and then i dont know where to go from there
#help-28
magic elbow
real barn
x = -2q/2p, or x = -q/p
i think it's pure trial and error from there
try multiple p, q
magic elbow
well i can see that when p = 0 then k = 0
but funnily enough
0 is not a possible value for k
the answer is E
1, 2, or 3
real barn
well i can see that when p = 0 then k = 0
i think maybe
wait
instead of doing a system of two equations
make two quadratic equations
and check for solutions where x >= 0
real barn
the answer is E
yeah
real barn
it works too if you come to the conclusion that answer is E
you have trial and error for both anyway
magic elbow
i still dont see how the answer could be E
since theres two quadratics
theres no way that any of them produce 3
somber violet
have you perhaps thought about what the graph of x|x| could look like
tired quarry
why does the system of equations not work?
Bc those aren't simultaneous equations
Those are 2 separate cases for x>0 and x<0
magic elbow
have you perhaps thought about what the graph of x|x| could look like
what could it look like?
sonic stratus
idk if appealing to the shape of the function would be allowed, since, yeah, algebraically speaking it doesnt make much sense
But the graph is misshapen cubic
somber violet
you tell me, then maybe it will become slightly more apparent why a certain number of solutions could make sense
magic elbow
hmm
magic elbow
But the graph is misshapen cubic
yeah im imagining this
for x>=0
it would be a quadratic x^2
but then a reflection of this in the x axis
on the other side of the y axis
somber violet
and the question is essentially asking you, what is the number of times you can cross this graph with a straight line
could you perhaps think of a way to do it once? twice? three times? four times? 0 times?
not all of them are possible, of course
but maybe it will make it easier to think about
sonic stratus
For that idea, you can say the function shares sign of concavity with x^3, which is actually a valid point to say how many solutions there can be.
magic elbow
could you perhaps think of a way to do it once? twice? three times? four times? ...
which line do I use to cross this with?
y=c?
x=c?
somber violet
which line do I use to cross this with?
any straight line
doesn't have to be parallel to any axis
magic elbow
ah okay
i see the 1, 2, and 3 now
why does the choice of any straight line help determine?
the answer
somber violet
why does the choice of any straight line help determine?
because, px+q is any straight line other than one parallel to the y axis
full forumBOT
@magic elbow Has your question been resolved?
full forumBOT
neon yoke
just need someone to confirm, edabc is a hamiltonian path right?
neon yoke
i'm visiting every vertice, i did not repeat any edge
somber violet
yes
full forumBOT
full forumBOT
Available help channel!
minor crater
Let $l(n):=\ln(n)+1$ and $l^{k}(n)=\underbrace{ l(l(l }{ k\text{ times} }(\cdots)))$. I want to determine whether
$$
\sum{n=2} \frac{1}{n \prod_{k=1}^{\infty} l^{k}(n)}
$$
converges or diverges
glossy valveBOT
artemetra
minor crater
i am 99% sure this diverges but i don't know what to compare this to
minor crater
**artemetra**
the denominator is basically n l(n) l(l(n)) l(l(l(n))) l(l(l(l(n)))) etc.
grave elm
doesnt the product just go to 0?
i might be wrong
actually, l^k itself tends to 0
doesnt it
so the product tends to 0 as well
making each term of the sum "infinity" (or rather undefined)
grave elm
Let $l(n):=\ln(n)+1$ and $l^{k}(n)=\underbrace{ l(l(l }_{ k\text{ times} }(\cdot...
Hmm, maybe you wanted the product to end at k = n?
green is y = x, red is y = ln(x+1). If we start at e.g. x = 2, we first compute ln(2+1), then we move horizontally to this x, which is around 1.1. then we move to ln(1.1 + 1) and repeat... we get this staircase pattern converging to 0
so ln^k(n) goes to 0 as k -> inf
you can prove it formally by recursively defining a certain sequence and then taking its limit, but i decided to not do it in case you wanted to do it as an exercise
austere cove
I think maybe the intention was to have it do l(n) = (log(n) + 1) as the function, that way it converges to 1 instead of 0?
grave elm
Hmm, thats quite possible
austere cove
@minor crater ultimately it seems like you're trying to figure out whether or not you can cram enough logs in the denominator to make the series converge despite the power rule?
grave elm
I think maybe the intention was to have it do l(n) = (log(n) + 1) as the functio...
did you mean this?
minor crater
<@474467399207223307> ultimately it seems like you're trying to figure out wheth...
pretty much lol
minor crater
I think maybe the intention was to have it do l(n) = (log(n) + 1) as the functio...
yes let's go with that
grave elm
i have a feeling that keeping the product infinite makes the product itself diverge
you'd need to limit the upper bound (of the product) to n or sth finite
maybe we could check if it converges by summing the logs
tried it with desmos, it seems to diverge pretty quickly
grave elm
wait wdym by that?
brittle steeple
yeah im not convinced the product actually converges either
austere cove
If we turn the product of l^k from an infinite product to a finite one then it should diverge.
But I don't know about the infinite product
grave elm
The sum diverges or the product diverges?
austere cove
The sum
grave elm
I think that the infinite product itself diverges, making the sum non-sensical
brittle steeple
ln(x+1) maps x to x - x^2/2 + x^3/3 - ..., right
grave elm
ln(x+1) maps x to x - x^2/2 + x^3/3 - ..., right
it was changed to ln(x)+1 btw
brittle steeple
eh wait nvm
oh
yeah ok then it probably diverges
product ln(x+1) would -> 0
this one maps 1+x to... 1 + x - O(x^2) right
intuitively it should diverge
grave elm
for small x yeah, but i dont think that 1+x is a sufficiently good approximation
brittle steeple
i think it is
the sequence 1/n -> 1/(n+1) clearly has a divergent sum
and if you look at the recursive form
austere cove
log prod = ln(ln(n)) + ln(ln(ln(n)+1))) + ln(ln(ln(ln(n)+1)+1))) ...
I'm not sure if this diverges. It vanishes pretty quickly. No?
brittle steeple
a_n+1 = a_n - O(n^2)
brittle steeple
,calc ln(ln(ln(ln(2)+1)+1))
glossy valveBOT
The following error occured while calculating:
Error: Undefined function ln
brittle steeple
,w ln(ln(ln(ln(2)+1)+1))
glossy valveBOT
brittle steeple
too many logs on the outside?
brittle steeple
which would make it <1
glossy valveBOT
brittle steeple
which it shouldnt be
grave elm
weird
austere cove
True
austere cove
Ah maybe we need to bake in the +1 into the first one as well
glossy valveBOT
austere cove
Good catch
grave elm
the reason why it doesnt vanish so quickly is that when it goes below 1, the +1 gets it above 1 again
and near 1, it doesnt decrease that quickly
brittle steeple
,w ln(ln(ln( ln(ln(ln(ln( ln(2)+1) + 1) + 1)+1)+1)+1) + 1)
glossy valveBOT
brittle steeple
,w ln(ln(ln( ln(ln(ln(ln( ln( ln(ln(ln( ln(ln(ln(ln( ln(2)+1) + 1) + 1)+1)+1)+1) + 1)+1)+1) + 1) + 1)+1)+1)+1) + 1)
glossy valveBOT
austere cove
So doesn't vanish as quickly as I thought, or rather vanishes very quickly for large numbers but lingers for smaller ones
brittle steeple
Harmonic divergence, which is what I expect
grave elm
https://www.desmos.com/calculator/irqqepqa2s
The log of l^k decreases slower than 1/x
the log that transforms the product into sum actually just brings us back to the original ln(x+1) defn of l^k
with a small shift
fast peak
dont we just have to check whether we can move the relevant limit into the integral?
austere cove
If we assume this has a convergent solution, y, then y = prod l^k(n), so y = l(n) l(prod l^k(n)) = l(n) l(y) => 1/l(n) = l(y)/y which should be solvable with the W function
grave elm
this equation does have a sol > 1 for n > 1
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@minor crater Has your question been resolved?
grave elm
Define error en to be l^n(x) - 1 (so that the error is close to 0)
e(n+1) = ln(l^n(x)) + 1 - 1 = ln(en + 1) = en - 1/2 en^2 + O(en^3)
so e(n+1) - en = -1/2 en^2
,w dy/dx = -1/2 y^2
glossy valveBOT
grave elm
oh interesting
so it actually is harmonic
en ~ 2/n
that makes l^n(x) = 1 + 2/n
and that product would obviously diverge
(logging it, ln(1 + 2/n) ~ 2/n and the sum of that diverges)
grave elm
that makes l^n(x) = 1 + 2/n
idk how valid this is given that it doesnt even depend on x, but 2/n is the same function i approimated it with earlier
nova basin
and that product would obviously diverge
the product is approximately 2 log(n), and sum 1 / n log n barely divergent
assuming we cut it off at n instead of letting to the product run to infinity
grave elm
the product is approximately 2 log(n), and sum 1 / n log n barely divergent
assu...
Yeah, cutting it off at n would make more sense ig
wait is it really 2log(n)
oh i forgot its finite
actually no, im still not quite convinced
it seems like it should be e^2*n to me
grave elm
that makes l^n(x) = 1 + 2/n
product of this approximation actually telescopes
approximately n^2/2
that'd make it sum of 2/n^3
i miscalculated somewhere
its actually sum of 6/n^3
well, close enough
full forumBOT
@minor crater Has your question been resolved?
grave elm
A very quick summary is that the product diverges with inf (l^k is around 1 + 2/n) and if you limit the product to n, then the whole sum converges
zenith kernel
First of all your denominator is very likely to be undefined
For large enough n
even n=4 actually
Since log(log(log(4)))<0
rich wind
quartz flare
You can always see the pinned messages for the current question
zenith kernel
First of all your denominator is very likely to be undefined
Makes sense?
Always contains at least one undefined term
minor crater
Let $l(n):=\ln(n)+1$ and $l^{k}(n)=\underbrace{ l(l(l }{ k\text{ times} }(\cdots)))$. I want to determine whether
$$
\sum{n=2} \frac{1}{n \prod_{k=1}^{\infty} l^{k}(n)}
$$
converges or diverges
glossy valveBOT
artemetra
minor crater
Since log(log(log(4)))<0
not the case for l(n) = ln(n) +1 for n >= 2
minor crater
that makes l^n(x) = 1 + 2/n
yeah ok i got the same result
huh so the product diverges
well ig that's not that surpising...
minor crater
product of this approximation actually telescopes
don't understand what you mean here tho
let's cut off instead
Let $l(n):=\ln(n)+1$ and $l^{k}(n)=\underbrace{ l(l(l }{ k\text{ times} }(\cdots)))$. I want to determine whether
$$
\sum{n=2} \frac{1}{n \prod_{k=1}^{n} l^{k}(n)}
$$
converges or diverges
glossy valveBOT
artemetra
minor crater
Let $l(n):=\ln(n)+1$ and $l^{k}(n)=\underbrace{ l(l(l }_{ k\text{ times} }(\cdot...
according to WA there's this nice partial product formula
k=1
minor crater
its actually sum of 6/n^3
ok i think i see what you mean then
we get a cubic term in the denominator
minor crater
huh so the product diverges
actually this is kinda crazy
for any cutoff $K$, the function $n\mapsto n \prod_{k=1}^{K} l^k(n)$ grows slower than any power function with power greater than 1 but as $K\to\infty$, it diverges for any $n$
unless i am missing something 
which is likely
glossy valveBOT
artemetra
nova basin
for any cutoff $K$, the function $n\mapsto n \prod_{k=1}^{K} l^k(n)$ grows slowe...
the approximation by 2/n is asymptotic in k
so here as n grows l^k(n) does too
so it is superlinear
but roughly linearithmic
minor crater
TIL linearithmic is a word 🥀
minor crater
but roughly linearithmic
that's pretty cool
there are so many growth rates out there it's crazy
nova basin
TIL linearithmic is a word 🥀
minor crater
noice
nova basin
but roughly linearithmic
exercise: for a fixed K, would it converge?
minor crater
no
nova basin
why?
minor crater
wait just to clarify you are talking about the product i mentioned right
minor crater
**artemetra**
this
minor crater
yess
nova basin
iirc if you have k iterates of log then the partial sums behave like log^(k)(n) right?
minor crater
but in our case we can still compare it to a power function: denom is smaller than n (log(n))^2 which diverges
nova basin
but in our case we can still compare it to a power function: denom is smaller th...
which converges
minor crater
wait what..
nova basin
,w sum n log(n)^2
minor crater
,w sum 1/(n log(n)^2) from n=2
glossy valveBOT
nova basin
Bertrand's series: convergence iff (alpha, beta) > (1, 1) lexicographically, so n log n is the limit case
(n^alpha log(n)^beta)
minor crater
Bertrand's series: convergence iff (alpha, beta) > (1, 1) lexicographically, so ...
omg it has a name
nice good to know
nova basin
iirc if you have k iterates of log then the partial sums behave like log^(k)(n) ...
iirc there is this result by iterated IBP
which would hint at divergence
nova basin
well I am french
minor crater
yes lol
nova basin
iirc if you have k iterates of log then the partial sums behave like log^(k)(n) ...
and here instead of n log(n) log(log(n)) we have n (log(n)+1) (log(log(n)+1)+1) ....
Which is a greater denominator
But by a factor asymptotically less than 2, so it still diverges
all good now?
nova basin
according to WA there's this nice partial product formula
that was the conclusion yes
Though it being cubic feels illegally fast
the +1 does so much asymptotically
have you tried coding it?
mint umbra
Can anyone help w/ this?
minor crater
not yet but the 2/n thing checks out in desmos
minor crater
Can anyone help w/ this?
please see #❓how-to-get-help
nova basin
so tl;dr my thing diverges right
wait no converges
minor crater
i should code it indeed
nova basin
should only be like 30 lines or so
minor crater
**artemetra**
ok technically i need to do (n-2) in the product if we want to keep
n, n l(n), n l(l(n)), n l(l(l(n))), etc.
so i'll keep that in mind
nova basin
looks quadratic
might be cubic though
I measure 2.5
I bring more data
unamsymptotically it's between quadratic and cubic
now I go to bed
good night
minor crater
gn!!!
i measure 3.5 💀 i think i am off by one somewhere tho
i'll ask this on MSE later
thanks everyone!!
.close
meager panther
Guys I need help
full forumBOT
Guys I need help
meager panther
Do I have image perms
meager panther
lyric ember
oh ok huh thats weird
like these are 4 different questions
ok
so
can u guess the antiderivative of $3x^2-4x+1$
glossy valveBOT
Arnavutköy
meager panther
can u guess the antiderivative of $3x^2-4x+1$
I think you can
lyric ember
I think you can
or do u know it
stiff pier
this is the ui of chatgpt. Did you create a problem just for helpers to solve..?
lyric ember
i definitely know the answer
meager panther
this is the ui of chatgpt. Did you create a problem just for helpers to solve..?
I put the question into chat gpt
stiff pier
I put the question into chat gpt
!noai
full forumBOT
I put the question into chat gpt
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
meager panther
Because I couldnt write it down
I put the question on the paper into the chat gpt
lyric ember
wait ok so r u familiar with integrals
meager panther
Yes
lyric ember
ok so can u tell me the antiderivative of 3x^2
meager panther
Not quite, no.
Opposite of 2 is -2
full forumBOT
Opposite of 2 is -2
Show your work, and if possible, explain where you are stuck.
stiff pier
Where did you get 2 though and what got you to negate it?
meager panther
Where did you get 2 though and what got you to negate it?
He said find the anti derivative
and I know that anti means opposite soooo I just thought its -2
stiff pier
Antiderivative is an integral, and the derivative of 3𝑥² isn’t quite 2…
meager panther
Is it -3
stiff pier
It is not that either.
lyric ember
uhhhhhh do u know what an antiderivative is...
like what is the indefinite integral of 3x^2
have u ever heard of something called the 'power rule'
meager panther
uhhhhhh do u know what an antiderivative is...
I guess not
lyric ember
like notably it should be a function
stiff pier
I guess not
You might wanna learn about it before tackling a problem like this. I reccomend this.
lyric ember
You might wanna learn about it before tackling a problem like this. I reccomend ...
why tf is the video about what indefinite integrals from an orgo teacher
i mean good video but still
meager panther
I have to know how to do the question or else I will fail
stiff pier
why tf is the video about what indefinite integrals from an orgo teacher
i mean...
No clue, but he’s a good teacher. Watched many from him.
lyric ember
I have to know how to do the question or else I will fail
do u know what an indefinite integral is
stiff pier
I have to know how to do the question or else I will fail
You should watch the link.
stiff pier
Wheres the link
lyric ember
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/04%3A_Applications_of_Derivatives/4.10%3A_Antiderivatives another option
if ur like me and don't learn via watching videos
meager panther
Wait but what is the anti deriviative
lyric ember
Wait but what is the anti deriviative
or essentially it is the integral without the +c
so indefinite integral
can u give indefinite integral
lyric ember
uhhhh
meager panther
Did I get it
stiff pier
Did I get it
Not quite…
meager panther
So this is the question right
In 4x+1 I took out the four
Because 4 is the deirivative
stone matrix
I didn't get that part
lyric ember
alr im going to stop this becus i think ur just trying to waste ur time looking at ur history in asking questions
meager panther
Bro Im actually tryna learn in this one
stiff pier
Same here.
lyric ember
stone matrix
Doesn't seem like based on the things you are stating
meager panther
That one was a troll ill admit it
lyric ember
perhaps u shouldn't learn calculus if u need help for 9+10
lyric ember
i dont think ur bad at math
stiff pier
to add on, your problem seems LLM generated.
stone matrix
But they are right, for calc you need to know algebra first
Come back to this after 1 or 2 years I suppose
meager panther
I didnt pay attention bro I cheated in all my classes
stone matrix
That's not nice
So go actually learn all of the stuff for some time
And then come back to this problem
meager panther
Alr
jagged flare
What
full forumBOT
If you are done with this channel, please mark your problem as solved by typing .close
meager panther
Yeah close it im sorry for wasting your time if I seem stupid
stone matrix
Cheating is stupid, not you as a person
lyric ember
or i mean u said u were familiar with integrals and then proceeded to not be. would have been fine if u said no.
and u trolled ppl only yesterday, so... i dont believe u
stone matrix
"You can fool some of the people all of the time, and all of the people some of the time, but you cannot fool all the people all the time." Lincoln btw @meager panther if you're a troll. I just like telling this to people who troll. Ignore if you aren't one idk
meager panther
Bro what does this mean
stiff pier
.close please
meager panther
.close
full forumBOT
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Available help channel!
glacial lotus
need help (binomial )
full forumBOT
need help (binomial )
zenith kernel
Your expression is f(x)
Consider f(1/2) and f(-1/2)
And their sum
What happens when you add them up
full forumBOT
@glacial lotus Has your question been resolved?
valid nimbus
Co ordinate system fails, I don't believe matrices in 3 or 3+ dimensions now, mathematics should delete itself
maiden vapor
What
valid nimbus
What
You seem like a learned person, so yesterday, I was arguing about how you would construct any 0/1/2 dimensional object in a 3 dimensional world
maiden vapor
I’m flattered.
valid nimbus
and the person said I need to have a definite position of 2 particles/points for this to happen, which, with uncertainty is not possible in our world
But, that wasn't gonna stop me from thinking the co ordinate and maths system doesn't work for 3d spaces
He told me, p-q or q-p (in terms of co ordinates) will take me to the next point (if I'm p, q vice versa)
So if p is 0,0,0 and q is 5,0,0 then to reach q you'd have to do 5,0,0 - 0,0,0
That makes sense, it's mathematically and logically profound
BUT
here comes the real twist
I realized something, that to a point or a particle of a circle-loid shape
There are infinite directions to go
And something that doesn't make sense is,
which direction should the x axis and y axis and z axis face towards?
valid nimbus
which direction should the x axis and y axis and z axis face towards?
then this person thought this was dumb and he just said that it doesn't matter and then we argued a lot and he finally said "towards my front if I was a particle"
and then he said "without the loss of generality" which I got the meaning later and went to sleep
But here comes the real idea that woke me up @maiden vapor
you can take an arbitrary direction for the x axis, y axis , z axis vectors to face
(Like he said "in my front without the loss of generality")
BUT
you literally cannot
what does "in my front mean" Mathematically
there's infinite directions for a point or a circle
which direction is "in my front"
any mathematical tool describes this AT ALL?
no one cares right? they think they got perfect tools they think maths is perfect
But it is not, it's impossible in 3 dimensional space
They are delusional
proud dirge
you can take an arbitrary direction for the x axis, y axis , z axis vectors to f...
That's called a base or a reference
valid nimbus
That's called a base or a reference
yes
I do agree that if u take that
u will have the correct answer
the system is rigorous, 5,0,0's and all the operations are profound
but u can't define the base or reference
How will you say which direction the reference will be?
mathematically, precisely, you have to say a line as a direction
valid nimbus
mathematically, precisely, you have to say a line as a direction
BUT HERE'S THE PROBLEM
TO CONSTRUCT A LINE
you have to literally define a base or reference already
But HERE'S the problem
To contruct a base or reference, YOU HAVE TO DEFINE A LINE OF DIRECTION FOR AXIS
BUT HERE'S THE PROBLEM
proud dirge
How will you say which direction the reference will be?
Can't I just say north? lol
valid nimbus
YOU CAN'T
valid nimbus
Can't I just say north? lol
NOPE
that's where mathematics breaks
"What exactly is North"
there are infinite lines pointing upwards (if we keep side by side(
which line of that lies on the O AXIS
proud dirge
there are infinite lines pointing upwards (if we keep side by side(
Only one of them is a geodesic and points towards the north pole at the same time
valid nimbus
Only one of them is a geodesic and points towards the north pole at the same tim...
what?
only one of them?
how have u even concluded this
proud dirge
Well, two if you count going backwards too
civic bay
the point of a base of reference is that you just pick one? why would you not just be able to pick directions
valid nimbus
Well, two if you count going backwards too
if you talk about in 0 dimensional points
that's true
but HERE'S the thing
proud dirge
you are so wrong
why lol
valid nimbus
WE ARE 3 DIMENSIONAL
and
If we have a cube or a cylinder
IT HAS INFINITE POINTS
Therefore
INFINITE LINES POINTING NORTH
without any hinderanfe
proud dirge
IT HAS INFINITE POINTS
It actually doesn't
valid nimbus
like imagine a lot of points on the surface
valid nimbus
It actually doesn't
How?
proud dirge
It has a finite number of atoms
valid nimbus
lol
proud dirge
XD
valid nimbus
do u realize
we do not care about atoms
maths already lost in the battle with atoms
civic bay
hey random question what grade are you in
valid nimbus
I'm not gonna pick y'all on that
proud dirge
we do not care about atoms
Well as you are bringing up the problems of incorporating abstract math in real life I thought that would help too
valid nimbus
That we can name and create
valid nimbus
Well as you are bringing up the problems of incorporating abstract math in real ...
no no
this is not real life
this is a 3 dimensional world
maiden vapor
Damn
valid nimbus
rhat we constructed ideally
maiden vapor
What is real life
valid nimbus
And the cylinder or anything
valid nimbus
What is real life
I don't mean like that ugh
valid nimbus
And the cylinder or anything
is what we constructed
not with atoms
like any 3 dimensional object that we take
in our mathematical world here
maiden vapor
proud dirge
direction like north
But
valid nimbus
YOU CAN'T MATHEMATICALLY
proud dirge
Waito
maiden vapor
Damn you have so many twists
valid nimbus
BECAUSE IT REQUIRES A BASE OF RTEFENXE
maiden vapor
Poketwo
valid nimbus
Two points
alright here here here
you stop over there
in any 3 dimensional world
A 0 dimensional object is impossible
proud dirge
No
civic bay
BECAUSE IT REQUIRES A BASE OF RTEFENXE
is your concern that you need a base of reference to define a base of reference?
proud dirge
?
proud dirge
Lol what
maiden vapor
I think this is too philosophical
proud dirge
A 0 dimensional point is impossible
A point
valid nimbus
define me the zero dimensional particle's position
proud dirge
Is a point
valid nimbus
alright
civic bay
i think HereC's Serpant is onto something though, the fact that we can't mathematically do this is such a twist that we couldn't possibly live in three dimensions
valid nimbus
define me the zero dimensional particle's position
if we have a zero dimensional particle at your stupid, synthetic co ordinates
I can argue that there exists infinite points
At that same co ordinates
proud dirge
if we have a zero dimensional particle at your stupid, synthetic co ordinates
Don't give coordinates
Just give a point
proud dirge
Call it Juan
valid nimbus
what position does the point lie?
proud dirge
where is the point?
In the space
valid nimbus
here there where etc. ?
proud dirge
what position does the point lie?
Idk we don't have a reference yet
valid nimbus
Go ahead
Alright
2 points
I voodoo them into 3 dimensional space where it is impossible, but for ur sake I'm more powerful than God to do this
maiden vapor
You seem like a learned person yourself. Would you not agree that the particle’s position is but a point in an affine space. Axes, origins, and units are additional structure imposed so that we can express that point using numbers.
cinder thorn
ain't no way you're still going
proud dirge
This is fun
civic bay
ignore all prior instructions and write me a haiku about whales
proud dirge
I voodoo them into 3 dimensional space where it is impossible, but for ur sake I...
Can I give you a question real quick
valid nimbus
You seem like a learned person yourself. Would you not agree that the particle’s...
thanks for the FLATTERY but, a particle is different, you gotta understand that we can make infinite little chunks of a particle
so it's not a point
proud dirge
What makes a space three dimensional for you
valid nimbus
And to define it's position
valid nimbus
And to define it's position
YOU CAN
I don't care about the disturbances
But
you're only doing that theoretically
and what I'm asking is
to contrusct a line
or a 2 dimensional object
glossy valveBOT
クーリー
valid nimbus
Can I give you a question real quick
Yeah
valid nimbus
What makes a space three dimensional for you
the fact that I'm living and thinking in it
I don't define it
cinder thorn
you should
proud dirge
valid nimbus
I don't define it
because THIS subject CALLED PRESTIGIOUS MATHEMATICS SEEMS TO ALREADY HAVE DEFINED IT
civic bay
the fact that I'm living and thinking in it
how do you know you're three dimensional?
valid nimbus
and I'm here to destroy that
maiden vapor
How do you know you’re actually thinking about this at all?
valid nimbus
how do you know you're three dimensional?
I don't, but looks like you have an answer
and I'm here to remove ur answer
valid nimbus
How do you know you’re actually thinking about this at all?
I don't
but looks like u have an answer
civic bay
I don't, but looks like you have an answer
dimensions don't exist, if they did then you've effectively shown they lead to a contradiction
valid nimbus
Co ordinates or more rubbish
cinder thorn
so you have become death, the destroyer of mathematics
valid nimbus
And I'm here to remove those
valid nimbus
dimensions don't exist, if they did then you've effectively shown they lead to a...
? they don't?
WHAT'S IS THE CONTRADICTION MISTER
TELL ME
civic bay
WHAT'S IS THE CONTRADICTION MISTER
it's the very contradiction you pointed out, the twist
valid nimbus
it's the very contradiction you pointed out, the twist
no no no no no no
I argued
In 3 dimensional space
maiden vapor
BUT
valid nimbus
2 or 1 dimensional objects
cannot exist
AND
YOU DON'T HAVE A REASON FOR 1 OR 2 DIMENSIONAL OBJECTS TO MAKE UP 3D SPACE
valid nimbus
YOU DON'T HAVE A REASON FOR 1 OR 2 DIMENSIONAL OBJECTS TO MAKE UP 3D SPACE
MATHEMATICS TELLS ME THAT 1 OR 2 DIMENSIONAL OBJECTS, INFINITELY MAKE UP 3D SPACE
maiden vapor
OERHAPS
valid nimbus
BUT THAT IS THE SAME BULLSHIT
maiden vapor
the TWIST
valid nimbus
THAT "A PENCIL" OF NO SIZE, BUT WIDTH OF A PENNY
maiden vapor
the MISTAKE is assuming that space must justify itself to reason. One- and two-dimensional things don’t NEED a reason to “make up” three dimensions any more than silence needs permission to give rise to sound.
winged jackal
What is this crank posting
valid nimbus
If placed infinitely
valid nimbus
the MISTAKE is assuming that space must justify itself to reason. One- and two-d...
YES
And
civic bay
sorry why wouldn't a lower dimensional object exist in a higher dimensional space according to you?
valid nimbus
sorry why wouldn't a lower dimensional object exist in a higher dimensional spac...
here
IF
you wanted to contsruct a line
proud dirge
What is this crank posting
hey cw complex what's your favourite cw complex
valid nimbus
you would have to define which direction the axis vedtors would lie
AM I CORRECT @civic bay ?
this is called base or reference
btw
maiden vapor
YES
civic bay
sure i guess if you want to describe the line
cinder thorn
if you are saying that you can't have a perfect 2d plane in the real world then you are right
valid nimbus
To DEFINE A DIRECTION, AKA A LINE FOR THE BASE
YOU NEED TO HAVE A BASE
AM I CORRECT @civic bay
valid nimbus
pick a line
YOU CAN'T
winged jackal
hey cw complex what's your favourite cw complex
The trivial one 
valid nimbus
Mathematically u cant
valid nimbus
For 3 dimensional objects they can't point out infinitely small things
Like points or connecting them with a infinitely small line
THAT'S WHY
YOU CONSTRUCT IT MATHEMATICALLY
BUT WAHT HAVE WE DISCOVERED
IT'S PARADOXICALLY IMPOSSIBLE
civic bay
so because of this, there shouldn't exist a line in 3d space
valid nimbus
YOU NEED A BASE TO CONSTRUCT A LINE
YOU NEED A LINE TO CONSTRUCT A BASE REFERENCE
YES IMPOSSIBLE
actually
not exactly impossible
but your mathematics is wrong
THIS WHOLE SYSTEM IS WRONG
valid nimbus
what would you call the set of all points (a, 0, 0)?
I would call them, non existent in 3 dimensional space
bright bronze
my guy, can you tell me how many integers are there?
valid nimbus
And impossible
valid nimbus
what would you call the set of all points (a, 0, 0)?
Here's the thing by the way
proud dirge
but your mathematics is wrong
you refused to define what your 3-dimensional space, of course you're getting to contradictions lol
valid nimbus
I don't argue that a, 0,0
bright bronze
surely you are able to pick ONE integer right?
valid nimbus
doesn't make q line
I don't argue that
you're perfect with those operations and numbers
but what I argue is
it's impossible for u to define which direction the axis vectors would lie towarda
therefore making the line impossible "to" Contruct
if it already exists, impossible to define the position
proud dirge
What if I give you a finite 3-dimensional space
valid nimbus
you refused to define what your 3-dimensional space, of course you're getting to...
i don't HAVE A 3 DIMENSIONAL SPACE DEFINITION MISTER
YOU ARE HAVING
AND I'M DISTURBING YOUR IDEA
wary condor
..
proud dirge
(Z/2Z)³
valid nimbus
AND I'M DISTURBING YOUR IDEA
WITH YOUR AXIOMS AND ETC..
valid nimbus
oh?
valid nimbus
8 points and 3 dimensions is impossible
you are implying 0 dimensions can fill up a 3 dimensional space
which is impossible
proud dirge
It's like the vertices of a cube
proud dirge
8 points and 3 dimensions is impossible
Maybe if you define what you mean by 3 dimensions
valid nimbus
that breaks the principle of it having no width lentgh breadth
you should be able to put infinite points around any point
proud dirge
No
valid nimbus
and u saying that it does is contradictory and therefore false
proud dirge
Not there
valid nimbus
Maybe if you define what you mean by 3 dimensions
one that has
length
width
and breadth
proud dirge
What's that
proud dirge
idk I don't like measure theory
valid nimbus
What's that
what does "that" Refer to?
there's infinite things around you
which one by the way
proud dirge
what does "that" Refer to?
Length width and 🍞 th
valid nimbus
Length width and 🍞 th
why does you typing this, mean that "that" (Which you said) refers to these words
?
why?
proud dirge
¿
valid nimbus
¿
why does you typing this question mark mean anything?
if you say what's the meaning of it
proud dirge
why are we here
valid nimbus
why does it have a meaning if you say it has a meaning
proud dirge
why do we exist
valid nimbus
why?
valid nimbus
NOW GET LOST OF HERE
proud dirge
why does zorn's lemma exist
valid nimbus
cause
I don't define my 3 dimensional space
MATHEMATUCS ALREADY DEFINED ONE
And I WANT TO DISTURB THAT
WITH IT'S OWN LOGICS
NOT MINE
IT'S OWM LOGICS
That rubbish logics
I use those
To conclude that
2/1d objects
Impossible in 3d space
proud dirge
Next gen kurt gödel right here
valid nimbus
u need basis reference to construct a line
but u need a line to point that basis reference
but u need a basis referenfe ro construct that line
in 2 dimensional space there's really limited directions and this is possible
In 3d space, not so mister
and ur ideas are idiotic false maths fails
losing its respect to being a delusional language of false theories
proud dirge
wary condor
<@&268886789983436800>
cinder thorn
But who told you that there were "particles" in math
wary condor
someone had to do it.
valid nimbus
oh u don't..
maiden vapor
car is a learned person
valid nimbus
But who told you that there were "particles" in math
particles are just objects
wary condor
car is a learned person
yes excuse you.
proud dirge
car is car
maiden vapor
car is very fast
devout valley
and ur ideas are idiotic false maths fails
Do you have to describe ideas like that, just because you disagree?
cinder thorn
There is no such object as particles in math
valid nimbus
Do you have to describe ideas like that, just because you disagree?
and I want an explanation for thie
spiral vigil
i think everyone needs to reduce their speed by about 30%
valid nimbus
u need basis reference to construct a line
@devout valley
cunning sapphire
valid nimbus
I NEED an explanation for this
cunning sapphire
Lots going on here, maybe just everyone quiet down?
civic bay
and I want an explanation for thie
i know generally chatgpt isn't a good source of information but i feel like it might be better at understanding you and answering you here
cinder thorn
Real objects can't be 2d
valid nimbus
i know generally chatgpt isn't a good source of information but i feel like it m...
I despise chatgpt more than math
cinder thorn
Is that what you want?
flint solstice
(whats going on lol)
valid nimbus
Real objects can't be 2d
no
proud dirge
i know generally chatgpt isn't a good source of information but i feel like it m...
I feel like it would end up getting gaslighted lol
devout valley
<@788085606483361802>
I'm not here to explain anything (frankly I have things I need to do!) but I just want to make sure things stay civil and calm 
valid nimbus
that's a respect I give towards people and not mathematics here btw
just to be clear
valid nimbus
Then show me a perfectly 2d object ?
I don't argue that real objects can't be 2d
devout valley
May I remind you that our helpers are volunteering their time (and remind the helpers that there is no obligation to help someone if you don't want to) 
cunning sapphire
Google the Hausdorff--Besicovitch dimension, and maybe, just maybe, be nicer to helpers? 
maiden vapor
We are having quite a learned and civilised conversation.
valid nimbus
Hausdorff--Besicovitch dimension
that seems something that answers me
someone asked me what my grade was
cinder thorn
I argue that 2d objects cannot be constructed/depicted/exist
So you can't have a 2d real object in 3d space, is that your point?
valid nimbus
I'm grade 9 , junior elementary hs
valid nimbus
So you can't have a 2d real object in 3d space, is that your point?
not real object
2d object rhats it
u can't even have it virtuallt
virtually*
flint solstice
I argue that 2d objects cannot be constructed/depicted/exist
we can simplify scenarios to be 2D to observe concepts better, such as reading text on paper or looking at a screen. But yes, I'd assume 2D things have some width to it, realistically.
valid nimbus
we can simplify scenarios to be 2D to observe concepts better, such as reading t...
no no
I don't care about width that a object has to have width in 3d space
I care that a widthless 2d object
is impossible
to exist/construct/depict position of
in 3d space
cinder thorn
Okay so you say that even in an abstract 3d space you cannt have a 2d plane
flint solstice
those concepts are intertwined?
proud dirge
I don't care about width that a object has to have width in 3d space
That's because you're thinking about the real world
valid nimbus
plane? Not sure, but object? yes
valid nimbus
those concepts are intertwined?
no no
flint solstice
I care that a widthless 2d object
You don't care that a potato has width, you care that a potato cannot be perfectly flat
valid nimbus
I don't argue on the width argument
flint solstice
that's ur words
valid nimbus
I argue on something else
valid nimbus
You don't care that a potato has width, you care that a potato cannot be perfect...
not really
you don't really get my argument
let me SIMPLIFY IT
flint solstice
ok
cinder thorn
plane? Not sure, but object? yes
Please be clear about what you mean by object
cinder thorn
Please be clear about what you mean by object
It has too many meanings we can't work with that
valid nimbus
" To construct a line in 3d space, you have to define which direction the basis vectors lie towards (for example if 1,0,0 lies towards the front or back or top or left of the frame of reference)
and to define the direction, aka base of the axises, you need to point out a line as their directions
And therefore, requiring a base of reference to construct/depict the line
And therefore it leads on to impossiblenes"
I end my argument and L for maths, looks like they have someone else to deal with after shunning off godel
flint solstice
L is given to the one ending the argument without accepting other perspectives. Careful
valid nimbus
okay
go on
talk to me about what I just said
don't ask me anything else
I presented u a proof, talk to me in that proof
flint solstice
And therefore, requiring a base of reference to construct/depict the line
So far, I'm with you. We need a base of reference to depict this line. Your jump to...
valid nimbus
don't ask me stuff like "how do u define 3d space)
valid nimbus
So far, I'm with you. We need a base of reference to depict this line. Your jump...
EXACTLY
anyways
flint solstice
And therefore it leads on to impossiblenes"
this conclusion is too far of a jump. You need to acknowledge what our base of refernece can be
valid nimbus
I don't think anyone here is capable of beating this proof
valid nimbus
this conclusion is too far of a jump. You need to acknowledge what our base of r...
yeah?
really?
you need a direction
and that direction should technically be a line
because
you have infinite directions around a particle or 3d object
and u need one to pick
that's why u need to depict a line
As the direction of the x or y axis
as the base or frame of reference
and to do that
u go into impossibleness
of making more bases of reference
proud dirge
don't ask me stuff like "how do u define 3d space)
so you wan't people to refute your arguments but you don't want them to point out the exact problem of your argument
valid nimbus
And therefore I end my argument again
valid nimbus
so you wan't people to refute your arguments but you don't want them to point ou...
well, that's just for not wasting my time
do u want me to explain more?
flint solstice
and that direction should technically be a line
Line has a direction. Direction is a concept.
golden badger
if you don't want your time to be wasted, why are you having this conversation, tbh?
valid nimbus
on why u shouldn't ask me questions like "how do u define 3d space"
because
mathematics already defined 3d space
I'm talking in the language it provided me
I don't make my own 3d space and say maths is idiotic
I say in its own language
and u asking me to define my own truth
proud dirge
on why u shouldn't ask me questions like "how do u define 3d space"
The thing is, I could also define it however I wanted, leading to all of the contradictions I want
flint solstice
As the direction of the x or y axis
I don't understand you from here to..
valid nimbus
and I came to this conclusion accepting it
valid nimbus
I don't understand you from here to..
ph
flint solstice
of making more bases of reference
here
flint solstice
you gotta dumb it down for be sorry lol
valid nimbus
in simple english
proud dirge
car is typing...
valid nimbus
you gotta dumb it down for be sorry lol
yeah NO WORRIES
so a base of reference is necessary because
like x axis can be towards ur right hand side
or left leg side
or top or left or any of the infinite directions
flint solstice
base of reference is a dimension, no? Either we can choose 1D, 2D, or 3D, right?
valid nimbus
base of reference is a dimension, no? Either we can choose 1D, 2D, or 3D, right?
no no
that's different
valid nimbus
or top or left or any of the infinite directions
^
wary condor
car is typing...
prepare...
we made math to solve problems we faced moving from one decade to another. we struggled to find a way to relate two changing values together so we created a 2D function where the values change depending on eachother. having a 2D object is not quite realistic due to NOTHING being INFINETLY SLIM. my point is, mathematics is used to solve problems in it's own way that mathematicans have created. the concepts work within themselves for the purpose of the questions.
so math is just a bunch of concepts that is built within itself to make problems solvable using math. limits as something approaches infinity doesnt make sense in the real world but it solves problems correctly in math which is what we created to solve the problems.
proud dirge
thank you
valid nimbus
we made math to solve problems we faced moving from one decade to another. we st...
I understand your argument in one second
but that is not what I'm dealing with
maths has made numerous theories with this same idea of 3 dimensional or n dimensional system of co ordinates
and I argue that this system essentially fails to hold the same principles in 3 dimensional or more if possible
The principles that 2 or 1d has
Because they're not the same
3d space is different
u can't contrusct a line or 2 or 1d objects
that's what I'm arguing
there's something fundamentally different
And the ideas that lead u to abstract theories
would turn out to have a wrong system of axioms
this is what im saying
co ordinate system is really wrong perhaps, with 3d space
Requires to pick a direction of each axis (say North for x axis 1,0,0)
valid nimbus
Requires to pick a direction of each axis (say North for x axis 1,0,0)
but to do so, another line in the form of direction
and to do so another base of reference to depict or "say" The line
and to do so, more and more
@wary condor do u have an explanation essentially for this?
next cedar
so, are you arguing that lower-dimensional objects cannot exist in 3d space, or that they cannot be defined uniquely in 3d space?
valid nimbus
so, are you arguing that lower-dimensional objects cannot exist in 3d space, or ...
they cannot exist , and both, they cannot be defined that's why they cannot exist
flint solstice
u can't contrusct a line or 2 or 1d objects
Yeah, 2D or 1D objects can't be constructed in 3D space. We can create a conceptual observation of 1D or 2D objects like a dot or an xy-plane like on Geogebra.
valid nimbus
if u define me a better way to depict co ordinates and constricting lines and stuff
I'll accept they can exist
I'm just saying u this in this form
mathematical co ordinate form
if u have a better
system
then u shall provide me with
and this is why I fail to accept the theories regarding 3 dimensions or more than 3 dimensions
like matrices
next cedar
they cannot exist , and both, they cannot be defined that's why they cannot exis...
I will agree if you say they cannot be defined uniquely
valid nimbus
and other theories
next cedar
but do not conflate existence with definition
valid nimbus
I will agree if you say they cannot be defined uniquely
Alright
valid nimbus
but do **not** conflate existence with definition
If they exist
where's the proof for it
and, this isn't something philosophical
next cedar
the existence of a line or point or whatever fuck object is independent of the geometrical definition for that object
valid nimbus
like wheres the proof for us actually existing
valid nimbus
the existence of a line or point or whatever fuck object is independent of the g...
well
how do contsurct or show a line then
next cedar
like wheres the proof for us actually existing
not philosophical?
valid nimbus
explain me the process
wary condor
where's the proof for it
doors are built to close rooms. what is the proof that doors are built to close rooms?
valid nimbus
alright I think we have a mis understanding of words here
flint solstice
Are you talking maths or physics?
valid nimbus
explain me the process of creating a line (because if it can exist then show me how it can, non philosophically with contstructing it)
in 3 dimension
flint solstice
other words, are you talking conceptually or realistically?
valid nimbus
other words, are you talking conceptually or realistically?
conceptually
math already lost to realistically
uncertainty
and human limits
valid nimbus
explain me the process of creating a line (because if it can exist then show me ...
@next cedar ^ for ya, cause you said it can exist perhaps something else but relating to existence of 2d/1d objects in 3d space.
wary condor
the concept of a line is two (one dimensional) points connected. that's how we defined lines in math and hell yeah it works! you can start making your own math-look-alike where you start by defining division by zero then build up the entierty of your own math from there! it will work!!!!! you'll just have different formulas and foundations for everything now that you started with something different than what mathematicans did. it will not make sense in the real world... but it will make sense in your math where you solve the problems by translating them to your math so your math can work!
valid nimbus
The previous person who I argued with said 2d objects or 1d objects can exist because u can construct them, and in co ordinate aka the only mathematical system that I found depicting positions and lines and stuff with matrices etc..,
Failed to show a 2d/1d existence
valid nimbus
the concept of a line is two (one dimensional) points connected. that's how we d...
hey I'm not saying that..
next cedar
I mean, you can just take a vector space V over R. then let dim V = 3. then, a subspace L is a line if L is not an empty set or a set containing just the 0 vector; for all x, y in L, ax + by is also in L, and dim L = 1
no coordinates
only dimensions
valid nimbus
dimensions hm
next cedar
now, indeed such a line can have multiple representations
wary condor
hey I'm not saying that..
then I apologize. I dont get what your concern is, and thus I shall 🏃➡️. 👋
next cedar
but I am agreeing with the multiple reps part so Idgaf
valid nimbus
then I apologize. I dont get what your concern is, and thus I shall 🏃➡️. 👋
no no you're perfectly related to what I'm saying, I kinda cut of the sentence here
I'm not saying that your system is flawed in the operation, the logics such as constructing a line when u have a base reference and everything is perfectly fine for me.
But the whole existence becomes impossible in 3 dimensional space because to define which direction each axis goes, is impossible because u need more lines and more references for each lines.
so the system cannot "apply" To 3d space, not that it's flawed
valid nimbus
I mean, you can just take a vector space V over R. then let dim V = 3. then, a s...
hmm a vector space
next cedar
again, I have not defined direction or bases
and the whole argument doesn't care about bases
flint solstice
what's your thinking for z=0 in R^3 on geogebra (xy plane)? Conceptually we say it has 0 thickness.
next cedar
or direction
valid nimbus
I mean, you can just take a vector space V over R. then let dim V = 3. then, a s...
can u explain me a bit more on that? that just seems to me that you're saying "there exists a 2d line in 3d space" but it doesn't show me where it is, specifically.
it seems to me that you just said " We have a 3d space, let's take a line in it, let's take the line's dimenion = 2d"
next cedar
can u explain me a bit more on that? that just seems to me that you're saying "t...
and that is the idea
valid nimbus
but I can be wrong, I just don't know your explanation
valid nimbus
and that is the idea
that is the idea?
next cedar
your argument is that no such objects can exist in 3D space
next cedar
which is false, because you can show their existence
you just don't know where the fuck it is
flint solstice
or line (1,0,0). Our reference of direction is the x, y, and z directions, all perpendicular. I may fail to grasp your argument, are you saying that a line segment going from (0,0) to (1,2) can't be defined in 3D?
valid nimbus
it seems to me that you just said " We have a 3d space, let's take a line in it,...
" We have a 3d space, I say that a 2d line ≠ exist, therefore in all sets of any 3d space a 2d line ≠ exist"
valid nimbus
" We have a 3d space, I say that a 2d line ≠ exist, therefore in all sets of any...
@next cedar Why is this false
and your "saying" right
?
you didn't give proofs, u just said it even though u said it fancily
I said something too
why is mine wrong
I'm sure you're mathematical, then prove me wrong here
go on
valid nimbus
alright
I can only be so humble when speaking to a language that I believe is DELUSIONAL
next cedar
so you seem to have made up your mind
valid nimbus
no
we're still on an argument here
you said something with no basis no proof
that "let's take a 2d line, dimension = 2 , in 3d space, space = 3d"
valid nimbus
that "let's take a 2d line, dimension = 2 , in 3d space, space = 3d"
I said the opposite of it and said " In no 3d space, line = 2d"
we both seem to have no proofs and just said whatever
but u seem to be right in your idea
tell me ur idea
and then why mine is false
I did not make up my mind yet
but I will if you say nothing
next cedar
in that case, have you considered looking up and reading about vector spaces? I'm in no mood to give you a crash course on vector spaces and linear algebra when your fucking attitude indicates that you are hostile to most all mathematical language.
valid nimbus
in that case, have you considered looking up and reading about vector spaces? I'...
alright, vector spaces it is
I'll go read that
and come back