general discussion

[open whale]

in 20 minutes i'll go back to practicing exams for set theory

derivative isn't what's important, it's relative slope

$\frac{f(z)-f(z_0)}{z-z_0}-kz\to0$

[vivid gulch]

yoavmal

[open whale]

this is better

what if i now uhhh

choose nonreal z

it still should satisfy the notion of being an extremum point

well uhh

yeah

$\abs{\frac{f(z)-f(z_0)}{z-z_0}-kz}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

i suppose that's the thing?

there is some k such that this formula works

no

$\abs{\frac{f(z)-f(z_0)}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

that feels better

does z^2 satisfy it?

$\abs{\frac{z^2-z_0^2}{z-z_0}-2(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0-2(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0-2z+2z_0}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{-z+3z_0}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{3z_0-z}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

that feels wrong

what if i do it generally

$\abs{\frac{z^2-z_0^2}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0-kz+kz_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z-kz+z_0+kz_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z(1-k)+z_0(1+k)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

not a good start

ah wait

z0 is 0

so this does work

what if i choose (z-1)^2

then z0 is 1

what happens then?

$\abs{\frac{(z-1)^2-(z_0-1)^2}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

now i need to show 1 does it

$\abs{\frac{(z-1)^2-(z_0-1)^2}{z-1}-k(z-1)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{\frac{(z-1-z_0+1)(z-1+z_0-1)}{z-1}-k(z-1)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

oh nvm i'm stupid yet again

$\abs{\frac{(z-1)^2}{z-1}-k(z-1)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{(z-1)-k(z-1)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

right, so this works too

what about the earlier case, z^2+z^4

$\abs{\frac{f(z)-f(z_0)}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{\frac{z^2+z^4-z_0^2-z_0^4}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{\frac{z^2-z_0^2+z^4-z_0^4}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0+\frac{(z^2+z_0^2)(z^2-z_0^2)}{z-z_0}-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

$\abs{z+z_0+(z^2+z_0^2)(z+z_0)-k(z-z_0)}<\varepsilon$

[vivid gulch]

yoavmal

[open whale]

now i want to find for which values of z0 there is some k that does this

i know it owuld work for z0=0

but it should also work for...

just that

cool, it works nice

@normal arrow i believe i have generalised the concept of extremum point to complex functions

now we don't have just minimum and maximum

but all angular choices

[normal arrow]

oh sick

[open whale]

it's kinda cool

since

[normal arrow]

no idea how and i will not understand it in a while but cool

[open whale]

no no

it's actually quite intuitive if this works

basically

you know how z^2 has a minimum point at 0?

[normal arrow]

yeah

[open whale]

well

it's not actually a minimum point in the complex numbers

since if you go along the imaginery line for example

it's actually a maximum point

so, i reckoned

[normal arrow]

oh right

[open whale]

it's clearly an "extremum" point

in some sense

so, i checked the derivative

and indeed, it always points away in the same way you're going

if you drew the derivative around the point with arrows

you'd get that they all point away

[normal arrow]

oh

[open whale]

and then i thought

well, if it were -z^2

then they would all point in

but it'd still maintain all properties we'd consider for an extremum point

and then i thought

well, what if it were iz^2?

and so on

and so i thought, well, an extremum doesn't have to have a derivative

so i looked at the slope rather than the derivative

and indeed, it does work

so i think

$\abs{\frac{f(z)-f(z_0)}{z-z_0}-k(z-z_0)}<\varepsilon$

[normal arrow]

hmmm

[vivid gulch]

yoavmal

[open whale]

if there is some k that satisfies this

(this is simply to say that they all align in a certain direction)

[normal arrow]

oh god

[open whale]

(with some error because we need the limit, not the actual slope)

then z0 is an extremum point

[open whale]

not as bad as it seems

it's literally just saying that they all go in some direction

(z-z0) is just the direction relative to the point

and k is the rotation and scaling factor so it indeed works

and not just acts odd

[normal arrow]

hmm

[open whale]

i haven't checked if this indeed matches reality

but it should be consistent

and if not, it might not be far off

now if i manage to prove that if a point satisfies this then it has a derivative 0

and then show that if two points of a function satisfy this, there is some c in their environment that is an extremum point

then i believe i have proven taylor's theorem for complex numbers

[normal arrow]

so cool

[ruby helm]

chainz alt has been timed out for 5m
Reason: Similar-Messages Spam

chainz alt#9994 | 1071974067852288010

chainz alt#9994 has been timed out temporarily for 20m

chainz alt#9994 | 1071974067852288010

[rich tendon]

sis

sis

[hollow ice]

what is the going on

[lethal wigeon]

if $\zeta(s)$ is only defined for values $s>1$, then what is $\zeta(1)$ evaluated to with its analytic continuation? is it still infinity or a finite value?

[vivid gulch]

happy aqua

[crude bone]

I just solved the hardest problem of my goddamn life

Solved part b. it took an hour and a half. I had solved part a) a long time ago, so I had some familiarity with these sequences but I never even attempted b until now

Basically s_18=8 implies s_10=8. Also one of s_11, s_12, …,s_17 is 9. So for condition 3 to be satisfied, the rest must even. this means that s_1, s_2,…,s_9 must all be odd (we run out even numbers). Also either one of s_1, s_2 must be 7, and one of s_1, s_2 must be 5. with all these facts in mind, we see that sequence must start off as 7,5,1,1,3,9,5,7,3
So the sequence is 7,5,1,1,3,9,5,7,3,8,s11,s12,s13,s14,9,s16,s17,8
The only numbers we have left to choose from are 2,4,6
If you have a feel for skolem sequences it’s clear that s_11=s_17=6, s_12=s_16=4, and finally s_13=s_15=2
So the one and only sequence that satisfies the conditions is 7,5,1,1,3,9,5,7,3,8,6,4,2,9,2,4,6,8

[crude bone]

I looked at the solutions page and it said “this problem was easier than usual and only required that you fiddle with the concept a little bit”

[crude bone]

Like go fuck yourself

[open whale]

the analytic continuation is an analytic function which agrees with the original sum wherever it is defined

oh i see what you mean

no, it's still infinity

[lethal wigeon]

okay

[open whale]

yeah

[violet condor]

I want to generate a bijection between my (procrastination) and my (ability to do work) when Im told to

[open whale]

lmao

[static rune]

why doesn't binomial theorem work if one of the term isn't 1 and other isn't very small?

for fractional and negative index

stupid question

[lethal wigeon]

negative index?

i dont understand

what do you mean

[static rune]

like 1/(1+x)

its because the series will diverge

it was a stupid question

[lethal wigeon]

(1+x)^-1?

[static rune]

yeah

[lethal wigeon]

i think it works

[static rune]

or -2 -3

[lethal wigeon]

it works im pretty sure

[static rune]

only if x is b/w -1 &1

[lethal wigeon]

so with n=-1

we get an infinite series

[static rune]

yes

[lethal wigeon]

hmm veritasium has a good video on this

[static rune]

I think its the video where he explains how newton found a better way to calculate pi

[unreal tundra]

Is this always true for all complex numbers? (including real numbers). I know it seems simple, but I can't think of a way to prove it (perhaps I am being stupid)

[ancient helm]

Set e = ac
b^2 > 4e so b^2 > 3e
If e is positive real, this is true as 4e > 3e
Say e is negative (ex: -1)
b^2 > -4 so b^2 > -3
Try to contradict this by having
-3 > b^2 > -4 being true (satisfied first condition without second)
Could you think of some b value (complex) that satisfies this

[woeful snow]

I finished 8 chapters in 8 hours. The 1st chapter took me 1.5hrs to complete. The rest of the questions take me equal time to complete.Find the time taken to complete the rest of the chapter if I take a break after every 10mins

Solve this

[normal arrow]

also b has to be a multiple of i and e has to be real

[ancient helm]

Yea I was hinting at the fact that if b is complex/multiple i, b^2 can be negative, making the contradictory equation true

[normal arrow]

no its just that if b is not a multiple of i, then we cant compare numbers

we cant compare complex numbers

[ancient helm]

Oh you mean b MUST be a multiple of i

[normal arrow]

yeah

[bright fulcrum]

I just found 0 is 1

If a to the power 0 is 1 so 1 to power 0 is 1 and 1 to the power 1 is 1 so hence 0=1

[lethal wigeon]

i believe that

[ancient helm]

Yea seems legit

[bright fulcrum]

Give nobel price or smthn

[ancient helm]

Ok here you go
🔕

Also why tf is there an emoji for no bell

[crude bone]

If ac>0 it’s true, if ac<0 it’s false

Nvm if ac<0 then b^2>3ac

Since 3ac would then be negative and a square is strictly non-negative

[versed comet]

hello!

OK So one of my favourite things to do is get drunk (or tipsy depending on what alcohol I have at my availability) and do math problems

So does anyone have any interesting problems. Pure Mathematics? Ideally no harder than Olympiad level / Year 13 A2 Further Mathematics level

[versed comet]

@vernal cape @marsh imp

[crude bone]

Determine all possible values of $\sin2x$ if $\\sin(\frac{3}{2}\sin x)=\cos(\frac{3}{2}\cos x)$ and $0<x<\frac{\pi}{2}$

[vivid gulch]

lightn#3358

[versed comet]

ooo this looks fun

I'll brb and then I'll try it

ok im back

so this is a transformation of functions question

So sin(x) and cos(x) intersect at every π/4 + nπ where n is any integer number

oh wait I didnt see there's an inside sin(x) too

hmm

so I've been working through

and so far I've got cos(x) = -2π +- sqrt(8-4π^2) all divided by 4

as a solution

so cos(x) = ( -2π +- sqrt(8-4π^2) +/4 + 2nπ

and then its just a translation

from cos(x)

to sin(2x)

and then seeing what values of n give an answer in the range where n is an integer

[sour sinew]

this question probably has an easy answer but;
given positive integer n
find the positiveintegersided rectangle or rectangular prism, or analogue in >1 dimension, with volume n
that among all of those possible ones, has the lowest perimeter/surface area/surface volume/etc
is this guaranteed to be >= 4sqrt(n)

[magic quiver]

can y'all solve any of these problems: https://medium.com/p/3ddc9ea0d0f3

[versed comet]

Hmm

this riddle is interesting

[ivory rivet]

Hey guys I have been researching equations for thermodynamics for around 3 days now trying to figure out how to make a simulation that will tell me the temperature of a heat exchanger.

1.)Their is a tank made out of high-strength steel that we will refer to from now on as the reaction chamber
2.)Inside the reaction chamber their are 50,000 fuel rods made out of zirconium, the zirconium is 1215C at max temperature, the fuel rods have a total surface area of 589,000meters^2
3.)Inside the reaction chamber their is also 100,000gallons of water, the reaction chamber is air tight meaning the only thing in it other then the fuel rods is water
4.)The pressure in the reaction chamber is 2,200PSI
5.)The amount of fuel rods
5.)Coming out of the chamber are two pipes forming a closed circuit, one pipe meant for water going out and the other is where the water comes back in. These pipes lead to another chamber that we will call the steam generator made out of carbon steel
6.)These pipes are made out of Inconel, the flow rate through the pipes is 20,000GPM, the total surface area of these pipes inside of the steam generator is 157meter^2
7.)Flowing through the steam generator is 300GPM of water, the steam generator has a typical pressure of 1500PSI, the steam generator makes steam at a rate of 3,333lb of steam per minute.

Now you can see why I am probably really struggling to implement all this math into a simulation... if your a mathematician please help me my brain hurts.

The goal is to simulate the temperature of the water inside the reaction chamber, the water in the steam boiler, the pipe temperature, the reaction chamber temperature, and the steam boiler temperature.

obviously their isn't just a single answer and what I'm looking for are the equations I can use, if any of you are familiar with python, you could 100% use python to format it, which is what im making the simulation in, in the first place.

to simplify it even more cause I'm kind of all over the place

Input(Number that I can change):
FuelRodTemperature
AmountCoolant
DensityCoolant
FlowRateCoolant
AmountFuelRods
SurfaceAreaPerFuelRod
PressureReactionChamber
steamGeneratorWaterFlow

Output(Numbers that are a result of what I put in):
FuelRodTemperature
coolantTemperature
steamGeneratorWaterTemperature
reactionChamberTemperature(the casing of the reaction chamber)
steamGeneratorTemperature(the casing of the steam generator)
pipeTemperature
rateOfSteamProduced

thats just a general outline and im sure their are a lot of other properties I missed

[lethal wigeon]

made a question

i know the answer, but i want to see who can solve it

**Find the limit of the following function as x approaches infinity:

f(x) = (3x^3 - 2x^2 + 5) / (4x^3 + 6x^2 - 3x)

**

[ancient helm]

Is it ||3/4||?

[lethal wigeon]

how did you get that answer?

[ancient helm]

||It equals limit x->inf of 3x^3/4x^3 by some theorem idk the name to and 3x^3/4x^3 = 3/4||

[lethal wigeon]

you dont have to use spoilers

[lethal wigeon]

also yes you are correct lol

[ancient helm]

If someone else wants to try it

[lethal wigeon]

so what i did was

to find the limit

||i had to divide the numerator and denominator by the highest power of x, which in this case is x^3.||

which is

||f(x) = (3 - 2/x + 5/x^3) / (4 + 6/x - 3/x^2)||

||and so as x approaches infinity, the terms with 1/x and 1/x^2 become very small compared to the other terms, so we can neglect them. Thus, we have: lim x->∞ f(x) = (3-0+0)/(4+0-0) = 3/4||

[ancient helm]

Then the const/x stuff approaches 0 right

[lethal wigeon]

yeah

[ancient helm]

Yea that’s my thinking aswell

[lethal wigeon]

alright cool

[ancient helm]

Everything except the highest degree is negligible

Is there not a theorem for that?

[lethal wigeon]

hmm

i forgot

im self-taught so i dont think so?

[crude bone]

It’s definitely a thing they teach

Never heard it being called a theorem

[magic quiver]

Check out this article if you're into STEM! - https://medium.com/p/3ce51be223d2

[lethal wigeon]

hola

so i was trying to prove this

but in this last time im kinda stuck

especially the right statement

can anyone help me

[median verge]

How to answer the second one?

[open whale]

¯_(ツ)_/¯

how do you read the rules

[median verge]

I dont understand

[ancient helm]

Don’t ask for help in discussion chat, that’s what #1015578016606343218 is for

[median verge]

Oh ok sorry

[ancient helm]

👍

[median verge]

Its bc i saw the messages up are also about the same topic

[sour sinew]

is there some proof that the series tan(n)*n^x from n = 1 to infinity, diverges for all real x?

essentially asking how good you can expect infinitely many approximations of pi to be

wolfram alpha claims very confidently that lim x to infinity tan(x)/x^4 does not exist

I am unconvinced

oh I know the issue
limit test doesn’t work here
it is very trivial to find a function over the reals that has no limit but which is 0 at every integer
sin(2pix)

sum of sin(2pin) is clearly 0

actually that’s not why nvm

wolfram alpha isn’t that dumb

[sour sinew]

ah yes very helpful

[ivory rivet]

How would I find the max pressure before a container failure, taking in factors such as temperature, pressure, material, thickness, shape?

[sour sinew]

simulate in computer
I doubt a math model exists that accounts for everything and is still accurate

[ancient helm]

Idk much physics but you could probably approximate it using some equation

[crude bone]

Wolfram is right

The function has infinitely many vertical asympototes

Oh if you’re taking the discrete limit then idk

[sour sinew]

yeah

[crude bone]

It honesty seems to be 0

[sour sinew]

someone in another server said it may be related to how irrational pi is
pi has an irrationality constant between 2 and 7.2

so maybe tan(x)/x^8 has a limit?

I don’t think wolfram can help with this

[crude bone]

Idk it’s not obvious to me why the irrationality of pi should have anything to do with the power of x

[sour sinew]

if you have an integer that’s really close to pi*n + pi/2 its tangent will be very high

and tangent looks like 1/x near the asymptote

not sure

[storm parrot]

A simulation of infinity:
T(x) = T(x+1)+T(x-1), where T(1) = 1 and x>1
or is it

T(x) = T(x+1)+T(x-1) where x>1 and T(1) = 1
let x = 3 for example
T(3) = T(3+1) + T(3-1)
     = T(4)+T(2)
     = T(4) + T(3)  +T(1)
     = T(4) + T(3) + 1
T(3) - T(3) = T(4) + 1
T(4) = -1
counter-intuitive isn't it?
T(4) = T(3) + T(5)
     = T(2) + T(4) + T(5)
     = T(1) + T(3) + T(4) + T(5)
     = 1 + T(3) + T(3) + T(5) + T(5)
     = ....... seems to go on forever
how does this seemingly infinite series converge then
let us make up a representation of this function
T(x) = T(x + 1) + T(x-1)
let x = 2
T(2) = T(3)+T(1)
     = T(2) + T(4)+1
     = T(1) + T(3)+ T(4) + 1
     = 2 + (T(3) + T(4))
here lets assume that the endless  T(1)s add upto infinity and the remaining part n = T(a) where a is unknown
Therefore, T(x) = Infinity + n
Now, if T(4) = -1
    Infinity + n = -1
    n = -Infinity 
    which means, InfinityA + (-InfinityB) = -1
                 InfinityA < InfinityB by 1
    which means infinities differ in size
Also there is another interesting nugget to be looked at
T(5) = T(6)+T(4)
     = T(7)+ T(5)+ T(4)
T(5)-T(5) = T(7)+ T(4)
0 = T(7) -1[since we know that T(4) = -1]
T(7) = 1
since T(x) = Infinity + n
T(7) = InfinityA - InfinityB = 1
Therefore InfinityA > InfinityB by 1 

call me stupid

[normal arrow]

thats actually pretty interesting

[storm parrot]

something even more interesting is that why does it happen to x =4 and x =7 and not to any other number

[normal arrow]

okay so my idea is to use uh

difference equation to try to find such function T

D^2 + D + 1 = 0

[storm parrot]

ic

[normal arrow]

right so

there are two functions T that uh

satisfy these properties:
T(1) = 1
T(x) = T(x-1) + T(x+1)

however

they're scary

one of them is

$T(x) = \left(\frac12 + \frac{\sqrt{3}}{2}\right)\left(\frac12 -\frac{\sqrt{3}}{2}\right)^x$

[vivid gulch]

John Math

[normal arrow]

@storm parrot

[storm parrot]

yes

[normal arrow]

and another one is obviously

[storm parrot]

one sec

[normal arrow]

$T(x) = \left(\frac12 - \frac{\sqrt{3}}{2}\right)\left(\frac12 + \frac{\sqrt{3}}{2}\right)^x$

[storm parrot]

i went afk

[vivid gulch]

John Math

[storm parrot]

let me read your prev messages

[normal arrow]

oh and theres nothing infinite about it

[storm parrot]

i dont get this

i dont get the jargon

why fractals

pls explain

[normal arrow]

wdym

there are no fractals

oh wait oops i forgot the imaginary unit

[storm parrot]

yes

[normal arrow]

$T(x) = \left(\frac12 + \frac{\sqrt{3}}{2}i\right)\left(\frac12 -\frac{\sqrt{3}}{2}i\right)^x$

[vivid gulch]

John Math

[storm parrot]

ic

it was a command

iam stupid

[normal arrow]

happens

so anyways

by solving a difference equation, we obtain that

[normal arrow]

this is our function

[storm parrot]

yes

[normal arrow]

but thats cool that you were able to derive some of its properties without using its exact formula

oh, we can simplify the function

$T(x) = \left(\frac12 -\frac{\sqrt{3}}{2}i\right)^{x-1}$

[vivid gulch]

John Math

[storm parrot]

(1/2 + (sqrt(3)/2i))(1/2-(sqrt(3)/2 i)^x-1, x = 4 =>```
T(4) = (1/2 + sqrt(3)/2i)(1/2 - sqrt(3)/2i)^3
-1 = (1/2 + sqrt(3)/2i)(1/2 - sqrt(3)/2i)^3
(-1)^2 = (1/2 + sqrt(3)/2i)(1/2 - sqrt(3)/2i)^3^^2
1 = (1/2 + sqrt(3)/2i)(1/2 -sqrt(3)/2i)^9?
T(16) = (1/2 + sqrt(3)/2i)(1/2 -sqrt(3)/2i)^9
Therefore T(9) = 1?

[normal arrow]

not quite

[storm parrot]

forgot to look at x-1

one sec

[storm parrot]

yes pls

[normal arrow]

no

[storm parrot]

T(4) = (1/2 - sqrt(3)/2i)^3
-1 = (1/2 - sqrt(3)/2i)^3
(-1)^2 =(1/2 - sqrt(3)/2i)^3^^2
1 = (1/2 -sqrt(3)/2i)^9?
T(10) = (1/2 -sqrt(3)/2*i)^9
Therefore T(10) = 1?

[normal arrow]

im going to analyse this function later

im busy now

and also T(7) = 1, T(10) = -1

its periodic

[storm parrot]

no

[normal arrow]

prove it

[storm parrot]

#1018226029376053319 message

correct me if iam wrong

later since you are busy

[storm parrot]

another thing

[storm parrot]

you said its periodic which means T(7) = 1 and T(10) = -1 and T(13) = 1 and so on

T(7)= T(6)+ T(8)
    = T(6) + T(9) + T(7)
    0 = T(6) + T(9)
also T(4) = T(3) + T(5)
          = T(2) + T(4) + T(5)
Therefore T(2)+T(5) = 0
And taking the ones already proven as axioms, i.e T(4) = -1, T(7) = 1, T(10) = -1 ..
T(x) + T(x + 3) = 0
which means in for example T(6) + T(9) = 0
T(6) = -n or n and T(9) = -n or n
where T(6) does not equal T(9) right?
T(x) = -1 * T(x+3)
which means the numbers which do not belong series -> T(1), T(1+3) , T(1+6),..
also have values

[normal arrow]

nope

its periodic but in the wrong way

oh wait

you made a typo

nvm

[storm parrot]

where

[normal arrow]

T(x) + T(x+3) = 0, not 1

[storm parrot]

yes

but later on

i corrected it

[normal arrow]

well good job

the numbers between 3n+1 depend on our choice of function

remember how i said there are two solutions?

it means that there are two functions with exact same properties BUT have different values between, say, 1 and 4

$T_{1,2}(x) = \left(\frac12\pm\frac{\sqrt{3}}{2}i\right)^{x-1}$

[vivid gulch]

John Math

[normal arrow]

i could also

$T_1(x) = e^{(x-1)\frac{\pi i}3}$

i think

[vivid gulch]

John Math

[normal arrow]

yes

[crude bone]

There’s no infinite sum

[storm parrot]

for what

[storm parrot]

fine dont base that

[crude bone]

Seems to just be a finite, telescoping sum

[storm parrot]

actually not T(7) = 1

[storm parrot]

this is starting to get complicated

[crude bone]

I didn’t really read it fully but you seem to think that since you can make the sum have as many terms as you want, it’s an infinite sum

[storm parrot]

yes i did and didnt

@normal arrow T(3) = -n and not n(where n is any number be it real or int)

hence T(6) = n

and T(9) = -n

[normal arrow]

that is a bold claim

[storm parrot]

T(3^x) = -n and T(3n) = n

i think so

[normal arrow]

but

T(2x-1) = T(x)^2

[storm parrot]

yes

[storm parrot]

actually

thats the inverse

[normal arrow]

wh-

okay

[storm parrot]

T(3^x) = n

[normal arrow]

what

where did you get that from

[storm parrot]

yes its correct now

[normal arrow]

it doesnt make sense

[storm parrot]

T(3) = [1/2 - sqrt(3)/2]^2
T(3) = [(1 - sqrt(3))/2]^2
Since 1 < sqrt(3)
1-sqrt(3)/2 results in a negative number
squaring that negative number gives us a positive number
Therefore T(3) = +n

T(3^0) = 1(+n)

[normal arrow]

no

[storm parrot]

T(3^1) = n

[storm parrot]

ok

[normal arrow]

first of all, if you were right, you'd still be wrong

[storm parrot]

ok

[normal arrow]

squaring that negative number gives us a single specific number, not a whole set of it

[storm parrot]

yes

[normal arrow]

second of all

[storm parrot]

oh yes

[normal arrow]

you forgot the imaginary unit

[storm parrot]

then T(3^x) = T(3n)

[normal arrow]

its ((1 +- sqrt(3) i)/2)^(x-1)

[storm parrot]

which violates the rule

[storm parrot]

fine

[storm parrot]

T(x) = -T(x+3) is the rule
T(x) = T(x+3)
since T(3^x) = T(3n)
then T(3) = T(6) and T(6) = T(9) which is wrong

[storm parrot]

yes

[covert juniper]

WHAT THE FUCK

[eager hatch]

basically its assuming that y-2p is a factor of f(y) but only plugs it into the function f(y)

since y-2p is zero it basically tells you where to find the factors of f(y)

[magic quiver]

https://medium.com/p/1eaea5769e2c

[ancient helm]

GANs

[lethal wigeon]

what is the specific heat of a susbstance formula

calorimeter formula

C = Q / (∆T m)

[lethal wigeon]

PLs help me whit this. What will be incrase in length of a steel rod of lenght 0.5m when its temperature is increased by 60 degree Celcuis The coefficient of linear expansion of steel is 0.000013 (1/degreeC).

[lethal wigeon]

PLs help me whit this. What will be incrase in length of a steel rod of lenght 0.5m when its temperature is increased by 60 degree Celcuis The coefficient of linear expansion of steel is 0.000013 (1/degreeC).

[ancient helm]

@lethal wigeon stop pinging others and asking for help on your questions

[lethal wigeon]

ok sorry

[ancient helm]

Ask for help in #1015578016606343218

[lethal wigeon]

can you solve it?

PLs help me whit this. What will be incrase in length of a steel rod of lenght 0.5m when its temperature is increased by 60 degree Celcuis The coefficient of linear expansion of steel is 0.000013 (1/degreeC).\

[ancient helm]

Again, ask for help on questions in #1015578016606343218 . This chat is for discussion on math, not help

[crude bone]

PLs help me whit this. What will be incrase in length of a steel rod of lenght 0.5m when its temperature is increased by 60 degree Celcuis The coefficient of linear expansion of steel is 0.000013 (1/degreeC).

[stuck kelp]

Calculus is taught in high school in USA?

[eternal verge]

Any suggestions for wut properties and stuff I should add to this document?
https://docs.google.com/document/d/1--uVk0OQ1q5chgEj1yVsBCxji_JynTICGtuJ9Ku5FAc/edit#

[eternal verge]

In the form of Advanced Placement classes, I think.

[normal arrow]

oh my fucking god

i thought i'd never see it again

i mean, in general

its not a new thing

in fact, you are certainly not the first to generalise operators

googologists did it way before you

but

what you should do is to try to analyse the operators you derived more

maybe try to even expand the domain and go beyond natural numbers

or solve equations

also

associative property

and prove that operators dont commute after n = 2

[hollow ice]

He already gave a “proof” they were exponential. To disprove commutativity one can just offer 3^2 and 2^3

[normal arrow]

well fair

[hollow ice]

I advise he use LaTeX for stuff

I got into using media wiki recently

[normal arrow]

true

[hollow ice]

https://formalization.org

This notation becomes much more “strange” for non-natural terms

I have been experimenting with in this case his 4-bracket hyperoperator

I made significant progress on non-integer tetration

[normal arrow]

how?

im curious

[hollow ice]

You try to find a closed form for tetration using double sums

You convert this infinite sum into a product

In this case a double product it turns into

You take the double product and plug in n=3.5 and x=3 for 3^^3.5

[hollow ice]

I got it into double sums but I ended up doing so using discrete operators :(

[normal arrow]

you say that as if its trivial for me

[hollow ice]

It’s sums!

We are past 1600s

[normal arrow]

i know what sums are

i dont know how to express tetration using double sums

[eternal verge]

Wut's a googologist?

[eternal verge]

How do I prove 3 ｢n｣ 2 ≠ 2 ｢n｣ 3?

[eternal verge]

Who?

[eternal verge]

How do you think kindergarteners would react if you told them to find the area under a curve because "It's sums?"

[eternal verge]

Can you pweez show me?

[hollow ice]

3^2 = 9, 2^3 = 8

8 != 9

[hollow ice]

they wouldn't understand most likely

most people are incredibly stupid

[eternal verge]

But why is that true for all values of n?

[hollow ice]

what do you mean

n {3} n = n {3} n

it isn't

[eternal verge]

How do I prove 3 ｢69｣ 2 ≠ 2 ｢69｣ 3?

[normal arrow]

maybe math induction?

like how we established that n {3} m != m {3} n

and if n {a} m isnt commutative, then so is n {a+1} m

but idk

[hollow ice]

easiest way is probably induction

show that noncommutativity for n implies noncommutativity for n+1

then show for 3

but

specifically level 69?

I have no clue

[normal arrow]

just said that

[eternal verge]

Why does it need to imply it?

[eternal verge]

But n ｢3｣ m is equal to m ｢3｣ n...sometimes.

Like when n = m or n = 4 and m = 2.

[normal arrow]

well sometimes isnt always

commutativity states that for all a O b = b O a, where O is some operator

if there are elements for which a O b != b O a, then its no longer commutative

[hollow ice]

because that is the easiest way to show 3 {69} 2 != 2 {69} 3

easiest way

show that a {n} a+1 != a+1 {n} a implies a {n+1} a+1 != a+1 {n+1} a

[signal hawk]

Hi Can anyone help me understand Galois field and its primitive irreducible polynomials and Chaotic Lorenz System

[eternal verge]

But implying something isn't the same thing as saying something...

[hollow ice]

You are dumb, extremely dumb. Implication means it results as of.

I.e., if one says $P: x \mapsto x+1$ is a bijection, then this implies that $x = y \rightarrow P(x) = P(y)$.

[vivid gulch]

Magma <3 (SL_2(R) Group)

[frail oracle]

do you guys accept the posts from the people who help students with their homework and online classes? We at hiradu provide online class help, exam help and homework help.

[eager hatch]

yes

[hollow ice]

Read much?

[hollow ice]

@eternal verge

These middle schoolers be on the peak of Mt. Stupid.

[eternal verge]

Who?

[hollow ice]

You. Obviously.

[eternal verge]

A "logical consequence" is not the same thing as "something that must be true."

[eternal verge]

Wut makes you think I'm a middle schooler?

[hollow ice]

It is. Do you not know what words mean?

[hollow ice]

Your roles + your comprehension level.

[eternal verge]

Aren't you also a middle schooler?

[hollow ice]

Yes but I have basic comprehension of English words and mathematics.

[eternal verge]

Hush now.

[hollow ice]

A logical consequence of A is something that must be true assuming A.

Oh so beloved dictionary!

I am not so cripplingly unable to comprehend basic principles and not acknowledge them. I say you are on the Mt. Stupid mainly because of your issue with the Quadratic Formula. Otherwise, I would just say you lack comprehension, which is to be expected of a middle schooler.

[normal arrow]

lmfao

[north oasis]

what its supposed to be

what it really is

acc no they were never intelligent

they did have negative intelligent

intelligence

what it really is

[hollow ice]

Choose a better function that approaches zero like -1/x^2.

[north oasis]

oh yh thats much better

[hollow ice]

Canis was too hurt when I exposed him for absolutely 0% comprehension.

[north oasis]

wait isnt he the guy who as asking wether 4=2 or not

when there was a world war on the quadratic formula

[hollow ice]

He was the guy who started the war.

[north oasis]

ye lol

[hollow ice]

He was so disingenuous too.

[north oasis]

but isnt he in middle school

[hollow ice]

People like him do not deserve any legitimate thought.

[north oasis]

i think bro should know that 4=2

[hollow ice]

I genuinely do not give two fucks what grade he is in.

It was so clear that he was wrong to everyone after the explanation, he should've conceded.

He didn't. The pretentious fuck just wouldn't give up his superiority complex.

[north oasis]

😂

[hollow ice]

I know, right? He is laughable.

[north oasis]

abysmal

[hollow ice]

He could be 2 years old for all I care.

[agile roost]

you expect me to read this.

[hollow ice]

A fucking 2 year old would admit defeat.

[hollow ice]

Just read my scathing comments.

[north oasis]

well im assuming u jus did considering ur asking whether u shouldve read that or not

[hollow ice]

He did.

[agile roost]

I haven't

[hollow ice]

It was funny, so he can't say that.

[agile roost]

I read 3 lines up at the "generalising operators" thing

[hollow ice]

Read from here.

[agile roost]

then skipped down here

[north oasis]

to him, everything is mid.

[agile roost]

nothing can compare to the height of my comedy

correct

[north oasis]

no

[hollow ice]

You will enjoy those 30 seconds of reading, I assure you.

It is unironically funny.

[agile roost]

I read it

[north oasis]

i knew ir

it

[agile roost]

when you reach my age you find stupidity crippling emotionally

[hollow ice]

I hate this kid with such passion.

[north oasis]

i alr do

only when its not done o purpose

[agile roost]

it reaches a point where everything you do is hopeless, purely because people like canis exist

[hollow ice]

I know.

It is just the fucking worse.

[agile roost]

it's just depressing

[north oasis]

especially when the woke gen z kids do it

[hollow ice]

I genuinely cannot even comprehend how you can be this dumb, unironically.

It astounds me someone can unironically be this stupid, on multiple levels.

Canis is like an onion of stupidity, getting dumber with every layer you unpeel.

[agile roost]

the anvil 17cm away from your skull at it's terminal velocity, moments after you rejected gravity:

[north oasis]

making u cry each time

[hollow ice]

He quite literally screencapped an image "debunking" me providing the definition of the word as I defined it.

[agile roost]

ogres are like onions.

[hollow ice]

You can't get stupider than that.

It astounds me he can read.

[north oasis]

logical consequence \neq it is a result of according to sir canis the fourth

[hollow ice]

@sour sinew read this, you will laugh so hard.

[north oasis]

shrek = onion

[hollow ice]

From here.

[agile roost]

$F=ma \implies E^2=(mc^2)^2+(pc)^2$

[hollow ice]

Oh gos no

Stop now

Stop it you fucker

[vivid gulch]

Professor mid. FRS CBE

[north oasis]

obviously dude

[hollow ice]

Stop now please

[north oasis]

thank god u wrote the true formula tho

[agile roost]

THEREFORE

[north oasis]

not E=mc^2

[agile roost]

Schrödinger equation

[north oasis]

string theory

[agile roost]

not far off

[hollow ice]

Therefore time mass dilation\

[north oasis]

therefore the universe is expanding

[agile roost]

therefore special relativity

[hollow ice]

Therefore laws of the QHO

[agile roost]

mass is energy is velocity

[north oasis]

therefore this is the value of the cosmological constant

therefore QCD is right

[agile roost]

therefore the reduced planck constant

[north oasis]

\hbar > h

just saying

[agile roost]

therefore top quarks

[north oasis]

just better

[hollow ice]

These people are what keep me battling with eugenics. If not for my moral values I'd probably be like every 20th century Nobel Prize winner.

Their life must be so sad.

[north oasis]

therefore higgs field "giving" mass is true

[agile roost]

Feynman slash your wrists xx

[hollow ice]

$\hbar$ is hot goddamn

[vivid gulch]

Magma <3 (SL_2(R) Group)

[north oasis]

it is

[agile roost]

feynman slash both your wrists

immediately

[north oasis]

just so much better than what that lil fucker plank came up with

[hollow ice]

$\Delta E \Delta t \ge \frac{\hbar}{2}$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[hollow ice]

Goddamn hottest possible

[north oasis]

the true uncertainty principle

who gives a fk about position and time

[hollow ice]

@agile roost I have a question for you.

[north oasis]

energy

https://tenor.com/view/thanos-infinity-war-avengers-gif-14003260

[agile roost]

you BLACK SPEAR CHUCKING PIECE OF SHIT NI-

[sour sinew]

I read it but now I must know whether 3 {69} 2 = 2 {69} 3

[agile roost]

times actors weren't acting^^

[north oasis]

lol

[hollow ice]

You agree Canis a fucking charlatan not deserving of any consideration, right?

[agile roost]

"adam, your line was "YEAH YOU DRIVE AWAY""

[hollow ice]

No, it's not.

[sour sinew]

nol

[hollow ice]

It is impossible.

[sour sinew]

I agree anyone who disagrees with the quadratic formula does not deserve thought

[hollow ice]

One can prove 3 {69} 2 is odd and 2 {69} 3 is even.

[sour sinew]

oh yeah

true

[north oasis]

whats the curly braces

[hollow ice]

Some shitty notation Canis invented.

Which is just a shittier version of Knuth's arrow notation.

[sour sinew]

I think multiplication is {2} and exponentiation is {3}

tetration is {4}

[north oasis]

oh k lol

[sour sinew]

etc

[north oasis]

brej

[hollow ice]

It is Knuth's arrow notation for hyperoperations but shittier and defined in a Google Doc.

Not even using LaTeX 🤣 .

[north oasis]

notepad*

[agile roost]

pentation

please stop

[hollow ice]

Plaintext and Markdown are super based, don't knock them.

[sour sinew]

ok lemme just write 2 ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑ 3

[hollow ice]

You can just write 2 { ^ ^ } dots under with count 3

[hollow ice]

Like we usually do

[sour sinew]

in discord?

[hollow ice]

Use LaTeX.

[north oasis]

lahhtek

[sour sinew]

this is easier

[north oasis]

how to pronounce latex 101

[agile roost]

latex is pronounced Taylor Swift

[hollow ice]

$2 \underbrace{\uparrow \uparrow \dots \uparrow \uparrow}_{69} 3$

[sour sinew]

taylor swift is pronounced

[north oasis]

thats the formal way of saying it

[vivid gulch]

Magma <3 (SL_2(R) Group)

[normal arrow]

i caught up with the conversation pog

[hollow ice]

Much sexier.

[agile roost]

please just delete everything

[north oasis]

ayo whats that

oh underbrace

[agile roost]

nothing can recover this

[normal arrow]

$2\uparrow^{69} 3$

[vivid gulch]

John Math

[agile roost]

we're all going to perish

[north oasis]

thats not too bad

[normal arrow]

i saw this notation being used

[sour sinew]

that's better

[hollow ice]

That is uglier, in my opinion.

[agile roost]

+close

[north oasis]

its better than this

[agile roost]

man

[normal arrow]

thats more compact and clean than yours, imo

[hollow ice]

no this is hot

[north oasis]

and that is hotter

[hollow ice]

I don't care to much about compactness.

If you really want cleaner

[sour sinew]

then write ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑

[agile roost]

what does the International Mathematical Olympiad have to do with this?

[normal arrow]

lmao

[north oasis]

mid

[agile roost]

-mute

[sour sinew]

he was addressing the imo committee

[north oasis]

https://tenor.com/view/facitlities-f-or-that-big-man-big-shaq-interview-gif-17777771

[hollow ice]

$2 \stackrel{69}{\uparrow} 3$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[agile roost]

I don't support corruption, I do support abuse of power

[hollow ice]

this is better fuckers

[sour sinew]

no still worse

[hollow ice]

How?

[north oasis]

its basically the same thing

[hollow ice]

Genuinely how

[sour sinew]

the bracket was better

because I can understand it

[hollow ice]

oh my god no it isn't

[agile roost]

no, embrace reality

[hollow ice]

$2\uparrow 3$ = $2^3$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[agile roost]

write it in exponent form

[sour sinew]

I mean this was better

[agile roost]

write it in exponent form

[hollow ice]

oh the other one is the same

[agile roost]

do it

[hollow ice]

Just without brackets

[agile roost]

fucking do it

do it

do it RIGHT NOW

put it in exponent form

write it out

I dare you

[hollow ice]

$2\uparrow \uparrow 3 = 2 \stackrel{2}{\uparrow} 3$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[hollow ice]

and so on

[north oasis]

isnt ${^{b}a}$ the best tho

[vivid gulch]

madlad-mathemagician

[agile roost]

tetration 😦

[sour sinew]

no

[north oasis]

its the worstn't

[hollow ice]

That is just short form for tetration which is $2 \uparrow \uparrow 3$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[north oasis]

yh its more compact

[agile roost]

not enough sides on a square

[hollow ice]

Yes but we are discussing the properties of hyperoperations

Not specifically tetration.

[sour sinew]

to notate each type, rotate it by 1 radian

[hollow ice]

If it was specifically tetration, that'd be fine.

[north oasis]

well just slide that fucker somewhere else

like just put the b on top of the a

[hollow ice]

Only works for say 4 operations most then

It becomes taxing. This operation is cleaner by far.

[north oasis]

just move it bby 1 degree

[agile roost]

let's make numbers myriagons

[north oasis]

for a different operation

[hollow ice]

lol

[north oasis]

360 operations

easily identifiable

every single one of them

[agile roost]

triacosiahexecontagon or this

call them that

has cos

[sour sinew]

but no sin smh

[hollow ice]

Do you want to see a simple proof that $2 \underbrace{\uparrow \uparrow \dots \uparrow \uparrow}_{n} 3$ is even for $n \ge 2$?

[agile roost]

Christian

[vivid gulch]

Magma <3 (SL_2(R) Group)

[north oasis]

i mean ur probs gonna write it anyways so go on

[hollow ice]

Ok.

[agile roost]

proof by triviality

what the fuck shit is this

[north oasis]

bro starts writing topological equations now

"simple proof"

like

u call that simple

thatis

trivial

[sour sinew]

can we get a proof that 3 underbrace uparrow dot dot dot 2 is greater or less than 2 bla bla bla 3

[hollow ice]

It is pretty easy, as I believe this guy just stole the Ackerman notation.

[north oasis]

i dont understand it if u dont write it in latex

[agile roost]

guys look at my proof that $1 \underbrace{\uparrow \uparrow \dots \uparrow \uparrow}_{n} 9$ is 1.

[hollow ice]

Do so inductively. It's trivial.

[vivid gulch]

Professor mid. FRS CBE

[north oasis]

this must be some insane advancement in analytic number theory right

i think this is the key to the RH

[sour sinew]

I guess for a, b > e then the larger answer will be where the lower number is on the left and the higher number is on the right

[hollow ice]

Yes there is always an e where that is true.

[sour sinew]

is it not the same e

[hollow ice]

No.

[normal arrow]

how many divisors does $2\uparrow\uparrow\uparrow10$ have?

[sour sinew]

e_69

[vivid gulch]

John Math

[hollow ice]

Hmm. Presumably a lot.

[north oasis]

walter white

[normal arrow]

fair enough

[sour sinew]

presumably quite a few

[north oasis]

lets count em

one by one

like good ol nursery

or whenever u learn how to count

[normal arrow]

i say we count from 1 to 2 ||| 10 and check which ones divide the number

[hollow ice]

If I had to guess, I'd say $\left(2 \uparrow \uparrow 10\right)^{2 \uparrow 10}$ but i dunnno

[vivid gulch]

Magma <3 (SL_2(R) Group)

[normal arrow]

how big is 2 ||| 10

[north oasis]

it so easy

[hollow ice]

insanely massive

[agile roost]

proof: ||use your fucking brain for once in your entire miserable existence. I mean seriously, you're over a decade old and have achieved nothing of note, get your shit together. There are 5 year olds in this world who have progressed their field further than you and endured greater hardships than you. There are dead people with more bitches than you and prostitutes with more dignity than you. Get a fucking life, pull your miserable and worthless existence out of the rut of self pity that you have plunged yourself into for the last years. It's honestly pathetic; you're the future of this planet and you have already disappointed everyone you've ever known. Get your shit together.||

[hollow ice]

Let $a = 2^{2^{2^{\dots}}}$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[normal arrow]

you're such a cute little non-googologist shark boy

[agile roost]

hey guys!! this is a joke

[north oasis]

3am motivation

[agile roost]

nice cinematic experience

[hollow ice]

Then $2\uparrow\uparrow\uparrow 10 = a^{a^{a^{\dots}}}$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[hollow ice]

To give you a good idea: $2 \uparrow \uparrow 5 = \infty$ according to Desmos

[normal arrow]

yeah so uh

very small

[north oasis]

obv

[sour sinew]

0% of infinity

[north oasis]

compared to infinity

[vivid gulch]

Magma <3 (SL_2(R) Group)

[north oasis]

everything is zero

hence small

[normal arrow]

compared to BEAF

[agile roost]

does this break rule 1? @normal arrow

,m rule 1

[normal arrow]

not really

[north oasis]

pin that

[normal arrow]

you clearly didnt mean it

[north oasis]

i need it for 3am motivation

[agile roost]

aight cool, I'll start randomly pinging people with it

[north oasis]

he did

[agile roost]

shit

[normal arrow]

oh then you're demoted

[north oasis]

lol

[agile roost]

how would I mean it??

asking for a friend

[sour sinew]

when you get found out

[hollow ice]

I love how I can be insanely fucking rude to a middle schooler and get 0 repercussions but alex is scared af over an obvious joke.

[north oasis]

it was at this moment

he knew

he fucked up

[agile roost]

ok I didn't

it was directed at nobody anyway

well

[north oasis]

he personally aimed it towards me

[agile roost]

whoever clicked the spoiler

[normal arrow]

oh yeah but also still be less rude, esp since you want to become a manager

[hollow ice]

@normal arrow do you want to compute a lower bound?

[sour sinew]

2 ^^^ 9

[north oasis]

im in trauma rn

@normal arrow ban

[agile roost]

you clearly clicked the spoiler, so maybe

[normal arrow]

sure, how?

[hollow ice]

Logarithms

[north oasis]

john napier

[normal arrow]

well how do we apply logs to a pentation operation

[agile roost]

Helen Keller is a better mathematician than some of these mfs

[hollow ice]

Well, it is harder

[agile roost]

even if I cut off all her limbs

[hollow ice]

But it is possible

[agile roost]

and she's still fucking dead

[normal arrow]

what if we try it on tetration first

[hollow ice]

Why?

[north oasis]

i did that in 1924 to her

[normal arrow]

ooh let me write a hyperoperation function on python

[hollow ice]

$2 \uparrow \uparrow \uparrow 10 \ge 10 \uparrow \uparrow \uparrow 2$

[sour sinew]

2 ^^ 2 ^^ 2 ^^ 2 ^^ 2 ^^ 2 ^^ 2 ^^ 65536

[north oasis]

overflow error?

[normal arrow]

idk

[vivid gulch]

Magma <3 (SL_2(R) Group)

[agile roost]

overflow with some bitches, maybe???

[sour sinew]

this number strikes me as kinda small ngl

rather miniscule

[normal arrow]

yes

BEAF notation can reach larger numbers

[hollow ice]

$10^{10^{10^{\dots}}}^{10^{10^{10^{\dots}}}$

[normal arrow]

hell, even FGH can do that

[north oasis]

thats a hatrick right there

[vivid gulch]

Magma <3 (SL_2(R) Group)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[normal arrow]

now THATS big

[agile roost]

when will jaeger man stop waffling.

[normal arrow]

wait wrong psi

[agile roost]

he's done nothing

[normal arrow]

yes

[hollow ice]

@normal arrow you do agree though it is funny af to see me respond to middle schooler than way?

[normal arrow]

assuming Buchholz's OCF

[normal arrow]

absolutely

[sour sinew]

wait so this clearly has 2 ^^ (2 ^^ 2 ^^ 2 ^^ 2 ^^ 2 ^^ 2 ^^ 65536 - 1) + 1 factors

[north oasis]

its charlie chaplin all over again

[hollow ice]

I agree but probably not the most politically correct way

[agile roost]

I'd say that's more than 2

[hollow ice]

Is it possible for $a$ to have $a$ factors for $a > 2$?

[vivid gulch]

Magma <3 (SL_2(R) Group)

[hollow ice]

The answer is no, clearly.

[sour sinew]

indeed

[hollow ice]

If $a$ had $a$ factors, then $\forall x < a (\exists k (kx = a))$

[vivid gulch]

Magma <3 (SL_2(R) Group)

[sour sinew]

magma did you read my parentheses

[agile roost]

the answer is yes!
4 has factors
4 and 1, √2 and 2√2, 2 and 2, 1 and 4

!!!!!

[hollow ice]

fuck you

no

[north oasis]

well with that logic

[sour sinew]

sqrt 2 is an integer

[agile roost]

√2 is rational and an integer

[sour sinew]

so don't say it has more than 4 factors

[hollow ice]

it is pretty evident $2$ is the only value satisfying that property.

[north oasis]

every real no. has infinitely many factors

[vivid gulch]

Magma <3 (SL_2(R) Group)

[agile roost]

√2 is simply √2/1

hence rational

[north oasis]

lol

[agile roost]

and an integer

[sour sinew]

I agree with this

[north oasis]

mid.

[agile roost]

if a number can be divided by 1

[hollow ice]

@sour sinew are you religious?

[agile roost]

it's an integer

[sour sinew]

not really

[hollow ice]

Alright.

@normal arrow are you religious?

[agile roost]

π/1
e/1
γ/1

[hollow ice]

@north oasis you too madlad.

[north oasis]

theres a joke coming

isnt there

[hollow ice]

No, actually.

[agile roost]

religious these balls across your forehead

[hollow ice]

I am just interested.

[north oasis]

yh i am

[hollow ice]

@agile roost you are clearly areligious.

[north oasis]

....

[normal arrow]

i believe there might exist an omnipotent deity but we will never know for sure and i dont really care if it does or it doesnt

[sour sinew]

lol

[hollow ice]

Oh what religion?

[agile roost]

yup

[north oasis]

well im from india

[hollow ice]

Fair.

[agile roost]

I believe in myself

[north oasis]

so u can kinda guess it

[hollow ice]

Ah I assumed so.

[agile roost]

makes me a theist

[north oasis]

i am god

[hollow ice]

You are Hindi?

[north oasis]

no hindis a language

hindu is a religion

[hollow ice]

(it was a joke)

[agile roost]

unoriginal

[north oasis]

mb

[agile roost]

direct your eyes to the message directly above yours

[hollow ice]

I was asked unironically by someone in the states if hindi was a religion

[north oasis]

i mean i see the wall idk bout some religious message

[hollow ice]

They then proceeded to tell me how Bengali was a country

[north oasis]

wait agex which part of england do u live in

[agile roost]

the correct part

which part of the slums do you live in?

[hollow ice]

They saw me texting in Bengali

[agile roost]

I mean india

[hollow ice]

Asked me if I was religiously Hindi

[normal arrow]

how about we move to #geonosidan-prison-complex

[hollow ice]

THIS IS GENERAL DISCUSSION!!!!!

[north oasis]

the part where its supposed to be apparently the most expensive

[agile roost]

#1018226029376053319 is general discussion

[north oasis]

but its not that expensive

agex do u live in essex

[sour sinew]

bengali is a country

[agile roost]

no

[normal arrow]

and #geonosidan-prison-complex is general-er

while this

[north oasis]

nvm then

[normal arrow]

is under GENERAL MATHS

[north oasis]

i was thinking we couldve possible met

[normal arrow]

and india is not maths iirc

[hollow ice]

No it is a region in Bangladesh.

[north oasis]

cuz thats the part i lived in

but then i remembered

ur 20

and u liked maths since u were 14

[agile roost]

what

[north oasis]

so ur probs not going outside that much

[agile roost]

14?

no

[north oasis]

when then

[agile roost]

way earlier

[north oasis]

wherever

[hollow ice]

There are the Bengali people in Bengal.

[sour sinew]

hm
I was only aware of its use as the language

[north oasis]

that doesnt help the situtation

[hollow ice]

@north oasis how old are you unironically?

[agile roost]

part of the reason I can speak languages is because of maths textbooks (I'm literally Erdős)

[north oasis]

i was always good at maths i just found interest in it at around 10 yrs old

[hollow ice]

Also everyone we should hop into a VC.

[north oasis]

14

[normal arrow]

im so old

im so impossibly old