#Is it possible to find a function that behaves exacly like this graph?

518 messages · Page 1 of 1 (latest)

wicked crest
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Just for fun but I am curious to see if their exists a function that can behave like this graph.

meager ingotBOT
idle ginkgo
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Ohh i Will try

wicked crest
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gl

idle ginkgo
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,w plot xcos(x)

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Okay no wrong one

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,w plot x^2cos(x)

wicked crest
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closest ive been: ln(x)/(sin(x))

idle ginkgo
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,w plot ln(x)/sin(x) from x=-2 to x=100

idle ginkgo
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Not baadd

wicked crest
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/:

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not good either

idle ginkgo
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Yeah not good but hey you got it better than me

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,w plot 3xsin(x) from x=0 to x=100

idle ginkgo
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WOAHH

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I just found a beautiful function

wicked crest
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umm...

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I guess?

idle ginkgo
wicked crest
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but you know

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I gave its roots, max local point and the point where it actually starts decreasing all the way to -infinity

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I was thinking it might help

wicked crest
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yeah

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here it is again

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all roots are of the form npi where n is an integer ofc

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then the max local idk

idle ginkgo
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What I’ve seen is that it intercepts the x axis every pi

wicked crest
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yes

idle ginkgo
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Hmmmmmmmmm

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Most likely a sun function then

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Sin

wicked crest
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exacly

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since as x->npi then f(x) -> infinity

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thats why the closest ive come is ln(x)/(sinx)

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where ln(x) comes from the tail of the function

idle ginkgo
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Your graph is continuous

wicked crest
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?

idle ginkgo
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I mean the curve can be drawn without leaving any gaps. Just like 1/x is not continuous

wicked crest
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yh

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well

idle ginkgo
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If sin(x) is in denominator and that x=2pi or 2kpi then it’s not continuous

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You will have something divided by 0

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But in your graph there are no gaps

wicked crest
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k

idle ginkgo
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But your right about considering sin though

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Maybe even ln(x)

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But sin is definitely not is denominator

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ln(x) can’t be there either because at x=0 there is a defined value in your graph

wicked crest
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but we can do ln(x+a)

idle ginkgo
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Yeah that

wicked crest
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but again if we inster -a we would get a singularity

idle ginkgo
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Wait it can’t be that either

wicked crest
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yh

idle ginkgo
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Just keep sin

wicked crest
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and cos since we are hitting every npi

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but where can cos even go

idle ginkgo
wicked crest
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sure

idle ginkgo
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DANGG

wicked crest
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not continuous (obviously)

idle ginkgo
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It is continuous because i see no gaps, do you see some?

wicked crest
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yes

idle ginkgo
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Where

wicked crest
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everywhere

lucid ridge
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What is going on here

idle ginkgo
wicked crest
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k

lucid ridge
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👀

wicked crest
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point is

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can we get a function out of this graph

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for now the most suiteable is somewhere around (lnx)/(sinx)

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even tho its not even close

wicked crest
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but yh

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What I also did was trying to make a infinite product series expansion

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since we have npi

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also dint quite work either until I got this

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that was the same product infinite series expansion but with some modifications

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kinda used Euler's method for that

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but still wasnt what I was looking for

lucid ridge
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Where did you get this graph from

wicked crest
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but it isnt a full closed in function

slow marsh
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are the gaps due to asymptotes, or are they due to a curve that has an extremely high max/low min

idle ginkgo
# wicked crest

I don’t think you would need to go that far but i honestly don’t know either.. Also i noticed that starting from x=8 approximately, the function “jumps” very high

wicked crest
idle ginkgo
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,w plot sin(x)tan(x) from x=-3 to x=100

idle ginkgo
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Nah it’s bad

tepid fiber
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,w plot 2^xsin(x)

lucid ridge
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Is it continuous

wicked crest
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try desmos

idle ginkgo
wicked crest
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it is

tepid fiber
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,w plot 2^xsin(x) from x=-10 to x=100

tepid fiber
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close

idle ginkgo
lucid ridge
tepid fiber
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,w plot 2^xsin(x) from x=-10 to x=10

wicked crest
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oh wait

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let him cook

tepid fiber
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i mean you can piecewise

idle ginkgo
wicked crest
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basically

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2^x sin(x) is now the closest so far actually

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im quite surprised

idle ginkgo
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,w plot sin(x)tan^2(x) from x=-3 to x=100

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Dang it

wicked crest
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yh

tepid fiber
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does wolfram supports piecewise?

wicked crest
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idk

tepid fiber
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,w plot (-2)^xsin(x)

tepid fiber
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what

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oh

wicked crest
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oh

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hold on

idle ginkgo
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,w plot (2^x)sin(x)tan(x) from x=50 to x=70

wicked crest
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but its on imaginary plane

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complex plane I mean

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rip

tepid fiber
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,w plot \begin{cases} x&x>0\0&x<0\10&x=0\end{cases}

wicked crest
idle ginkgo
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CASE COUNT LETS GOOO

tepid fiber
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$\begin{cases} x&x>0\0&x<0\10&x=0\end{cases}
$

mystic cliffBOT
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Tangent
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

tepid fiber
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oops

idle ginkgo
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Nah tangent cooked with its function proposal

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W tangent

wicked crest
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yh

tepid fiber
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$\begin{cases} x&x>0\0&x<0\10&x=0\end{cases}$

mystic cliffBOT
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Tangent

tepid fiber
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oh

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ok

wicked crest
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not bad

tepid fiber
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whats case count?

idle ginkgo
tepid fiber
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lol

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lets use desmos

wicked crest
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its better

idle ginkgo
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,w plot (2^x)xsin(x) from x=-3 to x=30

idle ginkgo
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I just copied lol

tepid fiber
slow marsh
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i found this

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oh wow thats

wicked crest
slow marsh
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beautiful

idle ginkgo
slow marsh
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the desmos thingy

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not mine

slow marsh
wicked crest
slow marsh
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yep

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it isnt even close

tepid fiber
idle ginkgo
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Let me try a function

slow marsh
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but i was finding it when yall were doubg your first attempts

lucid ridge
idle ginkgo
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,w plot 2x

idle ginkgo
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I got the best one

tepid fiber
tepid fiber
slow marsh
idle ginkgo
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Thank you thank you

wicked crest
# tepid fiber

I checked and the beginning of the graph doesnt really quite match but with some coefficients here and there it probably would end up matching

tepid fiber
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yeah

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also doesnt have to be a variant of -x^2, thats just the first thing i thought of

wicked crest
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also you did set up boundaries /:

tepid fiber
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wait i have an idea

idle ginkgo
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Never thought i would have some pleasure finding functions lol

tepid fiber
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without piecewise

wicked crest
slow marsh
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we dont look to heaven and we put math first~

wicked crest
idle ginkgo
wicked crest
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not rlly...

idle ginkgo
slow marsh
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bros locked in

wicked crest
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appart from being closer to my goal then I was before

slow marsh
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you sound like a very math-oriented anime villain

wicked crest
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?

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no

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buuuuuuut

slow marsh
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ye

tepid fiber
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W math

slow marsh
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no buts

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YESS WE LOVE TO SEE HER

wicked crest
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im obsessed

wicked crest
junior sundial
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may i earn these graphing skills

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preach

slow marsh
slow marsh
wicked crest
idle ginkgo
slow marsh
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anyway

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yall are the goats

wicked crest
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also

tepid fiber
slow marsh
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this was extremely fun

slow marsh
wicked crest
slow marsh
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desmos music video im crying

wicked crest
slow marsh
tepid fiber
wicked crest
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k

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x\prod_{n=1}^{100}\left(1-\frac{x^{3}}{n^{3}\pi^{3}}\right)

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but its an infinite product

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thats what I hate

slow marsh
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bestie chill

wicked crest
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and thats why I came here

tepid fiber
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uh oh where do you graph it

wicked crest
tepid fiber
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what since when desmos has $\prod$

mystic cliffBOT
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Tangent

tepid fiber
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yoooo

wicked crest
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bro

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just go on desmos

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and write the following

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prod

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boom

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here it is

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anyways

tepid fiber
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dunno

wicked crest
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or just look up I guess

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I have a course in like 20 minutes so Ill leave and you guys can keep trying and compare with the real graph if you want. Ill come back in around 3 hours or so

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gl

slow marsh
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kk bye man

tepid fiber
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thats betetr

slow marsh
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how are you doing this you absolute whiz

tepid fiber
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i got better

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$\frac {2^x\sin x\left(\frac {|x-\pi|+x-\pi} {15} + 1\right)} {e\left(\frac {|x-\pi|+x-\pi + 1} {2} + 1\right)}+\frac{|x|(-x^2)} 5+\frac{x^3}5$

mystic cliffBOT
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Tangent

hardy gazelle
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lemme try lmao

wicked crest
# tepid fiber

nice👍 Maybe try a bit more until it matches perfectly. Ill test this function on my side.

hardy gazelle
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god dayum

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$y=(2^xsin(x)((abs(x-pi)+x-pi)/12+1))/(2.718281828*((abs(x-pi)+x-pi)/2+1))-(abs(x)*x^2)/6+x^3/6$

mystic cliffBOT
wicked crest
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nice!

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Now can you guys measure the error between the starting function and the one you found??

hardy gazelle
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my hands are hurting lmao can u send the starting fucntion

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pws!

wicked crest
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sure

hardy gazelle
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i have been working on nimbus ( google cloud from past 5 hours almost) and well finialsed it rn, its just storing up

wicked crest
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well hope its going well

hardy gazelle
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ahh it is

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lemme do it

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it got saved

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ahhhh

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okk

wicked crest
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no pressure

hardy gazelle
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as under my own perspective, the starting fucntion is controlled

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but yea i'll be writing aa long asss shiitt for explanation i can feel. already on it tho. can say 13% done

wicked crest
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thats fantastic!

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just take your time

slow marsh
hardy gazelle
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mother fuckaaa

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i got it

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*The starting function is
f(x) = x ∏ from n = 1 to 100 of (1 − x^3 / (n^3 pi^3))

This function is a finite Weierstrass-type product. Its structure is completely determined by its zeros and by polynomial growth.

First, the zeros.
The factor x forces a zero at x = 0.
Each factor (1 − x^3 / (n^3 pi^3)) becomes zero when x = n pi.
Therefore, the function has zeros at x = 0, pi, 2pi, 3pi, … , 100pi.

These zeros are polynomial in nature. Near x = n pi, the function behaves like a linear factor multiplied by many nonzero constants. This gives smooth, flat crossings of the x-axis with no sharp cusps or switching behavior.

Second, smoothness.
The product consists only of polynomials. Therefore f(x) is smooth and differentiable everywhere. There are no absolute values, no exponential switches, and no artificial cutoffs. Every change in the graph is dictated by algebraic structure alone.

Third, growth behavior.
Each factor contributes a cubic term in x for large x. Since there are 100 such factors and an additional x in front, the overall growth of f(x) behaves like x to the power 301. This means the function grows polynomially, not exponentially.

The constructed function is

g(x) = (2^x sin(x) times a switching factor) divided by a constant, minus a polynomial correction term.

This function is not a product approximation. It is a curve-fitting construction.

First, zeros.
The sin(x) term forces zeros at x = n pi for all integers n, not just up to 100. These zeros are trigonometric in origin, not algebraic. Near each zero, sin(x) crosses the axis linearly, which is a different local behavior than the polynomial factors in the original product.

Second, growth behavior.
The dominant term in g(x) is 2^x. This introduces exponential growth. Exponential growth cannot approximate polynomial growth over large intervals. Even if the graphs look similar in a small window, they diverge rapidly as x increases.

Third, switching terms.
The absolute value expressions introduce piecewise behavior. This creates nondifferentiable points where the original function is perfectly smooth. These switches do not exist in the product and therefore introduce structural error.

Fourth, artificial damping.
The polynomial subtraction terms are used to suppress unwanted growth on one side of the graph. This is not derived from the original product but is added by hand to force visual similarity.
The error between the two functions can be understood conceptually as follows.
Near x = 0, the two functions can be made to look similar because both behave like low-degree polynomials.
Near x = n pi, the zero locations match, but the local shape does not. The original function has algebraic zeros coming from product factors, while the constructed function has trigonometric zeros from sin(x). This creates noticeable local curvature differences.
For larger x, the error grows rapidly because the original function grows like a high-degree polynomial, while the constructed function grows exponentially. No choice of constants can reconcile this difference globally.

Conclusion would be that -

The starting function is a structurally defined algebraic object whose behavior is dictated by a finite product and polynomial growth.
The constructed function is a visually motivated imitation that matches some qualitative features, such as zero locations and spike placement, but does not preserve the underlying mathematical structure.
Therefore, the difference between them is not a small numerical error but a fundamental theoretical mismatch in growth order, smoothness, and functional origin.*

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@everyone

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@slow marsh @wicked crest @tepid fiber

hardy gazelle
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my hands lmao

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typing all this

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im gonna rest now

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u read it

slow marsh
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EYE

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HOLY

slow marsh
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THIS IS SOME SHEER DEDICATION

wicked crest
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ill be reading it later because I have a tutorial to attend to but honestly this deserves a round of applause

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👏

slow marsh
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👏👏

hardy gazelle
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but why aint these peeps approving my graduation + role

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ouchie

wicked crest
hardy gazelle
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sad sad

wicked crest
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very sad

hardy gazelle
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wtf why i got undergraduate math?

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did helping kids made me undergraduate level

wicked crest
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¯_(ツ)_/¯

hardy gazelle
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wwwaaa

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bro

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undergraduate is opening advanced-lounge

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wtf

wicked crest
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is that even a thing?

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"advanced lounge"

hardy gazelle
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yea bro

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lmao

wicked crest
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ok

hardy gazelle
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bro u got contact with admin or mod

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duh i need my graduation + role

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lmao

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i mean post graduate

wicked crest
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no. I tend to work alone on a white board then spending time in this math server. I only come to give side problems when they come as an obstacle in my mathematic research

hardy gazelle
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lemao

wicked crest
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make sense

hardy gazelle
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i mean, being senior developer alot of things are on ur shoulders, and i needed a brain teaser for myself

wicked crest
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of course

hardy gazelle
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so what u do?

wicked crest
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alright

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so

idle ginkgo
#

You guys are still on this ??

hardy gazelle
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i get horny studying maths or physics

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these are my turn on

wicked crest
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basically a guy named Euler one day said to himself "Why cant I just factor sin(x) as a infinite polynomial" and so he did. Then, he proceeded to ask what would happen if we de-factorized the infinite product series he built and that reveald to him something interresting because the second term of the original taylor series of sin(x) which is -(x^3)/3! but then when expanding the infinite product series we instead get (when tracking all that has x^3): -x^3 (1/(pi^3) + 1/(2^2 pi^2) + 1/(3^2 pi^2) + ...). Logical thing he did: Since it will eventually make the -(x^3)/3! term he set them equal on both sides: -(x^3)/3! = -x^3 (1/(pi^3) + 1/(2^2 pi^2) + 1/(3^2 pi^2) + ...) and later found out that eventually (pi^2)/3! = 1 + 1/2^2 + 1/3^2 + ... = zeta(2) therefore claiming that zeta(2) = (pi^2)/6.

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Here its quite similar but the starting point is another infinite product series

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in this case that one:

hardy gazelle
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mhm...

wicked crest
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here if we are able to find a function that is related to this infinite product series then its bingo since we also have its taylor series

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and thanks to you

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I also found the following equality

hardy gazelle
#

ayy no worries, my pleasure

hardy gazelle
wicked crest
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zeta(3) = (theta)(pi^3)/4! where theta ~= 0.930436310465

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try it out if you dont believe me

hardy gazelle
#

god dayum, im hard

wicked crest
#

oooookay

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pause

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rewind

hardy gazelle
hardy gazelle
hardy gazelle
wicked crest
#

ill comeback in 2 hours lecture starting now

hardy gazelle
#

for sure

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cya

hardy gazelle
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and im finished

junior sundial
hardy gazelle
#

i would have studied enough to like be that cool guy in society, and will continue my own reasearch after it

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like im a CSE major

idle ginkgo
hardy gazelle
#

but, maths is love lmao

hardy gazelle
idle ginkgo
junior sundial
#

since im a first year

hardy gazelle
#

in simple words, im programmer

hardy gazelle
#

from where u doing it

idle ginkgo
hardy gazelle
#

god somebody kick my ass

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there's this guy in #1464335239672500507

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god

idle ginkgo
#

Import numpy as np
A=np.array([1],[2],[3])
B=np.array([4],[5],[6])

t=np.dot(A, B)
print(t)

32

idle ginkgo
hardy gazelle
tacit furnace
#

@tepid fiber

Bro. You're a graphing genius!

tepid fiber
#

ty ig

tacit furnace
hardy gazelle
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bro himself is a tangent

tacit furnace
tacit furnace
hardy gazelle
#

damnnn

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thanks

tacit furnace
tepid fiber
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same

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i'm currently reading a book about you, zeta

hardy gazelle
tacit furnace
tacit furnace
tepid fiber
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yeah

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"the music of prime numbers" by marcus du sautoy

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recommended although he started saying stuff aboit physics that i dont like

tacit furnace
tacit furnace
hardy gazelle
#

wanna here smth guys?

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broo i have been up soo muh

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i can see my text going into fourth dimension

tepid fiber
#

he said that there's a chance physicists will prove reimann's conjecture

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shame.

tepid fiber
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yuck

tacit furnace
tacit furnace
hardy gazelle
#

This looks like calculus until you write it down carefully, then it turns into analysis, then functional analysis, then probability, then you realize it was information theory the whole time and the problem was never about numbers, it was about you.

tacit furnace
# tepid fiber yuck

They're like mathematicians with more formulas, and less "mystery solving" type math.

tepid fiber
#

nooo they're different. they do not prove things

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also lets go to #discussion

tacit furnace
hardy gazelle
#

for sure lmao but i guess i'll be sleeping now

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i ejaculated enough

wicked crest
wicked crest
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for more context, your name is zeta yk zeta function haha get it? breadpensive

slow marsh
tacit furnace
tacit furnace
wicked crest
# tacit furnace What!? Impossible. Tell me your findings!

Not literally XD. For example: zeta(3) = (sigma)(pi^3)/4! where sigma = - (d^4)/(dx^4) (x product(k>1) (1 - (x^3)/(k^3 pi^3)))|(x=0) ~= 0.930435923838 and normally we want a clean (pi^3)/4! so then to find the missing percentage we do (1 - sigma)(100) ~= 7% so we are missing zeta(3) by just 7%. Crazy right?

hardy gazelle
#

ayoo gois wassup

wicked crest
#

But the general formula should be zeta(s) = -(pi^s)/(s+1)! (d^(s+1))/(dx^(s+1)) (x product(k>1) (1 - (x^s)/(k^s pi^s)))|(x=0)

hardy gazelle
#

yooooooooooooo

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oh wait smth serious is goin

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@idle ginkgo @tepid fiber @tacit furnace ayo guys

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i bought a new superbike, 4th in my collection

slow marsh
slow marsh
tacit furnace
tacit furnace
hardy gazelle
#

cuz it rained here

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its the aprilla rsv4

tacit furnace
#

That's gonna be sick!

hardy gazelle
#

waddupp zetaa

wicked crest
# tacit furnace You know way more about this than I do, lol. You deserve the title zeta.

I guess… but it’s not enough tbh. That’s why I’m now trying to find the multiplication of multiple converging functions that is equal to the infinite product of 1 - (x^3)/(k^3 pi^3). This will allow (if found) to find the full Taylor series of that function which would help defining sigma as a combination of transcendentals and fractions/irrationals since Apéry never mentioned that zeta(3) !=?/? + ?/? if yk what I mean… he only said that zeta(3) !=(pi^n)/a where a is a number and n also.

tacit furnace
hardy gazelle
#

ay ping me what's the prob im bored rn

wicked crest
hardy gazelle
#

mhmmmm less seee

wicked crest
hardy gazelle
#

roughed out like 4 papers rn

wicked crest
#

Damn

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I already used 10 chalkboards to find a closed form expression and got really close to find one

hardy gazelle
#

aghhhhhhhhhhhhhhhh

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i might have gott itt

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MIGHTT

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but i would say one thing

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**There is no elementary closed form like
sin(x)sinh(x)/x
for the product

product over k>=1 of (1 - x^3/(k^3 pi^3))

The reason is that this product has three sets of zeros (coming from cube roots of unity), unlike the x^4 case which splits nicely into sin and sinh.

The best possible closed form is in terms of Gamma functions:

product over k>=1 of (1 - x^3/(k^3 pi^3))
= C / [ Gamma(1 - x/pi) * Gamma(1 - omega x/pi) * Gamma(1 - omega^2 x/pi) ]

where
omega = exp(2 pi i / 3)
and C is a constant (can be fixed by normalization).

So the conclusion, in one line:

There is no representation using only sin, cos, sinh, etc.
The natural closed form lives in Gamma / Barnes type functions.**

#

$prod_{k>=1} ( 1 - x^3/(k^3*pi^3) )
= S_3( x/pi | 1,1,1 )$

mystic cliffBOT
hardy gazelle
#

$S_3(z | 1,1,1)
= prod_{n1,n2,n3 >= 0}
( n1 + n2 + n3 + z )
/ ( n1 + n2 + n3 + 3 - z )S_3(z | 1,1,1)
= prod_{n1,n2,n3 >= 0}
( n1 + n2 + n3 + z )
/ ( n1 + n2 + n3 + 3 - z )$

mystic cliffBOT
wicked crest
slow marsh
#

wow i understand none of this but my love for yall has increased exponentially

slow marsh
#

wait i js realised

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the mathematics servers gif is the rainbow pride flag and trans flag

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ohh

tepid fiber
#

no, its the rainbow pride flag and lesbian flag

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nvm u r correct

hardy gazelle
#

yo guys i was working out on relativity theory and i came across a theory of my own

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@tepid fiber u think that the universe is observer dependent?
@slow marsh @wicked crest @tacit furnace my bad for mass tags but its just going over my head i hope you get me

wicked crest
hardy gazelle
#

bro but If two observers can record different times and lengths for the same event, then reality itself is observer dependent, not fixed.

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and doesnt it challenges newtonian ideas?

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Time flows the same everywhere

Space is rigid and absolute

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these ideas

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what do u say

wicked crest
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its not a bad idea tbh

hardy gazelle
#

yea that's what im sayinggg

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ayoo wake these nuggas up

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lets hit vc

#

im having a rot

wicked crest
hardy gazelle
wicked crest
#

💀

hardy gazelle
#

i love this guy

wicked crest
#

yk 9/11 was to cover up the mestirious money that vanished from the government and a excuse to go to iraq to get oil

#

just cool fun fact nothing personal

hardy gazelle
wicked crest
#

😭 🙏

hardy gazelle
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💀

wicked crest
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watch it

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¯_(ツ)_/¯

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you might learn something

hardy gazelle
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best one i got

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bro did a one shot

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-9999 HP

wicked crest
hardy gazelle
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hey twitch

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Relativity does not merely revise measurements of space and time,
it destroys the existence of a global, observer-independent temporal order.

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and if that happens then

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Time is not an intrinsic feature of the universe.
Space & time does not exist as a fixed container.
Reality is relational, defined only through physical interactions.

tepid fiber
# hardy gazelle

btw this guy just planned this. he didnt fly in the plane, and also the plane didnt just drop a bomb it FLEW RIGHT IN THE TOWER