#serious-discussion

1 messages · Page 174 of 1

ocean harbor
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lets get good first noob

coral terrace
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😔

ocean harbor
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ive seen a lot people make crazy games tho

coral terrace
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what is this song

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i said MOEW

ocean harbor
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I said meow

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yeah

coral terrace
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by azazal and said

ocean harbor
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yeye

coral terrace
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more like 8 stars

ocean harbor
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how

coral terrace
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youre overestimating a 3 star level

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its pretty much baby mode

ocean harbor
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:3

coral terrace
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like 4 clicks maximum in the level

ocean harbor
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as long you get enough likes tho

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thats what im gonna do

ocean harbor
coral terrace
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yeah

ocean harbor
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maybe this level will be hard +5 stars

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or harder

coral terrace
ocean harbor
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:3

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I should :3 at the end

coral terrace
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i respect fellow rectangle haters

coral terrace
rocky shuttle
ocean harbor
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:3

coral terrace
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@ocean harbor oki so how long do you want it to be

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also add me

fresh comet
rocky shuttle
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:3

placid wedge
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I miss my best friend

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no I miss the good old memories

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but time flies

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we rarely talk now

fresh comet
rocky shuttle
coral terrace
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@ocean harbor did you die..

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rest in peace

ocean harbor
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send me a fr

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ill accept it later once i finsih daily

coral terrace
ocean harbor
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oh

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there

neat lintel
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I don't want to bother or anything but does anyone know math? and that he is between 17 and 20 years old? To help me with math please?

ocean harbor
humble ridge
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Hi, mathcord. I'm a 15 year old currently stusdying in secondary school. However, the math teachers in my school are completely useless and I have learnt nothing from them. Hence, I decided to take my learning to here, this server, in the hopes that someone has the patience to teach me. I believe I have potential and I believe in myself. I am patient, diligent, and willing to learn

gusty socket
gusty socket
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you can take your learning here because you want to accelerate your learning, and this is a good place for that, and also you don't really need a mentor

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but not becuase you find your teachers bad and just want a new teacher

reef geode
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I have been having such hard imposter syndrome with my math knowledge. I have bits and chunks of knowledge from linear algebra, multivariate calculus, and basic analysis and I constantly am learning more and I know that is what matters but I struggle to keep motivation sometimes.

Probably not the best time or place but I wanted to put it somewhere

neat lintel
neat lintel
uneven tinsel
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Thank god I am 13 years and 1 minute old

fervent oyster
static loom
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or they're lying on the internet, tough call

fervent oyster
static loom
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😮

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why would you do such a thing

fervent oyster
static loom
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😮

loud snow
ripe rampart
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Hi guys! I have a question. What do you think is better in terms of job prospects, a double major in math and stats or a masters in applied math?

loud snow
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Employers don’t necessarily care what its in all the time

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For the most part math wont give any more jobs then a stats major would give

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And a masters is just another cert that employers would like to see

uneven tinsel
grand pecan
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if convenient can someone tldr the proof that sqrt(2) is irrational

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got it

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basically

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2=a^2/b^2

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2b^2=a^2 so a^2 is even so a is even

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2a^2=b^2 so b^2 is even so b is even

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sqrt(2)=a/b in the simplest form, yet they are not coprime so contradiction

chilly hull
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2=a^2/b^2 does not imply that 2a^2=b^2

grand pecan
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let a/b be rational in the simplest form. does this mean a and b have to be coprime integers

chilly hull
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a and b must be coprime otherwise we may find a factor

chilly hull
grand pecan
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a^2 is divisible by 2. a cant be a multiple of sqrt(2). 'a' has to be divisible by 2.

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are these right or

chilly hull
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what else can we deduce about a^2

grand pecan
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sqrt(2)b=a?

chilly hull
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if we multiply an even number by an even number

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what else can we deduce about the product besides "it's even"

grand pecan
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e1=2x, e2=2y, e1*e2=2x*2y=4xy, e1*e2 is divisible by 4

chilly hull
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correct

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so a^2 is divisible by 4

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now what can we deduce of b^2 with this new information (and hence also b)

grand pecan
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b^2 is also even

chilly hull
grand pecan
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if a^2=2b^2, and a^2 is divisible by four, then 2b^2 is too, meaning 4n=2b^2, and 2n=b^2, b^2 is even

chilly hull
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your notation on "4xy" is a bit strange but i got it

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you're saying that if a^2 is divisible by 4 then we have that a^2=4n for some natural number

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and then 4n=2b^2 so hence 2n=b^2 and hence b^2 is even

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now what happens if b^2 is also even

grand pecan
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b^2 is even, hence b^2 =2n. since b is an integer, its not sqrt(2), so b has to be divisible by 2

chilly hull
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yes!

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so both a and b are even

chilly hull
grand pecan
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thank you 🐱 🍞

sudden spade
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Hello for the Julia users here what packages do you use for plotting?

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I've been using pyplot in the past but I find it quite unreliable and slow at times

visual topaz
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I would ask in the Julia server, but I think plotting speed depends on the backend

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Personally I'm used to Julia not being a plotter

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Because of the precompile times

sudden spade
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But yea good shout I'll probably go to the julia server

visual topaz
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Yeah why not use Plots.jl?

uneven tinsel
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Math Life

Middle School Sad

High School Sadder

College Saddest

static loom
raven plaza
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Indeed math comes before middle school

uneven tinsel
south yarrow
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Hello, my girlfriend will start her 3th undergraduate year, she is a bit lost if she should go in academia or applicatives math in industry, how can i make her try out applied math to see if she like it ?

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there exists things like kaggle, cryptohack, etc... but i wonder if that is appropriate, is there something heavy with differential equation ?

tawdry spindle
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Machine learning

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Uses a lot of math

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Like LA and stat, analysis

tawdry spindle
stone saffron
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Ok

south yarrow
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Ok so kaggle should be a good idea or i'm missing kaggle's topic ?

tawdry spindle
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Kaggle gives you datasets to train models on them

old oak
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Kaggle also has very good tutorials

pulsar finch
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how to learn order theory by myself

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i am still taking precalc, is possible?

uneven tinsel
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Order some books

solid snow
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why jump straight into that

uneven tinsel
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If there is will there is a way

pulsar finch
solid snow
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how is that relevant to my question

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order theory is too niche of a subject to be focusing on if you haven't learned any of the main subjects yet

pulsar finch
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I just wanted to understand Zorn lemma that I saw in elementary set theory book but I dont know what a poset or a chain is

solid snow
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it's also mostly just covered in book as needed from what ive seen

solid snow
pulsar finch
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what happened

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this is context

image0.jpg
solid snow
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so did you just jump to the part about zorn’s lemma or did you read everything before it?

fervent oyster
solid snow
# pulsar finch this is context

id say its unfair to call it merely “context” when it defines everything needed to understand the statement of zorn’s

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thats what those pages before zorn’s are for

ocean harbor
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precalc is ezpz if you used calc sotrue

pulsar finch
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is cofinality unskippable btw?

pulsar finch
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I need to put more effort

solid snow
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i would say dont skip any section

raven plaza
pulsar finch
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I thought set theory is the basics for proof writing and logic

raven plaza
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I don't think cofinality is needed to understand Zorn, but it comes up in set theory a lot

solid snow
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not a whole book worth no

raven plaza
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Just basic constructions like ordered pairs, Cartesian product, disjoint unions, etc

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And construction of some number systems

pulsar finch
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is cardinality of infinite well ordered sets essential?

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alephs

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what would be the pre reqs for set theory

latent edge
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nothing

quartz lintel
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When I'm doing complex algebra and the number looks a little too random angerysad

raven plaza
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5 is not a prime

alpine kindle
pulsar finch
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how does the cardinality of real nums compare to integers and naturals, what is continuum hypo

sturdy quarry
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continuum hypo states that there is no set whose cardinality is between that of integers and reals

sleek mural
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What is time?

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Every moment of it is moving but what is moving exactly?

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If we were to quantify time, then where is time?

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If time is relative, then if motion is relative, then we are all looking at things from our relative perspective
So how can we determine that what we see is the same as the others?

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Why is there time?

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very random philosophical questions lol

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Like shouldn't our world be static? Where is this continuous pushing of motion happening?

river moon
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you don't see what others are seeing

latent edge
pulsar finch
dense belfry
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The continuous pushing of motion is happening on a very small scale and then being amplified by causality to a large scale

sleek mural
sleek mural
latent edge
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Not all movements are in constant motion

sleek mural
dense belfry
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idk why forces cause things to move but it seems like the presence of forces cause things to move around

sleek mural
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Lmao

dense belfry
sleek mural
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but even if theres no force and everything remains motionless

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will time still exist?

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So what is time?

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or if time still has any purpose?

sturdy quarry
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you can compare them

vague crane
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Hello where u from

sturdy quarry
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you can prove that the cardinality of Z is the smallest infinite cardinality

pulsar finch
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i am peruvian , wbu

sturdy quarry
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and then you can define aleph_0 to be |Z|

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and some fancy c to be |R|

pulsar finch
sturdy quarry
dense belfry
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0,1,-1,2,-2,3,-3,...

sturdy quarry
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this is bijection between set of naturals and integers

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0 -> 0
1 -> 1
2 -> -1
3 -> 2
4 -> -2
5 -> 3
6 -> -3
....

pulsar finch
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sure

leaden torrent
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to clarify: all "same cardinality" means is "there exists a bijection"

sturdy quarry
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we can assign natural numbers to integers in a way that each natural number gets mapped to unique integer

leaden torrent
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more specifically, if there is an injection from A to B, that means |B| ≥ |A|

pulsar finch
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one to one correspondance or something

sturdy quarry
leaden torrent
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by a theorem of cantor and the axiom of choice, this is equivalent to there being a surjection from B to A

sturdy quarry
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theorem of cantor?

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which one?

pulsar finch
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cantor theo?

dense belfry
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It's called the cantor Schroeder Bernstein theorem

sturdy quarry
leaden torrent
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cantor first published it but without proof

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mathematicians worked different back then frfr

pulsar finch
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what about rational p/q numbers (Q)

leaden torrent
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same cardinality as ℕ and ℤ

sturdy quarry
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again, there is a correspondence

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ill send pic

sturdy quarry
leaden torrent
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its a "zigzag" method

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first note that there is a bijection between ℕ and ℤ²

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by just "spiraling" around the coordinate plane

image.png
pulsar finch
sturdy quarry
leaden torrent
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now we imagine this bijection, but instead of being from n to a point (a, b)

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it's from n to a/b

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but we "skip duplicates"

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for example, the points (1, 1) and (2, 2) correspond to the same rational

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1/1 and 2/2

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so we would just "skip" 2/2 in our bijection

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similar for, say, (1, 2) and (2, 4)

pulsar finch
leaden torrent
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doesnt need to be that shape

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its just an example

sturdy quarry
leaden torrent
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as long as its a bijection it works

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and this is clearly a bijection

sturdy quarry
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you could make it different, but spiral works well for the purpose of demonstration

pulsar finch
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is cardinality of complex numbers same as real

leaden torrent
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yes

sturdy quarry
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in general, cardinality of A is same as cardinality of A^n for infinite sets A

leaden torrent
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more generally, any sets of bounded-length lists of elements from the same infinite set will have the same cardinality

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complex numbers are just finite lists of real numbers

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since they all have the form a + bi

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speciifcally, theyre lists of size 2

sturdy quarry
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(a, b) -> a + bi is the obvious bijection between R^2 and C

leaden torrent
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this is a very important fact for theoretical computer science, among other things

pulsar finch
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a moment, is cantor theorem same as schroders bernstein theo

leaden torrent
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Cantor's Theorem is a different thing.

dense belfry
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Cantor's theorem is uncountability of the reals

leaden torrent
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i said "a theorem of cantor" earlier referring to cantor-schroeder-bernstein

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not cantor's theorem

leaden torrent
pulsar finch
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P(a)?

leaden torrent
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power set, i.e. set of all subsets

pulsar finch
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ahh

gritty crater
# sleek mural So what is time?

Time is just an illusion. If we can cause a chemical reaction to react faster then does that mean time has gone faster from their perspective? Why do we feel like so much time has passed when we sleep but in reality, it is just one hour? Does that mean the brain perceives time differently so everyone perceives time differently? If you are alone in the universe with nothing except darkness then how do you know you are in motion, how do you know what time is it? There is nothing like a system clock in the universe so how do we know exactly how much time has passed? Time is invented by humans to make things easier!!!

main elbow
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@zinc dock i finished up my (horribly inefficient) python code, and it seems to corroborate my hypothesis that you only get powers of 2

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i think it wouldnt be hard to prove even

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ig the nice thing is that its very easy to adapt the code to only allow for two term sums

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although i think for that specific case theres probably a better implementation

empty mirage
zinc dock
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Interesting

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What happens if you limit it to only two?

sleek mural
# gritty crater Time is just an illusion. If we can cause a chemical reaction to react faster th...

Yes
But time is but a creation of us in this constant progression in linear motion, so why do we have this linear motion to begin with?
Or if you look at things from a 3D down to a 2D perspective, and you imagine a room with infinite many of them from different times, what keeps them transitioning from one room to the room after that? In essence, why are we experiencing linear progression, where has "time" gone?

main elbow
zinc dock
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Neat

eternal crow
main elbow
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which is quick to prove

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show that 11, 12, 13 an in by hand

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then we can show by strong induction that all n >= 14 are in
n-2 and n-3 are both in so n = (n-2) + 2 = (n-3) + 3 and so n is in

zinc dock
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Huh

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That's really interesting
I didnt think about that

main elbow
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perhaps something interesting happens if instead of not having a unique sum you just say no sum ?

zinc dock
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Maybe

main elbow
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shall i try that with two term sums or any length do you think ?

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i can do both but which first

sleek mural
zinc dock
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Uhh

zinc dock
main elbow
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both super easy

zinc dock
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Fair enough

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Maybe any length just to see how it goes

main elbow
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alr

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powers of two again

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which makes sense

eternal crow
gritty crater
main elbow
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ok two terms is a bit more erratic, but still looks kinda regular

eternal crow
main elbow
# 
2, 3, 4, 8, 9, 14, 15, 20, 21, 26, 27, 32, 33, 38, 39, 44, 45, 50, 51, 56, 57, 62, 63, 68, 69, 74, 75, 80, 81, 86, 87, 92, 93, 98, 99, 104, 105, 110, 111, 116, 117, 122, 123, 128, 129, 134, 135, 140, 141, 146, 147, 152, 153, 158, 159, 164, 165, 170, 171, 176, 177, 182, 183, 188, 189, 194, 195, 200, 201, 206, 207, 212, 213, 218, 219, 224, 225, 230, 231, 236, 237, 242, 243, 248, 249, 254, 255, 260, 261, 266, 267, 272, 273, 278, 279, 284, 285, 290, 291, 296
#

@zinc dock

zinc dock
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Ooo

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This is pretty interesting

main elbow
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it looks like a repeating pattern mod 20

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no 30

zinc dock
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It is
Weirdly enough without the '4' term

main elbow
# 
[2, 3, 4, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 2, 3, 8, 9, 14, 15, 20, 21, 26]
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ah yeah

eternal crow
zinc dock
gritty crater
zinc dock
main elbow
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this was the two term

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the any-term just gave powers of 2 again haha

zinc dock
#

O lmao

main elbow
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i was kind of hoping for something more chaotic haha

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alas

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was fun to do some coding

zinc dock
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Looking on the pattern database, adding 1 to the list of allowed numbers is definitely a bit more chaotic https://oeis.org/A033627

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Makes me want to find the overlap between the normal primes and this set

main elbow
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besides 2

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if you look each term to the next is +3

zinc dock
#

In my defense i just woke up sad_gura

main elbow
#

happens to the best of us

zinc dock
#

That's unfortunate
Figured I could find a non-terminating parallel to the normal primes

main elbow
#

maybe looking at k-terms is more interesting

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like k=3 maybe

# 
[1, 2, 3, 4, 5, 13, 14, 15, 25, 26, 27, 37, 38, 48, 49, 50, 60, 61, 71, 72, 73, 83, 84, 94, 95, 96, 106, 107, 117, 118, 119, 129, 130, 140, 141, 142, 152, 153, 163, 164, 165, 175, 176, 186, 187, 188, 198, 199, 209, 210, 211, 221, 222, 232, 233, 234, 244, 245, 255, 256, 257, 267, 268, 278, 279, 280, 290, 291, 301, 302, 303, 313, 314, 324, 325, 326, 336, 337, 347, 348, 349, 359, 360, 370, 371, 372, 382, 383, 393, 394, 395, 405, 406, 416, 417, 418, 428, 429, 439, 440]
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i believe this should be right for 3 term sums

static loom
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whatcha playing with

main elbow
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even weirder it repeats mod 23

main elbow
#

the terms i just posted are for sum of three terms instead of two tho

static loom
main elbow
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not sure i would call it nice haha

static loom
#

yuck!

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lol yeah not looking too promising

zinc dock
main elbow
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im not sure

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but if you allow k = 2, 3, 4, ... all in one go then its powers of 2

zinc dock
#

Ohh you mean specifically k terms

main elbow
#

yh

zinc dock
#

That's actually pretty interesting

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This gives me an interesting (albeit a bit more complicated) idea
That being to see what numbers are invariant on k

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As in like
Given P_k = the set of additive primes derived via k terms, determining the set S where each element in S is also an element of P_k for all natural numbers k

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(P_1 is just ℕ)

static loom
candid mural
#

is discrete math hard

main elbow
#

if i start with [1, 5] in the set then i get two a(n+1) = 3a(n) + 2 and b(n+1) = 3b(n) - 2 in the set with a(1) = 9 and b(1) = 11

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which is kinda 3^n

main elbow
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but obv thats a total guess

zinc dock
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Actually

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Wait nvm

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I was gonna say "you can't represent the k+1th term in P_k" but that would make it an element of P_k

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So it's at least 1 and 2

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All numbers less than or equal to k are automatically in P_k by default as well

main elbow
#

oh right yes because P1 is N

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sure

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1 and 2

zinc dock
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This feels like a number theory problem (knows absolutely no number theory)

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3 is also in the set if we're not starting from 1

static loom
#

feels too closely related to goldbach, probably not easily doable

zinc dock
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Really?

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I mean it's involving "primes" but they seem relatively unrelated to normal primes

static loom
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I don't know what you're doing tbh

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like set of primes that isn't a sum of previous primes in the set?

main elbow
#

the set Sn contains 1, ..., n
the set Sn contains any number not expressible as the sum of n distinct elements of Sn

zinc dock
# static loom I don't know what you're doing tbh

Okay so
We define a set P_k to be the set of all natural numbers greater than one which cannot be created by summing k distinct elements of P_k
We're figuring out if any numbers are common elements of P_k for all natural numbers k

main elbow
#

i think its easy to prove that its just 1,2,3

static loom
#

the definition sounds too circular to me

main elbow
#

its a recursive definition yes

zinc dock
main elbow
#

here's how its stated on oeis for 3 term sum
a(n) = least positive integer > a(n-1) and not of the form a(i) + a(j) + a(k) for 1 <= i < j < k <= n.

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and for 2 term sum

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0-additive sequence: not the sum of any previous pair.

static loom
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I'm not sure this uniquely defines P_k though

main elbow
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howso?

static loom
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like there may be multiple self consistent definitions that satisfy that definition

main elbow
#

i think the 'least positive' part seen the 3 term def resolves that

zinc dock
# zinc dock It makes more sense if you think about it iteratively

P_2 is empty and we start at n = 2
2 cannot be summed from two elements nothing, thus 2 ∈ P_2
3 also can't be summed from two elements of P_2 since two elements don't exist, therefore 3 ∈ P_2
2 + 3 ≠ 4, therefore 4 ∈ P_2
But 5 is able to be summed from two numbers in P_2, that being 2 and 3
Therefore it is not an element of P_2

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And so on

static loom
#

doesn't smell right to me

zinc dock
static loom
#

How do you know that this defines a unique set: "a set P_k to be the set of all natural numbers greater than one which cannot be created by summing k distinct elements of P_k"

main elbow
#

by def start with 1, ...,n in the set
if you start with the empty set then the least positive integer that is not the sum of n distinct terms in the set is 1
then 2 then ... up to n because until you have 1,...,n in the set you do not have n distinct terms

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the least positive part is key

static loom
#

that's a different definition

main elbow
#

anyhow k+1 is not in Pk for any k>=2 because 1 and k are by def in Pk
therefore union Pk, k=1 to inf is {1,2}

zinc dock
main elbow
#

to answer you question about persisting values

zinc dock
#

But numerically they seem to give identical results

zinc dock
main elbow
#

oh wait lol brain fart moment

static loom
#

well I'm not trying to get on your case here I just didn't know what you were doing at all and still not sure I do lol

zinc dock
static loom
zinc dock
static loom
#

oh ok, I thought you were adding literal primes to the set if they weren't a sum of primes

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I think I'm on the same page now lol

zinc dock
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Lol

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Because with normal primes they're in the set of primes (we'll just call N because P is taken i guess) iff they cannot be represented as a product of at least two elements of N

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Doing "at least two elements" for adding instead of "specifically k elements" just gives you the powers of two but this seemed more interesting

main elbow
#

Pk contains 1, ..., k(k+1)/2 - 1

let X = union Pk, k = 2 to inf
1, 2 in X

know that for all k >= k' where k'(k'+1)/2 - 1 >= n, n in Pk
so want to know when n > k(k+1)/2 - 1
0 > k^2 + k - 2n - 2
(-1 + sqrt(9 + 8n))/2 > k

so n in X iff for all 2 <= k < (-1 + sqrt(9 + 8n))/2, n in Pk

zinc dock
#

👀👀

main elbow
#

we know that Pk has 1, ..., k(k+1)/2 - 1 becuase the smallest k-sum of elements in Pk is 1 + 2 + ... + k = k(k+1)/2

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so all numbers less than that must also be in Pk

zinc dock
#

Does that hold?

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Oh wait you said less than that

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Nvm

main elbow
#

to show that X is just {1, 2} we want to show that
for all n
exists k with 2 <= k < (-1 + sqrt(9 + 8n))/2
where n = a1 + ... + ak some 1 <= ai <= k(k+1)/2 - 1 and ai = aj iff i = j

#

it feels like that MUST be true

#

some kind of strong induction

#

but seems messy

static loom
#

I think we can do it, working on it

zinc dock
#

Surely you'd just have to prove that for some m, k+m is not an element of P_k

#

Because that would imply that no number greater than or equal to m is in the final set

#

And you could just individually do the rest

main elbow
#

i dont follow

static loom
#

I guess if it's gonna be easy for you to prove then we might as well generalize to something like whatever works $$\bigcup_{k\ge n}P_k = {1,2,\dots,\frac{n(n+1)}{2}-1}$$

fathom swallowBOT
static loom
#

something like that

main elbow
#

do you mean intersection ?

zinc dock
# main elbow i dont follow

If n is not an element of P_k for any k then n is by definition not in X
and if k+m is not an element of P_k then we can substitute k+1 into k
Thus m+1 is also not in X

main elbow
#

still not getting it

static loom
#

I think I see a way to do it

#

no nevermind lmao

zinc dock
# main elbow still not getting it

k + m is not in P_k for all k ⇒ (k+1) + m is not in P_(k+1) for all k
x is not in P_k for some value of k ⇒ x is not in X by definition

#

By induction
k + m is not in P_k for all k ⇒ (k+n) + m is not in P_(k+n) for all k

#

Thus
k + m is not in P_k for all k ⇒ m + n is not in X for n = 0, 1, 2, ...

#

I think

main elbow
#

there is no m such that k + m is not in Pk for all k

#

eventaully k + m < k(k+1)/2

#

and then k + m in Pk

zinc dock
#

Oh true

static loom
#

probably obvious fact, the only triangular number that can be in the set is 1 since P_k doesn't contain k(k+1)/2

main elbow
#

Define $a_i^k = i$ for $1 \le i \le k$ \ \
For $n \ge k$ define $$S_k^n = \left{ \sum_{j=1}^k a_{i_j}^k , \mid , 1 \le i_1 < i_2 < \dots < i_k \le n \right}$$
this is the set of all $k$-sums of the first $n$ terms of the sequence \ \
For $n > k$ define $a_{n+1}^k = \mathrm{min} \left{ \mathbb{N} \setminus S_k^n \cap \left(a_n^k, \infty\right)\right}$. In words this is 'the minimum integer that is not a $k$-sum of the first $n$ terms of $\left(a_i\right)$ that is greater than the $n$-th term'. \ \
Define $P_k = \left{a_i^k , \mid , i \in \mathbb{N}\right}$ and $X_n = \bigcap_{k \ge n} P_k$

static loom
#

can we write a formula for the next element in P_k after k(k+1)/2 -1

main elbow
static loom
#

it would be nice, then we could try to say for some n, it lies in one of those "windows"

zinc dock
#

This is a lot cleaner than i thought this would be

static loom
#

between k(k+1)/2-1 and the next element

#

or at least, that's the approach I'm thinking of trying

main elbow
#

i think it might be k(k+1)(k-1)/2 + 1

static loom
#

for k=3 it's 13 does that work

main elbow
#

yes

static loom
#

nice

main elbow
#

works for k=4 too

#

here was my thinking

#

we have 1, ..., k(k+1)/2 -1 in the set

#

if we think of starting a1, ..., ak as 1, ..., k we know we get k(k+1)/2

#

we can move ak up one at a time through to k(k+1)/2 - 1

#

and because we move ak by 1 each time we will not miss any numbers

#

then we can move a(k-1) up to k(k+1)/2 - 2

#

and so on until we get to a1 at k(k+1)/2 - k

#

and so we have found sums all the way up to k(k+1)/2 - k + k(k+1)/2 - (k-1) + ... + k(k+1)/2 - 1

#

and that is the maximum sum we can achieve with numbers available

#

so the number after that must be in the set

#

and that sum evaluates to (k-1)k(k+1)/2

zinc dock
#

My pattern recognition is telling me we should be putting this in terms of permutations

zinc dock
static loom
zinc dock
main elbow
zinc dock
#

k(k+1)/2 is just k+1 choose 2

#

We're dealing with combinations of numbers in a way so it seems relevant partially at least

static loom
#

at this point I think we just need to say for f(k) = k(k+1)/2 - 1 and g(k) = k(k+1)(k-1)/2 + 1 that we need to show g(k)-f(k+1) is positive and that will show that the lower bound of the k+1 "window" overlaps with the upper bound of the kth window.

#

so we get coverage for all n

#

since g is cubic, it's a finite check

#

we know it eventually overtakes the quadratic

zinc dock
#

Thus for all integers k > 2 it must be positive

static loom
#

yeah

opal lichen
#

hello

static loom
#

we need the gap to be larger than 1 after a certain point which is the finite check I mentioned

#

since that ensures we're really grabbing integers, we only care about it after 2

#

but I think this generalizes to the other case I mentioned earlier too

zinc dock
#

Yea

main elbow
#

if exists k s.t. k(k+1)/2 <= n <= (k-1)k(k+1)/2 then n is not in Pk and thus not in X
certainly exists k st k(k+1)/2 <= n < (k+1)(k+2)/2 and (k-1)k(k+1)/2 >= (k+1)(k+2)/2 for all k >= 3

so we need to check 3 <= n < 6 i.e. n = 3, 4, 5
3 is not in P2, 5 is not in P2
4 is in X
X = {1,2,4}

#

and yeah i think this result also shows your generalisation

#

nice stuff !

static loom
#

cooool teamwork makes the dream work

#

🤣

main elbow
#

might write this up more formally quite a fun series of results

static loom
#

also kinda reminds me of the chicken mcnugget theorem

main elbow
#

oh yeah

zinc dock
#

I have never heard of that theorem but that sounds beautiful

main elbow
static loom
#

I'm thinking to force the distinctness we can subtract 1, 2, ... from each set of "stars" between the "bars"

#

past that just spitballing

#

I don't think that's sufficient to get it to work either except for special cases

zinc dock
main elbow
#

i think it only had three because i started with [2,3]

#

if you start with [1,2] then it would just be powers of 2

zinc dock
main elbow
#

1 + 2 = 3 and is the biggest sum you can do so then 4 is in

zinc dock
#

Yea

main elbow
#

if you think about binary any these are 001, 010 and 100

#

so if you all any length sums you can get all binary number that are 3 digits

#

then the next number you cannot get is 1000 which is 8

#

and so on

zinc dock
#

Yea
Any number with more than one 1 in it could only be gotten by addition, so they're excluded
Everything else can't be

main elbow
#

these are when you allow sums of length at most h

#

and you can see with each increase you approach the sequence of powers of 2

coral terrace
#

who is Eliza

#

who is apoplecyappendix

#

isnt that your friend or something

#

what lol

#

thats weird

#

identity theft

neat lintel
#

pretty weird

#

right

coral terrace
#

hmm

#

elaborate troll perhaps

neat lintel
coral terrace
#

no but seriously

#

is this like

#

real

#

why would someone evem do that

#

if you dont know them

#

whats the point

neat lintel
#

maybe it’s someone u know trolling

coral terrace
#

probably

#

i mean the other option is a little more terrifying

#

or just like

neat lintel
#

very suspicious

coral terrace
#

her pronouns are she/her so im guessing its a woman

#

they didnt bother having the same pronouns as you

#

if they were trying to copy your account

#

again most likely someone you know pulling your leg

wooden falcon
#

In certain places I’ve heard a lot of stereotypes associated with like category theory/type theory/functional programming people being trans. Does anyone know where these stereotypes came from?

bronze pelican
eternal crow
#

@neat lintel weird, i had u in my dream for the 1st time ever in my life

neat lintel
#

Omg

#

I just woke up

eternal crow
#

We were riding a train/bus

#

Wow

neat lintel
#

Oh

eternal crow
#

Me too like about 15min ago

neat lintel
#

Wow

eternal crow
#

I kinda forgot the details but u were trying to avoid to pay

neat lintel
#

I see

eternal crow
#

It's like magic no one notices you

#

And u were in the back part of the train

#

And as the dream goes on, we were now on a bus instead of a train

neat lintel
#

I see

eternal crow
#

And when the conductor came I paid my fare and finally he started to notice you but you still can't pay I forgot why so I just paid for you. My payment was a whole bill and he hadn't given the change yet so he charged both of us for it

neat lintel
#

Oh

brave vapor
#

Hey I know this isn’t math related but can someone help me solve a Highschool level chem question in DMs?

eternal crow
#

Right here

brave vapor
eternal crow
#

Oh an image

brave vapor
#

I gotta do verification and shi not dealing with that

uneven tinsel
#

Going to select option A for all the questions hoping to get at least 45/100

eternal crow
uneven tinsel
#

Maths

north topaz
uneven tinsel
#

Will choose option A for this one

verbal karma
#

that's why I never have mcq question on my exam or if I were to give one, it will be either 30 choices or just 5 choice but 1 question.

pulsar finch
#

what would be a classic example of proving something by PHP? is social network a clear example or is there an essier one

#

(every user needs to he friends at least with someone I think)

raven plaza
#

Not "classic" but fun problem:

Consider a size pq+1 poset. There is a size p+1 chain or a size q+1 antichain.

#

||Apply PHP on the function that sends x to the length of the longest chain starting at x||

pulsar finch
#

this was what I meant btw

uneven tinsel
wheat merlin
#

HELP

#

I'm stupid as fuck rn

#

math crashes in 1month

neat lintel
#

what you think is harder:
quals problems or IMO problems?

raven plaza
#

IMO IMO qual as harder than quals

neat lintel
#

are you sure?

lusty atlas
#

is anyone here taking/taken RA courses?

pulsar finch
#

why not ask the question directly

lusty atlas
#

my questions are more the progress of the person when he took that class, I'm having a hard as a freshman and I wanted to ask others what was their progress like with assignments and such

lusty atlas
fresh comet
# lusty atlas it's not a 1 liner

Ask it anyways. Lots of people here have taken or are taking RA courses, but none of them can answer any questions or address any concerns you might have because none of us know what your question/concern is.

pulsar finch
#

eventually you would need to write it

tall solar
#

Anyone have an opinion on Zorich's analysis I & II?

#

I've been looking for a thorough & rigorous RA book. There are many, but life is brief 🙂

pulsar finch
#

Idk if rigurous but I personally like The big book of real analysis, I have checked zorich but only slightly, I havent taken ra yet formally so I can’t say

tall solar
#

Seems nice, thanks for sharing

river moon
#

it's a standard analysis text in eastern europe

#

it's not the toughest of the books, but should feature everything you care about in real analysis

tall solar
#

I see. What's an example of a tougher book?

pulsar finch
#

well I think Amann and Escher anal I and II is pretty rigurous but idk

neat lintel
pulsar finch
#

you can prolly get more rigorous I guess, havent taken ra yet

river moon
tall solar
#

Alright, thanks a bunch!

uneven tinsel
pulsar finch
#

which book explains hairy ball theorem

pastel current
pulsar finch
#

UNC?

pastel current
#

Like Lee's Intro to Smooth Manifolds

pulsar finch
#

is lees intro a well regarded introductory reference?

pastel current
#

I personally think it is very detailed

#

too detailed for a novice, but I appreciate detail

#

Taylor's book is too little detail, but it is useful as a guide

#

kind of like a list of important/cool topics

crimson vine
bright hill
#

@wild plinth I can access the article ig

#

do you want the html file?

wild plinth
#

yes! or pdf

#

i can only see two paragraphs of it

bright hill
#

it's not that big of an article tbh

wild plinth
#

thanks a lot! that's a saver

bright hill
#

maybe I can't see all of it either

bright hill
wild plinth
#

and how is the journal? do you have subscription?

bright hill
#

uh

#

it doesn't really ask me to subscribe

#

wait

#

lemme test something

#

yea, it was my adblocker LOL

wild plinth
#

i see, i was able to see the article as you sent be at the first time, but then i refresh the web, it disappear

#

but that's an inspiring article!

bright hill
#

it's a

UB8wD9P.png
#

opening in a pirvate tab does the trick ig

wild plinth
#

oh... didn't know that

sonic sentinel
#

thinking about that time i was in school in the chem lab with a teacher and like 15 other girls (p.e. teacher was absent, most of the boys went up to the library and i wasn't allowed to switch rooms for some reason) and, from what i gathered, the girls were watching disturbing horror movie scenes or something like that?

#

my reasoning is mostly based off of one girl that bragged about watching jigsaw when she was eight or something like that (and similar comments from her, i forgot what she said tbh)

#

and its like... what

#

why is "watching disturbing horror movies" a personality aspect they specifically only show when there aren't boys around

#

why did the girl watch jigsaw when she was eight 😭

#

was i even reading the situation correctly????

crimson vine
#

who bets how many dollars 50 coins of my country value?

sonic sentinel
fresh comet
#

If the world was ending tomorrow, what would you do today?

raven plaza
#

Commit minor felonies

latent edge
ancient lance
steep moth
#

if I was aware, why tell lmao

steep moth
north topaz
steep moth
#

it make me sad

raven plaza
#

The bearlain reacts

north topaz
#

why the reacts

steep moth
#

did you know that Michael Rosen Beichton, also known as "Narwhal Knight" used the pointy thing of a narwhal to impale his coworker in the arctic

He was last seen pieced in 10 places, all fatal wounds.

fresh comet
#

not a bad one, but it makes me feel sad

north topaz
#

you asked a sad question

#

hmmph

fresh comet
#

it didn't have to be sad!

north topaz
#

it's worse than "if you were going to die tomorrow"

#

cause if the world ends everyone dies

fresh comet
steep moth
#

hey

#

i fixed a manual fire bb gun

#

like you cock the thing and fire in between shots

north topaz
#

yeah if the world really were to end tomorrow I would be peaceful to everyone

#

it would be bad to argue

steep moth
north topaz
#

yeah like humans have done a lot of harm to the planet

ancient lance
#

sorry

steep moth
#

if im going down the mosquitos are coming with me

north topaz
broken marsh
#

Does anyone come to communicate

uneven tinsel
#

Where

slow pawn
#

@north topaz whose fyre

pulsar finch
#

no natural number is equinumerous to a proper subset of itself?

#

does equinumerousity imply same cardinality?

#

does it imply injectivity and surjectivity?

#

I was just looking for a pidgeonhole definition but how are the equivalence relations involved?

north topaz
raven plaza
sly jungle
#

How hard is the ODE section in Kreyszig Adv Engg Maths, if anyone's done it? I mean, is it mostly plug and chug or harder? Wanna plan how long it might take....

bright hill
raven plaza
#

Commit augmented felonies

rocky shuttle
deep mango
#

Hmm

#

Actually i think I trust myself to survive the end of the world, so maybe just a lot of DMT

jagged forge
#

i would spend time with my family

surreal sapphire
#

lmao

#

i dont think those drug interactions are a smart idea

#

better to focus on one

rocky shuttle
deep mango
#

also not every single

#

it would be like

#

cocaine -> heroin -> dmt i think? thats probably it

surreal sapphire
#

heroin last would be smarter

#

both cocaine and dmt do not last very long

#

i heard!

gritty crater
rocky shuttle
#

And maybe you notice what my pfp is

gritty crater
deep mango
#

I figured dmt would be a long thing

#

Oh well

surreal sapphire
#

pure dmt is about 30 mins maybe

#

if you mix it with some inhibitor (ayahuasca), it lasts longer

deep mango
#

It's not like I know how the world is going to end. Id rather be pretty out of it when it does

surreal sapphire
#

MAO inhibitors

#

its actually quite interesting

#

you can (often legally!) buy the mimosa plant, which contains dmt

rocky shuttle
surreal sapphire
#

but you have to consume beta carbolines with it

#

otherwise the dmt wont enter the bloodstream and thus brain

deep mango
#

Thanks loch

surreal sapphire
#

though to note buying the plant for dmt is illegal

#

it has other uses

#

there was a guy in germany who imported like 20kg of mimosa root monthly

#

claimed its for "dying shirts"

#

which is a use

#

but police got suspicious

#

he kinda ruined it for everyone

solid snow
#

dmt being illegal is literally NO FUN ALLOWED

deep mango
#

I guess several world end scenarios begin with police states

#

Maybe I should be careful

gritty crater
rocky shuttle
gritty crater
rocky shuttle
stone saffron
gritty crater
rocky shuttle
ocean harbor
#

kawaii

patent bone
#

hlo

#

i am new to this surver

ocean harbor
#

welcome

patent bone
#

thanks

#

who are you

ocean harbor
#

a random person sotrue

#

jk im akira

patent bone
#

boy or girl

#

??

ocean harbor
#

its readable next to my name

patent bone
#

a not kinda

#

it would be better if you tell

ocean harbor
#

my roles here are not fake

#

also i always get my name is a boy name and pfp

#

doesn't mean im a boy

patent bone
#

so you are a girl

ocean harbor
#

yes

patent bone
#

ok

#

so what do you do in this surver

ocean harbor
#

math

#

help people from math and you also learn from others

patent bone
#

ok so can you help me in maths

ocean harbor
patent bone
#

what are unit digits

ocean harbor
#

what does that mean

patent bone
#

that is what i am asking

ocean harbor
#

you mean a math help?

patent bone
#

yes

ocean harbor
#

well i told you where to get help

#

I'd like to help you but i got meeting in 5 minutes lol

#

and show them the full content

patent bone
#

ok fine thanks

gritty crater
uneven tinsel
neat lintel
#

@neat lintel

#

hi

#

..

patent bone
#

can you tell me what is unit digit

neat lintel
#

u know i dont have much time... i got an exam to prepare for

neat lintel
patent bone
#

8

#

you

neat lintel
#

11

#

but u should know about unit digit....u are in 8 th grade

patent bone
#

it is new

neat lintel
#

u know about digits?

patent bone
#

this is why i asked

#

yes

neat lintel
#

and about places...like unit place tens place or so?

patent bone
#

yes

#

ones tence hundred etc

neat lintel
#

so the digit at unit place is what we call unit digit...its just a short phrase for that

patent bone
#

ok thanks

#

can i ask another question

neat lintel
#

eg in 1234567 the unit digit is 7

neat lintel
#

hurry

patent bone
#

in my book this is the question

neat lintel
#

yes tell me about that....

#

( presonally i hate asking for help on help channels)

patent bone
#

what will be the unit digit of the square of the following number

#

81

#

272

patent bone
neat lintel
#

no i hate the help channels

neat lintel
patent bone
#

yes

neat lintel
#

but would u like to calulate the square of 4567398293?

patent bone
#

ok let me see

neat lintel
#

no

#

u would not

patent bone
#

why tho you asked for it

neat lintel
#

see...maths is not just calculation

patent bone
#

ok

neat lintel
#

u would have to dive a little deeper

#

give me any no.

patent bone
#

81

neat lintel
#

so canu write 81 as 80+1?

patent bone
#

i got this method mam told it to us

neat lintel
#

dont learn it...

#

feel the method hear me first

patent bone
#

ok

neat lintel
#

see u have to argue that why does it happen..feeling dont help in math solid proves and reasoning do

#

lets write a no. AB where A and B are its digits

patent bone
#

ok

neat lintel
#

now u can write it as A*10 + B

patent bone
#

a multiply syne it is ma

#

na

#

sorry

neat lintel
#

...in python we use * (asterisk for multiply sign)

patent bone
#

ok

neat lintel
#

can u write it as i told?

patent bone
#

yes i did

#

a * 10 + b

neat lintel
#

now u know about variables and algebra?

patent bone
#

yes

neat lintel
#

so i am gonna tell u a identity about square of (a+b+c+d+e+f...and so on)

#

i mean square of sum of any no. of variables

patent bone
#

ok

neat lintel
#

u know how to do (a+b)? tell me

patent bone
#

like

neat lintel
#

a^2 + 2ab + b^2

#

no?

patent bone
#

than

#

actually sorry for taking your time

neat lintel
#

...ok i know i am boring

#

just lemme tell u straight ahead

#

(u will learn all this whenu grow up)

patent bone
#

br

neat lintel
#

--> just square the unit digit and report its unit digit

patent bone
#

mean what you were telling me was for grown ups

neat lintel
#

like in 834579794...do square of 4 then u get 16...6 is ur answer

patent bone
#

back to my q

#

so square the no

neat lintel
patent bone
#

and find its ones digit

#

mean eg 81

#

81 * 81

neat lintel
patent bone
#

6521

neat lintel
# patent bone mean eg 81

for unit digit of square of 81...just square 1...u get 1...tell me the unit digit of this no. that will be one

patent bone
#

so 1 is the ans right

neat lintel
#

yes

patent bone
#

ok thanks

#

are you a boy or girl

neat lintel
#

...whyd u ask?

patent bone
#

just like that only

#

wana be friends

neat lintel
#

cant u see my pronouns?

patent bone
#

you can help me in maths

neat lintel
#

...sorry to say but i dont find enough time to use discord

#

and i am thinking of leaving discord soon

#

can i ask u something?

patent bone
#

ok it fine

#

thanks for help

#

yes

neat lintel
#

---> U have a gf?

patent bone
#

no

#

i am at 8 class

#

wth

neat lintel
#

... koi ni... but whenever u get one just take good care of her... maybe she can change u in a way u like... (i am just so happy todya)

north topaz
#

bruh

neat lintel
#

hi

patent bone
#

did someone leave you

quasi moat
#

hi

north topaz
#

technically you can have a girlfriend in 8th grade

patent bone
#

rip me bro

#

i will never in my entire life

quasi moat
#

no point to have one in high school gotta lock in

fervent oyster
#

I advise against it really

north topaz
#

just saying technically

fervent oyster
#

😭

patent bone
#

same

neat lintel
quasi moat
fervent oyster
patent bone
#

i dont want to have one

#

it is my choise

quasi moat
neat lintel
quasi moat
#

what yr u in

neat lintel
#

i think i should have joined a philosophy server

patent bone
#

me

neat lintel
quasi moat
#

if i were u avoid having a girlfriend from like past yr 7 or 8 u need to lock in

#

you have 1 year left

#

then u can do wahtever u want

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just work ur ass off now then ur good

patent bone
#

i am 8 so this is kinda adult talk so i am leaving thankyou

fervent oyster
quasi moat
#

wthhhh

fervent oyster
#

don’t ping mods yet

fervent oyster
quasi moat
#

i mean its good uve joined a maths discord at 8 i guess

neat lintel
#

a gf is not a adult talk

fervent oyster
neat lintel
neat lintel
fervent oyster
neat lintel
neat lintel
#

soture

quasi moat
neat lintel
#

true

fervent oyster
quasi moat
#

i wouldnt recomend tho still

fervent oyster
#

@patent bone edit your message so it doesn’t look like you’re actually 8 😭😭

quasi moat
#

fr

neat lintel
fervent oyster
quasi moat
#

if so youll be fine

#

you can manage both

neat lintel
#

...it seems to me yes

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cos i have to work hard... Ihave a purpose in life

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and it is her

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she is my purpose

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and if i cant get to spend my life with her... if i cant feed her... if i cant make her dreams true myself... then there is no purpose of living

quasi moat
#

i wouldnt look at it like that

neat lintel
#

and basically this is how i see life as

quasi moat
#

dont 😵 if she doesnt like u at a certain point u have other purposes aswell

neat lintel
#

... then (We cant talk about suicide in this server)

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..

quasi moat
#

alr mb

neat lintel
#

but yes i mean it.... i cant live without her

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literally

graceful flower
#

how old are you dude 😭

neat lintel
#

actually i am younger than what it seems...15

#

but still i have experienced too much of life

quasi moat
#

mate im 15 how th u in yr 11

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genius

graceful flower
quasi moat
#

and im a year infront of my age

neat lintel
#

i am immature i know... but sometimes i just cant let things go

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i wanna tell her how much i love her

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but when i see her... i just forget everything

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sometimes i just wanna hug her and cry

quasi moat
#

have u joined a philosophy server yet ?

neat lintel
#

no...would u recommend any

quasi moat
#

no idk about philosophy

#

ik maths

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(shocker)

neat lintel
#

what year u in?

quasi moat
#

10

neat lintel
#

great

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i am tired now

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bye i think i should go

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prepare for test

quasi moat
#

ye bruh its like 12 oclock where i am

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im down under

neat lintel
#

great

patent bone
#

a lot happend when i was not there but things settled

#

nice

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see you later by

quasi moat
#

bye*

uneven tinsel
#

Reality <—— 2 light years ——> People

magic hornet
#

Theres never a help channel open.....

vocal vessel
#

There’s 5

vernal token
neat lintel
vernal token
# neat lintel Nice pfp

It's not defined though. We don't know what sigma is [\sum_{n=0}^{\infty} \int_1^{\infty} \frac{e^x}{\varsigma(x)} \dd x]

#

I should also change the d from a $d$ to a $\dd$

fathom swallowBOT
neat lintel
#

you need more context

vernal token
#

I guess that's better