restive river Has your question been resolved?

[restive river]

for horizontal and slant asymptotes tho?

sorry im having trouble understanding the lessons from my class ;(

thanks in advance to those who answer <3

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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.

[little jewel]

If a triangle has sides ½(n!), (n-2)!, (2-n)!, How do I find it's numerical area?

[left robin]

we can use heron's formula

[devout snow]

@little jewel Has your question been resolved?

[little jewel]

Huh, wouldn't that end up with a super sized unsimplifiable square root?

[left robin]

yep

i just tried it

haha

[little jewel]

Ah damn

[left robin]

there must be another way

[little jewel]

<@&286206848099549185> any hint would be much appreciated

[devout snow]

@little jewel Has your question been resolved?

[violet wind]

Well

Factorials are not defined in any sort of way for negative integers

Do we know n is an integer then?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[little jewel]

.reopen

[devout snow]

✅

[little jewel]

It's not mentioned but yeah should be since it's in a factorial

[violet wind]

so n=2 is the only consistent choice

otherwise either n-2 or 2-n will be negative

and you can't take the factorial of a negative integer

[little jewel]

Interesting

[violet wind]

not even with the gamma function (extension of factorials to real numbers)

[little jewel]

Not familiar with that, but I will try to solve it with herons formula when n is 2

[violet wind]

that'll work yeah

[little jewel]

Ah an equilateral

Ig herons is too long, it's area is gonna be sin45

Gonna verify one sec

Ah doesn't work

All 3 sides should equal 1

[zinc veldt]

just use the area of an equilateral triangle formula

the sides are all 1

anyway

[little jewel]

I used 2 sides*sine of included angle

[zinc veldt]

that works too

[little jewel]

Yeah

Sin45

Not an available answer

All of the answers have sqrt (3)

[zinc veldt]

wouldn't the included angle be 60?

[little jewel]

Jesus Christ my bad

Yeah sqrt(3)/2 my brain automatically went for the 45 degree angles for some reasons

Thanks guys!

.close

[devout snow]

Channel closed

Closed by @little jewel

Use .reopen if this was a mistake.

[devout snow]

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.

[frozen flicker]

I dont get how to do this

[frozen flicker]

anyone can help?

[devout snow]

@frozen flicker Has your question been resolved?

[devout snow]

@frozen flicker Has your question been resolved?

[devout snow]

@frozen flicker Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

Channel closed

Closed by @sly hornet

Use .reopen if this was a mistake.

[median dirge]

StOP

opening help channels

[pearl plume]

.close

[hallow hazel]

@pearl plume its closed bruh

That guy closed everything

[devout snow]

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.

[radiant drift]

@half minnow

[radiant drift]

i think i know the answer to this

just want you to

confirm

so the first one, it converges at 1

because 1/n=0

and the second one

the denominator is larger if i compare the numbers one by one

so

2>1

4>3

6>5

is that right?

[half minnow]

u gotta prove them tho right..?

[radiant drift]

how do u prove it

..
?

[half minnow]

this looks like real analysis

[radiant drift]

wtf is that

is mine fake?

[half minnow]

LOL

what worksheet is this

[radiant drift]

like

all the other quesitons

i asked u guys

the same

[half minnow]

yea where did you get it from

[radiant drift]

my professor

gave me

[half minnow]

tf

[radiant drift]

?

wut

[half minnow]

it's just a conundrum because the way you did it is intuitive enough

and it relies on facts established beforehand

so if this wasnt a real analysis course, you are correct

[radiant drift]

but how would i actually prove it ?

[half minnow]

you would need to use the definition of convergent sequence

it goes like

[radiant drift]

oh ik

a limit exists

if its monotonic bounded

?

[half minnow]

yep

just show that

[radiant drift]

ive never done that,,?

lemme try

[half minnow]

ok the first one is easy to show monotonicity

yea u got this

[radiant drift]

monotonicity means bounded??

because it's intuitively increasing

that doesn't need proof??

[half minnow]

monotonicity doesnt imply bounded

montonically bounded does imply convergent tho

so you have to show the sequence is monotonic AND bounded separately

[radiant drift]

like how??? if n is approaching infinity, 1/n just becomes smaller so the entire thing is increasing?

like

how do you prove that

isn't that just fact

[half minnow]

that's the proof of monotonicity

[radiant drift]

do i do that by induction?

[half minnow]

you can just substitute the definition in

[radiant drift]

exaclty?

and thats

proven?

[half minnow]

well show that its true lol

subtract the ones off

move 1/n to the other side

[radiant drift]

ohohoho

lol

yay

[half minnow]

its monotone increasing now wooo

now you just need to show its bounded

[radiant drift]

how

[half minnow]

substitute definitions in, choose a convenient value of B

[radiant drift]

it's less than 2?

ig

[half minnow]

u can use <= 1

doesnt really matter

[radiant drift]

right

[half minnow]

ur subtracting something from 1, so its clearly less than 2

at the same time, it will always be greater than or equal to 0

just show that last part and you are golden

[radiant drift]

wait so now it's lim 1-1/n<= 1

[half minnow]

yea but thats guaranteed

n is a natural

and so 1/n will always be >= 0

therefore 1-1/n <= 1

[radiant drift]

right

right

OH

OKOK

lemme show u my work for confirmation

[half minnow]

ok

i think someone is watching me rn...

[radiant drift]

ew creepy

[half minnow]

yea perfect but just show 1-1/n >= 0 so you can drop the absolute value bars

[radiant drift]

okok thxxxxxxxxxx

as always

.close

[devout snow]

Channel closed

Closed by @radiant drift

Use .reopen if this was a mistake.

[devout snow]

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.

[fervent jewel]

when is a DE linear?

[fervent jewel]

nvm got it

.close

[devout snow]

Channel closed

Closed by @fervent jewel

Use .reopen if this was a mistake.

[devout snow]

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.

[real mist]

So i walked into my class and i dont understand how to do anything came in blind and i would like some assistance on my hw

[rare mantle]

what's the question?

[real mist]

"Solve the following equation for a"

[thin gust]

err

[rare mantle]

alright so you want to isolate a (essentially, "remove" the 5/6 from it)

[thin gust]

the qn only gave u this?

[rare mantle]

what can you multiply by 5/6 to get 1?

[real mist]

The yt video didnt help btw

[rare mantle]

because you want 1a

[thin gust]

oh in terms of n?

[rare mantle]

yeah

[thin gust]

okiee makes sense

[rare mantle]

@real mist

[real mist]

Hold on

tbh i dont know anything on how to do that

[thin gust]

oki for eg if u have 2x = 2

what is x

[real mist]

1

[thin gust]

how did u get that

divide 2 right

[real mist]

Yeah

[thin gust]

now for this qn

u have 5/6 a = n

what’s a

[real mist]

wait let me get paper

[thin gust]

okii

[real mist]

back

[thin gust]

hii

[real mist]

Its 0.03 right?

[thin gust]

what is 0.03?

[real mist]

n

waut

[thin gust]

the value of n?

[real mist]

Idk

[thin gust]

aren’t u finding a in terms of n

oki wait

if u have 2x = 2

u divide both sides by 2

[real mist]

yeah

[thin gust]

if u have 2x = 9

what’s x

[real mist]

4.5

[thin gust]

yes

if we have 2x = n

what is x

it’ll be n/2

[real mist]

Oh

[thin gust]

no need to find the value of n

can just leave as n

[real mist]

OH

that makes sence

[thin gust]

yesh

[real mist]

wait

so 5/6 should i turn it into a decimal

[thin gust]

errr if I’m not wrong that’s going to be a never ending decimal

[real mist]

O

so keep it as 5/6

[thin gust]

ya it’s better than way

so if u have 5/6 a = n

divide both sides by 5/6

[real mist]

isolate the a?

[thin gust]

yesh

[thin gust]

that’s why we do this

[real mist]

O

so n is the value of 1

so

1 / 5/6

[thin gust]

yesh gd!

[thin gust]

so what is this

[real mist]

1 divided by 5/6

[thin gust]

yes

what do u get

[real mist]

1.2

[thin gust]

ya

so final answer for a is?

[real mist]

a=1.2?

[thin gust]

1.2 n

[real mist]

a=1.2n?

[thin gust]

yesh

we have to leave as n because we don’t know what n is

[real mist]

so

[thin gust]

just write 1.2n

[real mist]

1.2n?

[thin gust]

no need write a

[real mist]

Thank you!

[thin gust]

welcc (:

but u understand right

[real mist]

Yeah

[thin gust]

okii

[real mist]

.close

[devout snow]

Channel closed

Closed by @real mist

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.

[real mist]

ok t*

[real mist]

I have no clue on what to do, I think i have to dispute the numbers but it comes out as 1b + 3f +1a=g i am stuck in the "1b+3f+1a=1g" because i do not know what to do next!

[tall knoll]

Do you know what it means to solve for a?

[real mist]

nrl

I got put into this class when i didnt sign up for it infact i failed the algbra test idk how im in it

[tall knoll]

A hint: the equation (b+3f)a = g is solved for g

[real mist]

so

dis pute it?

[tall knoll]

Que?

[idle jackal]

make a stand alone on one site

[tall knoll]

To dispute something is to argue about it

[little jewel]

Distribute?

[real mist]

YEAH

[little jewel]

You needn't to if you just want to isolate a

[real mist]

needn't?

[little jewel]

If you have AB = C can you isolate B

Like how C is isolated

[real mist]

no

[tall knoll]

Need not

[real mist]

Oh

[little jewel]

Ok what if you have 3X = 6 can you find the value of X

[real mist]

yeah

3x divided by 3 then 6 divided by 3 to get x=2

[little jewel]

Exactly you divided by 3 to isolate X

How would I do it in AB = C

If I want to Find B

[real mist]

ab divided by ab?

OH

ab divided by a?

[little jewel]

Yes

So what does b equal

[real mist]

c?

b=c

[little jewel]

No you divide both sides by A like you did in this example

[real mist]

how do u divide letters?

i mean 1c divided by 1b?

[little jewel]

You simply write it as C ÷ B

You cannot find the value of the division so you leave it as symbols

[real mist]

OH

[restive river]

So basically, you have AB = C and you want to isolate B right?

[little jewel]

Yeah hopefully they got it

[real mist]

so

brb im do on paper

[little jewel]

Oh my god I realized I mixed it up

[real mist]

?

[little jewel]

@real mist Ayo we are diving by A to isolate B my bad

[real mist]

Oh

[little jewel]

Well how did it turn out?

[real mist]

Idk i got stuck n redoing it

[restive river]

When you’re doing a problem like that, just remember that you can do any operation on one side of the equal sign. However, you always need to do the same thing on the other side of the equality sign. In your previous example, you had 3X = 6 and you needed to to isolate X. What you can do is divide both side by 3. On the left, you have 3X/3 which is equal to B and on the right, you have 6/3 which is equal to 2. You’re left with X = 2

[real mist]

so

[restive river]

You can apply the same thing with AB = C

[real mist]

my thing is on the question im doing "(b+3f)a=g" I have 3 letters on the other side

what do i do if i got 3?

[restive river]

What’s your question?

[restive river]

[restive river]

I’m not sure I understand this question properly, but I would have a = g/(b + 3f)

I don’t know what’s the thing with capitalization though

[real mist]

thats somethign else

dont worry abt that

[little jewel]

Ah guess I am a bit late

[real mist]

thats for the awnser so i dont f*** it up

[restive river]

Ha ok I think I might know where your confusion is

When you divide a polynomial by the same polynomial, you get 1

[little jewel]

I don't think they know what a polynomial is

[real mist]

nope

[restive river]

2

Is poly

It’s basically a thing with letters like X + 5X squared

It’s not the exact definition, but that’s it in a nutshell

[real mist]

Like i said i didnt go to summer school for algbra and i failed that test im litrally going in w/o any info like NOTHING I didnt even know what 3x=6 was

[restive river]

If you have X/X, what do you get?

[real mist]

1

1x*

[restive river]

1

[real mist]

Oh

[restive river]

Ok, just remember that when you divide a thing by the same thing, you always get 1

3/3 is 1

X/X is 1

[real mist]

Ye i understand that

[restive river]

(X + Y)/(X + Y) is 1

[real mist]

Yeah

because u do anythign on the left side to the right

[restive river]

This

[little jewel]

You wanted to do distribution earlier

[restive river]

You know that you have to divide both sides by B + 3F

If you want to isolate a, I wouldn’t recommend you distribute

[little jewel]

Ah yeah my bad

[restive river]

Just divide both sides by B + 3F

[little jewel]

They seem to need some practice in arithmetic

[real mist]

arthmetic?

[little jewel]

I wouldn't really consider this algebra, it's more arithmetic, but I guess you shouldn't worry about the difference for now

[real mist]

o

[restive river]

On the left , you have (b + 3f)/(b + 3f)

[little jewel]

You missed the a

[restive river]

Ha yeah sorry

[restive river]

I think I get where you’re confused

[real mist]

so like this?

[little jewel]

Yes

[restive river]

In this case, a is multiplied

[little jewel]

Do note that you wrote 35 instead of 3f

[real mist]

There

[little jewel]

By the way the a is multiplied as kvlt mentioned, it's (b+3f) x a, not +

But the answer is correct

[real mist]

Kvlt?

[little jewel]

You could think of it like this if you understand the AB = C example, b+3f is just a big symbol you are dividing by,

[restive river]

Ha ok. That’s what i originally thought

[little jewel]

Yeah satanic kvlt the person helping you rn lol

[real mist]

Oh

SO i got 1 more question

[little jewel]

Well I hope this has somewhat cleared up how this problem is solved

[restive river]

If you have AB/A, you can cancel the As

[real mist]

thats the way i turn it in?

[little jewel]

Yeah looks good, but the b is not capital?

The b shouldn't be capital

[real mist]

Yeah

[little jewel]

Yeah looks fine

[real mist]

Thank you so much 😭

[little jewel]

Yeah you did it! And do take those summer classes next time

[real mist]

I will

😭

[restive river]

There you go my friend 👍

[real mist]

Bro THANK GOD discord added the student servers

i do not wanna be grounded rn

[restive river]

My pleasure

[real mist]

so

it just changed on me to a whole diffrent unit

w**

all i do is basic algbra right

[restive river]

Exactly

[real mist]

Ok

thxs

Bye bye

[restive river]

Be careful with the inequalitie sign.

[real mist]

?

Wdym

That?

[restive river]

Yes that

[real mist]

Why tho-

[radiant arch]

when dividing both sides by a negative number, the sign switches around

[real mist]

Oh i know about that

but i understand that-

[restive river]

Exactly

[restive river]

Ha cool

[real mist]

Yeah

somethin i understand

🥳

.close

[devout snow]

Channel closed

Closed by @real mist

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.

[real mist]

bro

[real mist]

im getting upset w this **

I do not understand where i messed up

[little jewel]

What did you do in the 3rd step

[real mist]

There ?

[little jewel]

Yes

[real mist]

9w-36w>w+24 I collected terms

[little jewel]

9w-36w is not 45w

[real mist]

Thats a plus symbol

was i supposed to do (-) ?

[little jewel]

Wdym you wrote 9w-36w

It equals -27w

[little jewel]

I have no clue what that +36 is

[real mist]

9+36

adding

[little jewel]

What why

What does 5x+4x equal

[real mist]

Well ****** i got a new problem

[little jewel]

Can you answer this

[real mist]

O that was a question mb

9x

[little jewel]

Yes so what's 9w-36w

What is it equal to

[real mist]

45

or -45

[little jewel]

My man

[real mist]

?

[little jewel]

What's 3-9

[real mist]

oh shitt-

-6

[little jewel]

Yes so what's 9-36

[real mist]

-27

right?

[little jewel]

Yeah

With the w

[real mist]

-27w

[little jewel]

Ye now try to solve it

[real mist]

wait

I feel like im being dumb asf

im about to pull an all nighter studying

[little jewel]

My man

In the 2nd step

[real mist]

-4

[little jewel]

You are supposed to subtract 1w from both sides

But you are adding

[real mist]

OMFG

IM AN IDIOT

BRB

[little jewel]

Seems about right

I would submit as 6/7 though

[real mist]

Ok

IT WORKED YES

can i get help w one more quesetion

to make sure i got it?

[little jewel]

Sure

[real mist]

s0

-7c-(2c+2)>-4c-2+6c

I distribute the 2c and 2 with -1

[little jewel]

Yeah

[little jewel]

My maaan

[real mist]

?

[little jewel]

-7-2

[real mist]

-9

[little jewel]

Then why -5c

[real mist]

because i had to add

[little jewel]

I am not sure what you are adding -7c-2c is -9c

[real mist]

because i had to do what i did for both numbers-

[little jewel]

What is your thought process when doing -7-2

[real mist]

When I put collected the -2c i added it so i went to the -7c and added 2c what got -5c

[little jewel]

You do realize -7-2 is the same as -7c-2c

[real mist]

yeah

wait

i fucked up even after that-

Lemme redo-

so now im stuck

Thats just 0

so do i cancel it out right?

i feel dumb asf rn

[little jewel]

Idk what's the image about but yeah c< 0

[little jewel]

6c

Not 6

-4c + 6c

You forgot the c in the first step

[real mist]

OH

then

step 3 i messed up and it effected it right?

[little jewel]

1 was screwed so all the ones that followed were screwed but if you add the c in 3rd it could be fixed

[real mist]

Ok

now im confused-

[little jewel]

Clarify

[real mist]

all i have are "c" varibles

i do not have any constance

[little jewel]

And that's fine

[real mist]

O

[little jewel]

0 is a constant

[real mist]

so

[little jewel]

Solve it normally when you're at -9c > -4c+6c

[real mist]

O

[little jewel]

Is that an o or 0

[real mist]

so

awnser is c>-1.1

[little jewel]

How

[little jewel]

My man god forbid what's 6-4

[real mist]

2

[little jewel]

Then why 10

[real mist]

bc

-4-6

[little jewel]

It's -4+6

[real mist]

OHHHHHHHHHHHHHHHHHHHHHHHHHHH

im stupid at this point

[little jewel]

And you are missing the c

[little jewel]

No

You want to isolate c

Subtract 2c from both sides

[real mist]

how did u get 2

[little jewel]

Look what do you do to isolate X in 2x>x +1

[real mist]

2x divided by 2

then

[little jewel]

That wouldn't work since we still have X on both sides

[real mist]

o

Then no clue-

[little jewel]

Look take the x from the right and make it negative on the left, are you familiar with how to do this

[real mist]

nope

not at all

[little jewel]

Remember this

[real mist]

yeah

but i dont understand when to like do both and to not

wait ill show u

NVM

like i dont know when to do what

[main gull]

If you have the same variable on both sides, you need to get all the terms with variables on the same side, and everything else that doesn't have a variable to the other. That's when you need to do the opposite operation. If the variables are on the same side, you just need to perform the math with that sign

[real mist]

OH

thxs

[main gull]

That sign meaning don't do the opposite operation with that variable

[little jewel]

Yo dldh can you continue helping them with this problem, I suck at helping and it's 4 am so i gotta sleep

[real mist]

<@&286206848099549185>

acually im tired

NVM

.close

[devout snow]

Channel closed

Closed by @real mist

Use .reopen if this was a mistake.

[devout snow]

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.

[rotund gull]

how do i find both points that have the same y, but that are integers?

domain is all real numbers given that the graph is to the degree of 5

but I don't understand the middle 2 fields... any help is much appreciated

turns out it was (to the left) 3, -36 and (to the right) 7, 28

but why?

[devout snow]

@rotund gull Has your question been resolved?

[rotund gull]

.close

[devout snow]

Channel closed

Closed by @rotund gull

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.

[wet herald]

graphing

[wet herald]

so my question is the write the slope intercept form of the equation of the line through the given points

(-3,-3) (4,3)

I got y=6/7x but when I checked the answer sheet the answer was y=6/7x-3/7

and I'm confused as to where the -3/7 came from

[devout snow]

@wet herald Has your question been resolved?

[deep cove]

Your y-intercept calculation may be wrong. It should not be 0. You may want to check on that 🙂

[devout snow]

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.

[deft bridge]

Q: There are 20 used components in the box, 15 of which are working. Among them, 10 new components have been added (which are sure to work). The engineer takes randomly one. If it turns out to be working, how likely is it to be new?

I tried to solve the problem using
P(working) = 15/20 and P(new) = 10/20
15/20 * 10/20 = 3/8 (0.375)

This solution was not right. How should this be edited, as it doesn't seem as simple as calculating the odds of picking one working component and a new one?

[devout snow]

@deft bridge Has your question been resolved?

[devout snow]

@deft bridge Has your question been resolved?

[topaz axle]

It's just 10/25

the intuitive answer

P(working and new) / P(working) = (10/30)/(25/30)

[deft bridge]

I didn't note the +10 at all for some reason.. Thanks.

.close

[devout snow]

Channel closed

Closed by @deft bridge

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.

[pseudo basin]

this is dumb as hell but i'm drawing a blank:

how do i show that $y \notin (x-1, y^2)$? i'm sure the statement is actually true but i am just blanking on how to prove it properly

(for context, that is an ideal in the ring $\bC[x,y]$)

[woven radish]

Ann

[pseudo basin]

i would also like to avoid symbol-bashing if at all possible

i can show the original AG problem if anyone needs, though i'm pretty sure that i've reduced it to this correctly

[devout snow]

@pseudo basin Has your question been resolved?

[pseudo basin]

fuck it

.close

[devout snow]

Channel closed

Closed by @pseudo basin

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.

[deep quartz]

I am experimenting with combining unlike terms. Can somebody on this server please take a look at this and, without criticizing the formatting or complaining that it's hard to read, take a look and tell me if I've done everything correctly? If so then I'm inclined to say that our entire system of mathematics is inherently flawed (which I've been trying to prove/fix for months now). But then I would sound pompous and mathematically undereducated, both of which are intermittently true. Thank you.

Let x² + x = y,
so that x(x) + x = y.

Let y(x) + x = z,
so that x + x = z/y
and 2x = z/y.

xx + x = x² + x
x + x = (x² + x)/x
(x[x] + x)/x

Let (x² + x) = y,
shown by (x[x] + x)/x
as (x² + x)/x
as (y)/x
as y/x
such that x² + x = y.

x² + x = y
= x(x) + x = y
x + x = y/x
2x = y/x
2x(x) = y
= 2x(1x) = y
= 2x¹(1x¹) = y
= 2x² = y

2x² = y
2x = √y
x = (√y)/2
2x = √y
2 = (√y)/x

x² + x = y
y = 2x²
x² + x = 2x²

Algebraically sound, yes?
But then it falls apart numerically.

x² + x = 2x²

1² + 1 = 2(1)²
1 + 1 = 2(1) = 2

2² + 2 = 2(2)²
= 4 + 2
= 2(4) = 6

3² + 3 = 3(3)²
= 9 + 3 = 3(9) = 27
12 = 27 🚫

4² + 4 = 4(4)²
16 + 4 = 4(16) 🚫

Any thoughts? In the meantime, I'll be working on 2 = (√y)/x.

[deep quartz]

You don't want Artificial Intelligence built on flawed mathematics, do you?

"No." The correct answer is "no."

@left robin I couldn't resist pinging you for round two.

[left robin]

This is wrong:
Let y(x) + x = z,
so that x + x = z/y

[deep quartz]

That's mega wrong

that fuck was I even doing there lmao

lemme go look

I see what I did, stupid careless mistakes @left robin brb

I just realize how late it was. I am genuinely sorry for pinging you at this hour. I hadn't realized what time it was. @left robin

To anyone available:

is it

(SET A)
y(x) + x = z
y(x)/x + x = z/x
y + x = z/x

and

y(x) + x = z
y(x)/y + x = z/y
x + x = z/y
2x = z/y

or is it

(SET B)
y(x) + x = z
(yx + x)/x = z/x
y + x/x = z/x
y + 1 = x/x
y + 1 = 1
y = 2

and

y(x) + x = z
(yx + x)/y = z/y
x + x/y = z/y

?

I feel like set B is the correct one but I'm not sure

It feels like a five-way stop and every way but the way I came leads off a steep cliff. >___>

[devout snow]

@deep quartz Has your question been resolved?

[devout snow]

@deep quartz Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[deep quartz]

.reopen

[devout snow]

✅

[deep quartz]

I'm feeling stumped and could really use another set of eyes or two on this. Please && thank you. There are clear logical inconsistencies which are, for me, creating the mathematical equivalent of cognitive dissonance. Somewhat unpleasant. Am I hoping I'm just made some silly mistake somewhere.

ASSUME x = z + y
SO x = z + y
THEN y = x - z
AND z = x - y.

SO ASSUME 7 = 5 + 2
SO 7 = 5 + 2
THEN 2 = 7 - 5
AND 5 = 7 - 2.

SO x + z = y.

ASSUME x + x = y
SO x + x = y
THEN 2x = y
AND x = y/2
AND 2 = y/x.

SO ASSUME 7 + 7 = 14
SO 7 + 7 = 14
THEN 2(7) = 14
AND 7 = 14/2
AND 2 = 14/7.

Assume x² = y
So x² = y
Then x = √y
And y = x(x).

So assume 7² = 49
So 7² = 49
Then 7 = √49
And 49 = 7(7).

SO x² = y
THEN x(x) = y
AND x = y/x.

SO 3² = 9
THEN 3(3) = 9
AND 3 = 9/3.

%%%%%%%%%%%%%%%%%%

LET x² + x = y
SO x² = y - x
THEN x = √(y - x)
AND x = y - x².

SO 3² + 3 = 12
THEN 3² = 12 - 3
AND 3 = √(12 - 3)
AND 3 = 12 - 3².

SO x² + x = y
THEN (x • x) + x = y
AND x(x) + x = y
AND (y - x)/x = x
SO y/x - x/x = x
*SO y - x/x = x (someone please tell me I've made an error on any arrangement of these two lines in particular unless I actually haven't, then don't)
BUT (y - x)/x =! y - (x/x)?
SO y - 1 = x
SO y = x + 1
SO x = y - 1.
∴
SO 1² + 1 = 2
THEN (1 • 1) + 1 = 2
AND 1(1) + 1 = 2
AND (2 - 1)/1 = 1
SO 2/1 - 1/1 = 1/1 = 1
SO 2 - 1/1 = 1
SO 2 - 1 = 1
SO 2 = 1 + 1
SO 1 = 2 - 1
∴
2² + 2 = 6
THEN (2 • 2) + 2 = 6
AND 2(2) + 2 = 6
AND (6 - 2)/2 = 2
SO 6/2 - 2/2 = 2
SO 6 - 2/2 = 2 = FALSE
BUT y - x/x = x = TRUE (see above)
AND (6 - 2)/2 = TRUE
SO 6 - 2 = 2 = FALSE
BUT y - 1 = x TRUE
SO 6 = 2 + 1 = FALSE
BUT y = x + 1 = TRUE
SO 2 = 6 - 1 = FALSE
BUT x = y - 1 = TRUE.

y - x/x = x ?= TRUE?

What in the actual fuck is even going on here?

[midnight dirge]

...

maybe try

shortening the thing to your point

its a bit long atm

[deep quartz]

...I already have. Unfortunately.

Everything included is imperative to its full comprehension.

[stone stump]

(y-x)/x=y/x-x/x=y/x-1

that's not the same as just y-x/x=y-1

(unless x=1)

the SO and THEN and AND don't help with the readability

[midnight dirge]

agree

its like adding a THEREFORE in front of each statement

[deep quartz]

I did add a few of those. Lol.

I use those to keep my own thoughts straight. Read around them.

[midnight dirge]

ok just

[deep quartz]

It isn't difficult to skim over something with the eyes, last I checked. Takes about a fraction of a second and requires minimal effort (and then none at all).

[midnight dirge]

ill just say

everytime u do a

divide by x

add a

x is not zero for every line after

u did quite a few divisions

and that is nearly always the source of errors

[deep quartz]

What do you mean by this?

[midnight dirge]

this

[pseudo basin]

about half of that big message of yours is more or less walking in circles

[deep quartz]

x is no zero for any of these calculations. Yet. Lol.

[pseudo basin]

the meaningful part of any of this is that you go from y = x^2 + x to x = (y-x)/x = y/x - x/x, which is all correct

[deep quartz]

You say circle, which gets me back to where I started. I prefer to envision it as a spiral, ending in a new destination altogether.

[midnight dirge]

...

[pseudo basin]

oh sorry, do you want to argue semantics???

[deep quartz]

I wasn't arguing by any means. but now I'm not appreciating your hostile tone.

Please take your undue hostility elsewhere. Thank you. @pseudo basin

[midnight dirge]

well

this is hillarious

[pseudo basin]

didn't even manage to get to my point...

[deep quartz]

I'm not laughing and neither were you.

[pseudo basin]

but ok, i'm out

[deep quartz]

You're still welcome to make your point if you can make it tactfully.

[pseudo basin]

well i wasn't going to commit violations of tact at any point

but as i understood, you want me out.

[dapper gazelle]

It's actually very difficult to skim through poorly written deduction

[midnight dirge]

:c ann is super nice

[pseudo basin]

anyway!

[dapper gazelle]

If you really want a formal verifier run it through a calculator

[midnight dirge]

but is ok

[deep quartz]

Then can you suggested a preferential format so that I might restructure it?

[dapper gazelle]

run it through a calculator

[pseudo basin]

you go from y = x^2 + x to x = (y-x)/x = y/x - x/x, which is all fine and dandy
you also observe, correctly, that (y-x)/x in general need not equal y - x/x (i.e. y-1)
and then you seem surprised when that equality does indeed hold in a particular case, which one can only call a sheer coincidence.

[deep quartz]

Yes. I saw it this first time. What do I do when my calculator (which is Google) begins to refuse (as it seemed) to provide further calculations?

[dapper gazelle]

Get an alternate calculator

[deep quartz]

I do believe in coincidence, though unexpectedly so.

[pseudo basin]

well sometimes things Just Happen

an equality that need not hold in general may sometimes become true for a particular choice of values for its variables.

there is usually not much significance to that fact.

[deep quartz]

This seems good and fair to me. Any recommendations?

[deep quartz]

Lol tru

[pseudo basin]

ah, no, it appears you've run with x=y-1 and in the last paragraph keep proclaiming it as true bc it happened to be true when you put x=1...

[deep quartz]

But I'm still not satisfied. How can it hold true with variable notation but then crash and burn so gloriously when the numerics are implemented?

[pseudo basin]

at no point does it crash and burn

what actually happened is that you made a hasty over-generalization.

and are suffering the consequences thereof.

your asterisked line

SO y - x/x = x
is the source of all these evils

[deep quartz]

Haha. I can appreciate that. But I still don't quite understand. I did not equate x with 1 until after establishing the substratum of it all with variables. Or so I thought.

[deep quartz]

You are quick to judge a thing.

[pseudo basin]

judge?

[deep quartz]

Yes.

[pseudo basin]

you think i am making a value judgment here?

[midnight dirge]

kinda surprised u r actually helping him

[deep quartz]

I did, yes. Now you have administered a measure of doubt.

[restive river]

can you guys help me out with this please

[pseudo basin]

@restive river get your own channel. #❓how-to-get-help

[midnight dirge]

#❓how-to-get-help

[arctic field]

where did y - x/x = x even come from

[restive river]

ok

[pseudo basin]

ok well let me tell you that in fact there was no value judgment there at all

[deep quartz]

The pits of Hell, apparently. lmfao.

[deep quartz]

I understand. Then I apologize for assigning an unintended value to your statement.

[dapper gazelle]

,w x^2 + x - 1 = x

[woven radish]

Results provided by WolframAlpha

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

Requested by 草w#3875

[dapper gazelle]

Amazing

[midnight dirge]

is that relavant

[deep quartz]

I've never really used Wolfram Alpha before. I'll ignore your sour demeanor and thank your for the suggestion, instead.

I think I just mispoke. Forgive me. I apologize. @dapper gazelle

[pseudo basin]

anyway

word of advice

[deep quartz]

But can you explain your contribution just now to me? Or was it intended to be obvious? I am still a rookie mathematician in every sense of n00bness about it lol.

[deep quartz]

Yes, ma'am?

[dapper gazelle]

On assumption of y = x(x+1), then if y - x/x = x is an identity then it means nothing went wrong

[deep quartz]

I'm wondering the same thing.

[pseudo basin]

when you present your work for a math problem up for scrutiny, be it algebra or geometry or what
and people tell you that you messed up in a particular point in your argument/calculation/whatever
it means just that

it is never a value judgment

it is never a judgment on your personal character

nothing like that

[dapper gazelle]

But if it only holds for certain values of x, then an equation is being solved, rather someone manipulating both sides of an identity

[deep quartz]

It was your usage of the term "evil"
that I took an oppositional stance toward. Because I do these unusual things because I believe in a better world. That is why I wrongfully assumed.

[vast rain]

I was reading the long message

kinda lost on what it means at a high level

[midnight dirge]

there were a lot of unneccessary details which made it harder than needed to read

[vast rain]

like are the actual examples of the numbers necessary or am I ok just to skip them

[deep quartz]

I'm sorry about that. I wanted to ensure complete processional transparency.

[vast rain]

because I don't feel like checking all of that

[deep quartz]

The preliminary examples are unnecessary. I will cordone them off. Just a minute.

(I wouldn't say "unnecessary" but only for the sake of that discussion)

[vast rain]

so I'm struggling to see what you concluded here

[deep quartz]

So am I! 😂

[pseudo basin]

i use "evil" in this context in a somewhat tongue in cheek way to mean "things that get in your way"

[vast rain]

no like I don't know what you're actually stating

it's like you've written a bunch of statements down, some of which may be true and some of which may be false (I haven't checked them all)

but I don't see the high-level purpose of all of them

[deep quartz]

Start at %%%%%%%%%%%%%%%%%% for the meat of the post.

[vast rain]

like what unifies them all

SO x² + x = y
okay how did you conclude this

[deep quartz]

I haven't quite figured that out yet. Are you speaking mathematically, or of my personal intention for doing all this?

[vast rain]

can you just give a short definition of x and y

[vast rain]

no I mean mathematically

[deep quartz]

That should read "LET x^2 + x = y"

That was my mistake.

[vast rain]

you mean let x^2 + x = y?

[deep quartz]

Yessir. My mistake 2.0 lol.

[arctic field]

i still dont get how y - x/x = x

where did you even get that

[pseudo basin]

it's an ✨ algebraic screwup ✨

[arctic field]

amazing

[pseudo basin]

one i personally have seen many times, at that!

[midnight dirge]

from some addendum

[vast rain]

okay so you have y/x - x/x = x

how did you get to: y - x/x = x?

I agree that you can get to the former statement from your definition of "LET x^2 + x = y"

but I don't see how the latter statement follows from that

[pseudo basin]

do we need the same point made multiple times

[vast rain]

oh I must've missed that lol

[dapper gazelle]

bruh no quoting me

[deep quartz]

I thought someone had stated this to be correct previously?

[midnight dirge]

LOL

[vast rain]

I think we agree that y/x - x/x = x is ok

but not y - x/x = x

[dapper gazelle]

Oh

missing brackets

[pseudo basin]

yes as i said before

[vast rain]

In particular, a simple counterexample is where x = 2. In this case, you've defined y to be 6. Any you can see that y-x/x = 6-2/2 = 5 which is not equal to x

so there must be a problem with your logic between the two statements

or do you disagree?

[deep quartz]

I know that adding and subtracting fractions requires a common denominator. And so this intended to express that mechanic, if I recall.

[vast rain]

but that doesn't mean that you can simply get rid of the /x behind the y

[deep quartz]

I agree that a problem can currently be perceived to exist regarding these calculations. I haven't said beyond that.

[vast rain]

that lets you get (y-x)/x = x at best

but that doesn't mean that y-1=x by any means

[deep quartz]

I must have that somewhere in here. Let me look. One moment. Sadness (or whatever that was before I said no) is no factor here.

[vast rain]

I don't understand these two steps

If you've made a typo, I suggest you go fix it so we can be 100% sure about what you're talking about

[deep quartz]

Please pardon me. One moment.

[arctic field]

my mans trademarked the word amazing

[deep quartz]

Ah, yes. I will show you how the thought process looked in my head using pen and paper. Maybe that will help.

[vast rain]

I'd like to see how you got from the first statement to the second

[deep quartz]

@vast rain (The other day I also calculated a numerical value for i [I know this is impossible, yet...] and I would love for someone with your credentials to look over it. I spent about three hours on this server doing it publicly with other users correcting any mistakes as I went. The final calculation was i = 0.38107974512. I am aware that it must be erroneous.)

Now for that thought process I mentioned.

[vast rain]

what do you mean by i?

like the imaginary unit?

i^2 = -1?

[deep quartz]

Yes. √-1. That i.

The solution to x² + 1 = 0.

Here is that thought process. I think I may have found my error (t)herein.

[vast rain]

well, it's a fairly easy mathematical proof to show that no real number satisfies the equation x^2 + 1 = 0

[vast rain]

every step in there is correct

but that doesn't let you conclude that y-x/x = x

that lets you conclude that y/x - x/x = x

which is consistent with how you defined x and y

[deep quartz]

Yes. You're right. I cannot for the life of me recall where that came from (yet). It must have come from somewhere. Another moment, please.

Ah. I found it. Here it is:
y/x - x/x = x
y/x - 1 = x
y/x = x + 1
y/x - x = 1
@vast rain

But that isn't what was written and now I'm confused. ?__?

one sec

[vast rain]

yeah all of that is agreeable

[deep quartz]

Unless it was a transposition

[vast rain]

but that's not what was written

[deep quartz]

Which it may have been

[vast rain]

also you should check your work over computing the numerical value of i

because it certainly doesn't check out

[deep quartz]

Trying to work backwords from that point to figure out where I've gotten that from, I've tangentially gotten this (the following):

y/x - x/x = x
y/x - 1 = x
y/x = x + 1
y/x - x = 1
y - x = 1x
y - x = x
y = 2x
x = y/2

y - x/x = x
y - x = x²
y = x² - x
x = √(y + x)
x² = y + x

But still no luck on that peculiar line. Haven't quite given up yet though. I recall deriving (for lack of a better term) that line at least thrice over if not more and checking it against the similar parenthetical-inclusive entry. But now I cannot recall how I did so. Still trying tho. Although I feel like that (the above) included tangent is a fresh can of worms. Maybe. @vast rain

I already know

[vast rain]

how did you get from the first line to the second line?

[deep quartz]

I just saw ot

it

lol

yeah

whoops >___>

damn

Oh

Actually

I noticed my error before you did. Nevermind. 😋😇 I'll answer your recent question now.

That is another mistake. Thank you for correcting it. Here is the correction:

y/x - x = 1
y - x = 1 + x
y = 1 + 2x
y - 1 = 2x
x = (y - 1)/2

y = 1 + 2x
1 = y - 2x
1 + 2x = y

1 = y - 2x
1 - y = -2x
x = (1 - y)/-2

1 + 2x = y
2x = y - 1
2 = (y - 1)/x

2x = y - 1
2x - y = -1
2x = -1 + y
x = (-1 + y)/2
x - y = -1/2
x = -1/2 + y
-y = -1/2 - x
-y + x = -1/2
-1y + x = -1/2
(-1y + x)/-1 = (-1/2)/-1
(-1y + x)/y = (-1/2)/y

At this point I stopped and assumed more erroneous entries to be weeded out. I've underlined notably unusual suspects. @vast rain

[vast rain]

how did you get from the first line to the second?

I get y/x = 1+x, which is as close as I get

[deep quartz]

Is there; could there be; must there be a real number that sarisfies all of these conditions? Or would it be another sort of imaginary number?

[vast rain]

what conditions?

[deep quartz]

Another error. I always forget when shifting terms that it must be applied to that entire side of the equation rather than just its own coefficient. Or at least I'm pretty sure that is how it goes.

The correction:

y/x - x = 1
(y/x - x)x = 1x

What I did was this (is this actually erroneous as far as you presently conceive?):
y/x - x = 1
(y/x)x - x = 1/x
y - x = 1/x
[...]

[deep quartz]

That is a good question. I suppose what I meant was the conditions of these variables (presently x & y) to function as variables, and their cons(is)tancy once assigned/ascribed with/by (a) value.

I'm sorry if that is poorly worded. It was a difficult question.

[vast rain]

also at the risk of sounding dismissive, there's likely no mathematical way you're going to be able to algebraically manipulate these things into anything other than something that's easily rearranged to y = x^2 + x. It's just not how it works. Someone more educated on the whole mathematical logic thing might be able to bring in some proof of completeness and soundness for a restricted system of mathematics that encompasses what you're using (I don't know enough to say that)

but intuitively, there will always be a mistake in your algebraic manipulation if you're getting anything other than your assumptions

how did you get from the first line to the second?

[deep quartz]

I am not quite sure what this (the above quoted), or any of that (the above posted), meant or means. Sorry. 😅

[vast rain]

I mean you're not going to get anything deeper than what you've already defined: y = x^ 2 + x

[dapper gazelle]

If you assume x=x don't expect to get x = x + 1 unless x = x implies x = x + 1 in the system you are working in.

[vast rain]

and I know there are issues with proving that mathematics itself is consistent, but I don't think you're going to show an inconsistency through these manipulations

[deep quartz]

I'm working in an alternative system of mathematics that perfectly follows the rules of the standard system...?

[dapper gazelle]

What?

[deep quartz]

How is this system differentiated from traditional mathematics?

[vast rain]

as in the subset of algebraic manipulations you're using is probably proven to be complete and sound, i.e. what you're trying to do has already been proven to be impossible

[dapper gazelle]

did you just say no you to me?

[deep quartz]

I think I was confused by what you said lol.

[deep quartz]

wat

[deep quartz]

no u

j/k

[deep quartz]

but no I literally did not say that in any form on any channel of communication(s) lmao

[dapper gazelle]

What is your actual aim?

[vast rain]

anyway

before we get distracteed

[deep quartz]

To disprove modern mathematics.

[vast rain]

can you tell me how you got from the first line to the second line?

[deep quartz]

But I'll regret having said that.

[vast rain]

the term of art for this is to demonstrate the inconsistency of modern mathematics

[dapper gazelle]

Don't do this in the help channels

[deep quartz]

Because I know that that is impossible.

[vast rain]

but unfortunately, I think you need more powerful tools to do that

simple numbers and summing them up

[deep quartz]

Yessir. I like your phrasing much better than my own.

And then I hope to invent/discover a more consistent system as the fruit of my labors. (:

[dapper gazelle]

Seriously not a fit for the help channels either way

[vast rain]

I think that's proven, under some pretty weak assumptions, to be impossible without bringing in a higher level of mathematics

[vast rain]

hmm in this case, I agree. I dunno if it would include some of the deeper stuff in mathematical logic though

[deep quartz]

But I am a rookie mathematician seeking help from wiser a counsel. Is this not the case?

[vast rain]

like I think that incompleteness is a really deep topic that maybe might be worth talking about

[vast rain]

I'm just going to say that it's very unlikely that just using your techniques you'll be able to demonstrate anyhting

[deep quartz]

Some "incompleteness theorem" rings a bell in my mind. I am interested.

[vast rain]

if you're interested in things like mathematical proof systems + logical systems, might be worth picking up a book on set theory and mathematical logic

[deep quartz]

Meh. That's okay then. I also enjoy it, just for the fun of it all. Raw calculation is immensely satisfying to me.

[vast rain]

basically one of the deep philosophical problems in mathematics that emerged is that, in general, a mathematical proof system cannot show itself to be consistent

and so we can't really prove that our proof system won't derive statements that contradict each other

[deep quartz]

I'm definitely interested in set theory on a more philosophical level ("creatio ex nihilo").

[vast rain]

so the alternative is that we define restricted proof systems which are only allowed to use certain things

and then we use more powerful proof systems to prove that those proof systems are consistent within the more powerful proof system

[deep quartz]

Ah. Sounds like the same complaint folks have about God/the Bible. How interesting.

[vast rain]

but I don't think that this is what you're doing here

[dapper gazelle]

I should have seen this vague mix of words at first then.
"experimenting with combining unlike terms"

Make your aim clear before communication.

[vast rain]

well, it's more mathematical

[deep quartz]

Have I not done so at any point? And yet I have not the slightest inkling of your own intentions here in your criticism of my post(s). That isn't quite fair to me.

[deep quartz]

Indeed. So likely closed to truth (but only perhaps).

[dapper gazelle]

• These channels are for pre-university homework-type questions

[deep quartz]

Perhaps truth is formally inconsistent. Who knows. Haha.

[deep quartz]

Ah. In that case, you were correct. I had not seen that prior to using the help channels in recent days.

[vast rain]

I wouldn't say that. I don't think it's the same issue as the complaints against religion, which mostly involve circularity

there's a degree of self-reference involved, but the problem is that if you take mathematics as given, you can prove that there exist statements that are true that cannot be proven

and further that sufficiently powerful proof systems cannot demonstrate their own consistency

[vast rain]

oh yikes lol

that's somewhat related. I think that's more in line with reverse mathematics

[deep quartz]

Are there any pertinent examples?

I deleted that post up there incidentally. Not a worry though lol.

[deep quartz]

examples of this principle, I mean(t).

[deep quartz]

We did get distracted but I'd really like to know if this is indeed erroneous or not. Lol sorry.

[vast rain]

I believe it is erroneous

I don't see how you got from the first line to the second

[deep quartz]

Wherein?

[vast rain]

and I think the counterexample with x=2, y=6 is sufficient to show that.

[deep quartz]

Yeah, and I still never figured out where the y - x/x = x. I sure wish I could because that would really help. Maybe it was truly just an oversight. Could've be, could be.

Gonna take another few minutes to look it over. Maybe something will click.

[vast rain]

I'm pretty sure it was an oversight

because I'm confident that the rules of basic algebraic manipulation are consistent lol

the counterexample shows that whatever derivation you use will eventually derive 0=1

[deep quartz]

It interests me that it was those two lines where I noted that I must have made an error. But I only said that of 30+ minutes of verification. But now the logic of it has left me. Which kinda sucks lol. >:

[midnight dirge]

there u go, math is fake

[deep quartz]

yay
winner winner chicken dinner

[midnight dirge]

its a hoax

[deep quartz]

u right tho u right

big math has to keep us invested

xD

[deep quartz]

What counterexample? And how will this occur?

[vast rain]

I gave you a counterexample

x = 2, y = 6

y = x^2 + x, which satisfies your assumption

[deep quartz]

Could that have anything to do with the fact that zero = 1(0) (that is, one times [of] zero)? Meaning that it is a bit contradictory/paradoxical, for the empty/null set to actually technically be "one" empty/null set (because this implies that one is defined).

[deep quartz]

Ah. Where does 0 = 1 come into play?

[vast rain]

0=1 is just a placeholder for any false statement

the point is that your derivation is going to produce false statements

[deep quartz]

Understood.

[vast rain]

and these are worthless, because if you can prove a false statement, then you can prove anything

[deep quartz]

I may be approach a solution to the peculiarity. One moment.

[vast rain]

I don't think you can

it'd be tantamount to proving that 2 = 1 or something ridiculous like that

which might be what you're trying to do

[deep quartz]

Who is to say that "anything" is not the truth? What if nothing at all is objectively false? Then surely our mathematics should reflect this aspect of truth.

[vast rain]

but mathematicians will tell you this is almost certain to fail

[deep quartz]

But that is a bit philosphical and semantic-driven.

[deep quartz]

I've proven that 1 = 0 in the past. More than once, I think. Somewhere in my notes. That is not my intention here, but it would be a conclusion that I would be content with.

[vast rain]

then your proofs are likely not accepted because they contain flaws

technically speaking, your proof system is considered inconsistent, but in reality, we just throw those proof systems in the dustbin

[dapper gazelle]

https://en.wikipedia.org/wiki/Confirmation_bias
https://en.wikipedia.org/wiki/List_of_cognitive_biases

[deep quartz]

Yes. Thank you. Because I surely wasn't familiar with any of that content. Smartass. 😐

[dapper gazelle]

Inconsistency is a big problem unless it avoids issues of inconsistency

[vast rain]

if you have proven that 1=0, you have two choices: you accept your proof as valid and therefore you accept every possible statement as true, or you accept your proof is invalid and still can talk about things like truth

[dapper gazelle]

By that I mean, being able to 'prove anything'

[vast rain]

I always made a joke to my friends that my proof system is that "I'm always right"

[dapper gazelle]

If you speak about 'proving 1 = 0' unironically, don't expect mercy

[deep quartz]

Both options still offer a truth value. I tend to believe in a truly infinite reality as far as I can humanly conceive (of) it. Even in terms of truth and possibility and eventuality and falsehood.

[deep quartz]

Who are you that you would offer or deny mercy?

[vast rain]

no, the first option basically throws your hands up in the air and says that truth is meaningless because anything you can think of is true

[dapper gazelle]

I'm 'not anyone' but certainly you love making enemies, so good luck with that

[deep quartz]

Meaning that all things are true is truth.

[vast rain]

and while that may technically be an unusual way to look at things, in reality, people will just laugh at you

and the second option allows us to actually engage in logic, even in our daily lives, and this logic has proven useful

[deep quartz]

I do not count anyone as my enemy. But you can call me whatever you like to call me.

[deep quartz]

That is nothing new to me. Unfortunately.

[deep quartz]

This is agreeable.

I think I just figured it out. @vast rain

[vast rain]

well, if you accept your proofs as valid, then you also have to accept absurd things like "I (Saccharine) am the Pope."
A humorous proof from 0=1:

1. 1 = 2. (Add 1 to both sides)
2. The Pope and I are two men.
3. The Pope and I are one man (apply step 1)
4. I am the Pope.

I just don't think you're going to get anywhere with doing algebraic manipulations to try to prove something impossible. It doesn't work that way.
And for what it's worth, the way I find mistakes in your work is simply by looking for things that look impossible and searching for the last part when things were reducible to y = x^2 + x

[deep quartz]

Greeting, our father of the clemency!

...j/k sorry >___>