#serious-discussion

1 messages · Page 47 of 1

vale sapphire
#

how about 1x1

vast surge
vale sapphire
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shit onnnnnnnnnnnnnnnnnnnnnnnn

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how to get shit bitches

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ssssssssssssss

light needle
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i think u broke em zorn

narrow thicket
vast surge
#

Does that mean he's coming back from the gas station sometime soon?

fair mural
#

that’s not really that much i would say

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i have like 500 hours on a game i’ve played for like 5 months

balmy maple
#

This is a short, animated visual proof of the two-dimensional Cauchy-Schwarz inequality (sometimes called Cauchy–Bunyakovsky–Schwarz inequality) using the Side-angle-side formula for the area of a parallelogram. #math​ #inequality ​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #algebra #areas #mathema...

▶ Play video
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the music is making me fucking lose it

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"free clash of clans gems (WORKING 2012)" type beat

proud olive
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neat video, but yeah the music just completely ruins it

arctic cairn
#

Does x^2 count as a variable

river moon
#

yes

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x^2 + x^4 is a quadratic polynomial in terms of x^2, because by substitution t = x^2 you can see it's equivalent to t + t^2

torn willow
balmy maple
#

I have never been more engaged with studying, hats off to his son

neat lintel
# balmy maple the music is making me fucking lose it

ain't no way that music ain't ironic loooool. I think dude like just made this video and then for music he just wanted to show off what music he listens to because if you don't like it seems you can mute it without losing anything

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sometimes when I make videos on YouTube demoing some program I coded I leave my music running in the background if I know it won't be copyrighted

torn willow
#

The guy just asked his son to suggest music

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and this is what his son gave

deep mango
#

Loool

brittle socket
#

Hi ricey

deep mango
#

Hello grass

brittle socket
#

Two of my books will be arriving in two weeks time pandaHugg

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Then my copy of Schroder is gonna come late jan

deep mango
#

Exciting

arctic cairn
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worryeyes I see

wooden flax
#

dopium

severe swallow
#

has anyone else in here tried to talk with chatgpt about math?

rocky shuttle
# severe swallow has anyone else in here tried to talk with chatgpt about math?

As an artificial intelligence, I do not have the ability to participate in online communities or join Discord servers. However, I am able to answer questions about math and provide information and explanations on a wide range of mathematical concepts. If you have a specific question about math that you would like to ask me, I would be happy to try to help. Just let me know what you would like to know, and I will do my best to provide a helpful and accurate response.

rocky shuttle
# severe swallow

While it can be helpful to ask for help when you are struggling with a math problem or concept, it is also important to try to work through problems and challenges on your own as much as possible. This can help you to develop your problem-solving skills and deepen your understanding of the material.

neat frost
#

Can chatgpt do TeX?

rocky shuttle
neat frost
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Omg okay

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Ask it for a macro which creates lists in TeX

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Start with something easy

severe swallow
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now tell me fake AI

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what is the answer

neat frost
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Xan has left us. Chatgpt is dead.

severe swallow
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chatgpt is alive and well

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it's currently trying to give me an asymptotic bound for the expected injective norm of a gaussian tensor

languid haven
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Do they just tell you the answer

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I'm not tryna have a tutor rn

severe swallow
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yesn't. It provides a proof, but sometimes the proof is inacurrate lmao

rocky shuttle
neat frost
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No

rocky shuttle
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a bit lengthy answer

neat frost
#

NO

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that's not what I MEANT

rocky shuttle
neat frost
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I meant a list like in programming

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Indexable etc

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Okay how about a macro which gets the length of a string?

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See how it can fuck that one up

severe swallow
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you know, I'm somehow more impressed by the fact that the AI produces me wrong proofs instead of saying it doesn't know.

rocky shuttle
neat frost
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Is there more to the code?

rocky shuttle
#

\newcommand{\mystringlength}[1]{%
\countchars{#1}%
}

\newcommand{\countchars}[1]{%
\countcharshelp{#1}\0
}

\newcommand{\countcharshelp}[1]{%
\ifx\0#1\relax\else\advance\mycharcount 1\countcharshelp\fi
}
\newcount\mycharcount

neat frost
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Omg

languid haven
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Bruh the math people not even helping

neat frost
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Hmm

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Not quite I don't think

rocky shuttle
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I'm on my phone and too lazy to copy the whole answer

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Do it yourself smh

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It is entertaining though

neat frost
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Yeah it doesn't work, but it is close

#
\newcommand{\mystringlength}[1]{%
  \countchars{#1}%
}

\newcommand{\countchars}[1]{%
  \countcharshelp#1\0
}

\newcommand{\countcharshelp}[1]{%
  \ifx\0#1\let\next=\relax\else\def\next{\advance\mycharcount 1\countcharshelp}\fi\next
}
\newcount\mycharcount

\mystringlength{hello}
\the\mycharcount
fathom swallowBOT
neat frost
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I altered it a bit

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\countchars is unnecessary, but otherwise it's pretty close

rocky shuttle
neat frost
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This is actually really cool damn

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,ctan stringstrings

fathom swallowBOT
#

The package provides a large and sundry set of macros for the manipulation of strings. The macros are developed not merely for cosmetic application (such as changing the case of letters and string substitution), but also for programming applications such as character look-ahead, argument parsing, conditional tests on various string conditions, etc. The macros were designed all to be expandable (note that things such as \uppercase and \lowercase are not expandable), so that the macros may be strung together sequentially and nested (after a fashion) to achieve rather complex manipulations.
​ ​ ​ ​ ​ ​ Sources: /macros/latex/contrib/stringstrings
Documentation: README, Package documentation
​ ​ ​ ​ ​ ​ Version: 1.24
​ Contained in: TeX Live as stringstrings, MiKTeX as stringstrings
​ ​ ​ ​ ​ ​ ​ Topics: Text manip
​ ​ ​ ​ ​ See also: getargs
Read more at CTAN page of the package.

neat frost
#

Got that right too

rocky shuttle
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A bit unbelievable and eerie

neat frost
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Yeah it's really cool how accurate it is

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Also why was it so sudden?

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There was no buildup, they just released chatgpt one day it seems

rocky shuttle
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It will turn out that technology is already that advanced and half of the people here are AIs

neat frost
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Beep boop?

severe swallow
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what a casual scrub smh, artificial intelligence, more like artificial stupidity amirite?

rocky shuttle
#

@neat frost btw it doesn't only speak English, any questions you have in your language?

neat frost
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English is my language catscream

rocky shuttle
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...ok

neat frost
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Like I was born in the US I just moved

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But yeah sure

rocky shuttle
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I see

neat frost
#

מה דעתך על הממשלה הנוכחית?

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What's your native language Xan?

rocky shuttle
neat lintel
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hebrew?

severe swallow
neat frost
rocky shuttle
rocky shuttle
neat frost
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The answer is like "yeah I can't give you an answer. I am mashin."

rocky shuttle
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And what were you asking?

neat frost
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Its thoughts on our current government

rocky shuttle
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Oh lmao

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It rarely has an opinion, but if you ask it what a certain kind of person would think about it, then it'll give better answers I think

neat frost
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Oh

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I like unopinionated people

mint canopy
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Please laugh

neat frost
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catKing is a better reaction than a laugh

mint canopy
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Oh is this an opinion of yours?

neat frost
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Anyone can get a laugh, it takes someone truly special to get a catKing

mint canopy
#

Pathetic. Smh.

neat frost
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No it's a fact

neat frost
mint canopy
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Noooo nnooooo pandaOhNo

storm sage
brittle socket
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Lmao

granite barn
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what's the general consensus on self promo here? I wanna share my math stream here but don't wanna push on any rules/be annoying

zealous garden
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I don't really have an opinion on opinionated people

static loom
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lol

torn willow
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Opinionated people are good iff they agree with me

fiery sail
#

The help channels are bopping up and down and disappearing when I select one. Is everyone experiencing this? Makes it hard to keep track of which I've checked to see, if my skillset fits

sharp mulch
fiery sail
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Oh thought that was the category name for the help channels

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Haven't seen that discord function before

sharp mulch
#

The category name for the occupied help channels is help channels occupied or something like that

neat frost
jovial ember
#

rak bib

rocky shuttle
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chm nky

split island
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chm nky

neat lintel
#

chm nky

brittle socket
brittle socket
deep mango
#

rak bib

split island
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Hi grass

neat lintel
#

Hi kirby

split island
#

Flandre Scarlet

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I wish I could have found a Flandre fumo

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I found a Reimu one tho

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So worth it anyway

neat lintel
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Same here

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Nice

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Indeed

split island
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If you camp amiami.com, you’ll probably be able to find one for not hundreds of dollars

neat lintel
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Probably...

split island
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They have Patchouli and Alice in stock rn….

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And Marisa..

neat lintel
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I don't have patchouli

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;w;

split island
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I shall not spend so much money

sharp mulch
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Does mosque = masjid

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Ok

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Mosques all face towards Mecca right

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And the mosque in Mecca faces towards Medina?

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Or Jerusalem

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Oh sure

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But don’t they have the wall nook inside that shows which direction

brittle socket
brittle socket
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Enderton is my introduction to Algebra whatcanisay

sharp mulch
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Why is there a theorem 5ZG

lavish kayak
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Means it can monitor itself for truthiness somehoe

brittle socket
# sharp mulch Why is there a theorem 5ZG

Oh that's because for this particular chapter (chapter 5), the Z here represents the section on (constructing) integers. While the G here is the theorem numbering for this section on integers. So, Theorem 5ZG means the 7th theorem in the section of integers in chapter 5.

#

In other chapters idt there's this 'intermediary alphabet'

brittle socket
#

Perhaps why the author went with this here is because there are like 33 theorems in this chapter and there aren't enough alphabets. Or he thinks its easier to reference with that 'intermediary alphabet'.

sharp mulch
brittle socket
#

Just out of curiosity, what's particularly weird tinktonk

woven whale
#

please ping me when replying to my messages

brittle socket
#

Oh sorry

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Not everyone wants to be pinged when I reply so I turn it off by habit

cold needle
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Bruh

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don’t ghost ping people

#

o

sharp mulch
cold needle
#

O

#

alpine kindle
#

sharp mulch
#

T

fathom swallowBOT
sharp mulch
#

Sorry, but upon close inspection, this differs from a circle by 0.2%

fathom swallowBOT
midnight crystal
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If you could only take two additional classes after a first semester in analysis and a first semester in abstract algebra, which two courses would best prepare you to self study more math in the future

sharp mulch
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Have you done linear algebra

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Hmmm

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It depends on what sort of analysis class it was

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But I'm tempted to say a topology class

vast surge
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One of my big regrets is that I haven't been able to take a complex analysis class, because that's useful and comes up all over the place. So maybe consider taking complex, if your school offers it?

rocky shuttle
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One of my big regrets is that I haven't been able to take a measure theory class because that's useful and comes up almost everywhere.

bright hill
#

Wanna do measure theory together? sotrue

rocky shuttle
deep mango
#

surpass slurp

rocky shuttle
deep mango
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slurp is reading royden analysis

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which has measure theory

rocky shuttle
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ah

deep mango
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idk if that's the book id pick though

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i'd probably pick folland

rocky shuttle
rocky shuttle
deep mango
#

that's a well-liked one

vast surge
rocky shuttle
vast surge
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Then start reading books that already assume a knowledge of measure theory and sort of pick it up as you go

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That's how I did it

rocky shuttle
#

I kinda already know some of the results in introductory measure theory (Caratheodory, monotone convergence theorem, dominated convergence theorem)

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I just lack a lot of confidence because I never did the proofs and exercises

vast surge
#

What text did you learn those results in? You can try to do the exercises from that text to build up confidence

rocky shuttle
neat lintel
#

i am turkish student

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exams are very hard

vast surge
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Oh well then I can't help you that's basically what I did too

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(not diff geo, but recaps in other texts)

deep mango
deep mango
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rudin PMA measure theory chapter is notoriously bad

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folland does stuff in generality and does it in the correct order IMO

rocky shuttle
neat lintel
#

my math exam is 100/92 😄

deep mango
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damn

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nice

neat frost
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Gobble gobble

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Good morning ryc

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Hewwo xander

neat lintel
#

in turkey notes

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my notes

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exams

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biyoloji= biology

rocky shuttle
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\pagenumbering{gobble}

neat lintel
#

fizik= physic

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matematik=math

neat frost
#

Latex moment

neat lintel
#

kimya=chemistry

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yabancıdil=english

vast surge
rocky shuttle
#

XanTeX will be born soon

neat frost
#

Also turns out there's a major bug with my package 👀

neat lintel
#

yes

rocky shuttle
deep mango
#

contents of folland

neat frost
neat lintel
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LOL

deep mango
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(this is loss)

neat lintel
neat frost
#

Tbh I'd be willing to try out XanTeX

neat lintel
#

good/bad

deep mango
neat frost
#

Ryc is a physicist

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Ryc stfu stop lying ffs

vast surge
neat frost
#

Nothing to be ashamed about

deep mango
neat lintel
#

Shall I show you the exam question in Turkey?

neat frost
#

flonshed thanksie

neat lintel
#

university exam

deep mango
#

Sure

neat lintel
#

ok

deep mango
#

Xander was on Survivor 41

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He's really cute

neat lintel
#

i translate english ok ?

deep mango
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Ok

neat frost
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We're learning about skeletons in image processing

neat lintel
#

or math no problem

neat frost
#

Spookie scary

rocky shuttle
#

built-in package for better 3D visualization than tikz / pgfplots

neat lintel
#

math problem

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in universty exam

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:/

vast surge
neat lintel
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its example

neat frost
neat lintel
#

i show

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i dont need help

neat frost
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Also tikz has decent 3d

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Definitely not

deep mango
#

look at him

neat frost
neat lintel
#

lol

deep mango
#

his hair is so perfect all the time

rocky shuttle
neat frost
#

Who dat

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Xan doxxed?

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Omg

deep mango
neat frost
neat lintel
neat frost
#

Noice yohan of your mom

rocky shuttle
neat frost
#

Name is very familiar

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But i don't remember

rocky shuttle
neat frost
#

Oh LaTeX shithead

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Wow I always assumed it was a woman

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"Leslie"

vast surge
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Leslie is a man's name

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Leslie Nielsen, etc.

neat frost
#

Also a woman's name

neat lintel
#

want physich problem

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????

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why

neat frost
#

To Jill:
For your books and brochures.

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Wtf

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I added all those spaces and I removed them

deep mango
neat frost
deep mango
#

wrong

neat frost
#

Bad taste ryc

deep mango
#

you don't get it

neat frost
#

Correct

vast surge
#

He looks like the sort of guy who either doesn't do drugs, or who does a lot of drugs, and either way it's a large part of his personality.

neat frost
#

There's nothing to get

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I'd pay to beat him up

deep mango
vast surge
#

Yeah that makes sense, from the two pictures of him I've seen

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He also looks like a devout Christian who is simultaneously super into new age stuff

deep mango
#

to be fair this is how he looked before the game started

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a lot less like

vast surge
#

So a lot less like a hippie

deep mango
#

a lot less a lot of things, but mostly just a lot less hot

vast surge
#

Does his dad own a boat?

deep mango
#

i have no idea

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he went to UChicago for CS

vast surge
#

Because in that last picture from before the game he looks like the kind of guy who always talks about how his dad owns a boat

deep mango
#

so he's probably wealthy

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are you seriously reading the tex book

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A texnician

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a texromancer

vast surge
#

@broken crown ryc is trying to steal your thing

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Oh whoops that was a different JohnDS

deep mango
#

Lol

vast surge
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I actually remember when that other JohnDS joined the server. It was weird

deep mango
#

oh my god

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lmfao

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i remember that

neat frost
#

The first few chapters are not interesting ofc

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And a very quick read

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Chapter 7 is probably where things become interesting

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This is intended for people who have never used TeX before

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So ofc the first chapters are about the basics

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Takes a few chapters to get into depth

rocky shuttle
#

skip the texbook, just attend Xlurp's talk

red forge
#

Yo guys, I wanna hear ur answers to this, everybody says something different, so that kind of made me curious

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What is the correct order of the following words:

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( result / hypothesis / observation / question / curiosity / experiment )

surreal sapphire
#

alphabetical

rocky shuttle
#

lexicographical

red forge
#

No, logically, I mean what is the first thing that leads to the next. They all agreed that the result is the last, but they differ in the firsts order

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BTW i think that's: (observation / question / curiosity / hypothesis / experiment / result )

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Like , Doesn't it make sense?

neat lintel
#

I would put them like this

red forge
#

Why

neat lintel
#

Scientific method I guess

leaden torrent
#

yeah this seems vague and overly prescriptive but

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if i were to answer this assuming it was a weird high school question

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i'd answer what beijing did

red forge
#

I don't think it makes sense to just be curious like that

neat lintel
#

Sometimes you are

red forge
#

You will notice something first

neat lintel
#

Also you could notice something, but not be curious about it and ignore it. So Curiosity is what matters as first step

leaden torrent
#

you start with "curiosity", i.e. wanting to learn about some phenomenon or whatever — as you focus and refine, you "narrow in" your specific interests and formalize them as a question

red forge
#

But wait

alpine kindle
#

observation always appears at the experimentation stage but not necessarily at the first stage

leaden torrent
#

"an observation" in a scientific sense is a specific measured outcome of a trial (i.e. part of an experiment)

red forge
#

I see that if you notice something you will be curious about it or not

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Example

leaden torrent
#

scientific experimentation is the process of collecting observations

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admittedly tho not all of the terms used are scientific in the first place, i have no clue wtf "curiosity" means

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but it seems like this was structured as a way to basicall ytell students

leaden junco
#

hii

leaden torrent
#

"to start researching things, first you have to take your general interest in the topic and formulate it into a specific, answerable question"

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so im assuming they want curiosity to go before question to reflect this

red forge
#

Isaac Newton was not curious about gravity at all, when he noticed the fall of the apple and said why did it fall, he became curious and began to give his looks and research and gave experiments and then came to a conclusion

leaden torrent
#

that story is apocryphal btw

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the apple thing didnt happen

red forge
#

He wasn't curious and then asked

neat lintel
#

The people I think about are more like Francis Bacon and Galileo when it comes to Scientific Method theory.

leaden torrent
#

newtonian gravity came as an attempt to explain the orbit of celestial bodies

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i.e. the planets and moons

red forge
#

He was not curious, then he asked to notice something. When he thought with himself or asked himself, he became interested and curious

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You cant be curious out of nowhere

leaden torrent
#

in any case, my point is that i think youre misinterpreting what "observation" means

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in the context of a scientific experiment, an observation is a specific element (a quantity, a phenomenon, whatever) observed during the experiment

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not something observed before the experiment

red forge
#

The teacher said that by observation we mean the first thing we see apart from experience

neat lintel
red forge
#

So I said it's the first

leaden torrent
#

alright sure

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i can see that then

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but thats not the definition of "observation" i'd use

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when i hear "observation" wrt science, the first thing that comes to mind for me is techniques used to compare observed values and true values

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perhasp thats a very applied math-sy viewpoint

red forge
leaden torrent
#

(well, a righteous applied mathematician would reject the notion of "true values" in the first place)

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(and use "predicted values" instead)

red forge
#

Srry its on Arabic

neat lintel
#

we... don't understand it

red forge
#

But Written: A note or observe is the first, followed by a question

red forge
#

BTW What do ya think is the correct order as the last question?

violet wraith
#

what's a cool calculus fact

midnight crystal
#

probability is so hard

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im convinced my professor cant even do it

noble coral
#

Is there a particular problem that sparked this comment?

midnight crystal
#

well its more of how my class is set up. First of all its engineering probability so my professor is an engineer.

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Second he assigns these random homework problems and i realized hes not even doing the solutions hes taking them from a pdf he found online

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third the exams are wayyy too easy compared to the homeworks

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and when people ask for help he barely clarifies

noble coral
midnight crystal
#

electrical engineer

noble coral
#

I see

#

University professor?

midnight crystal
#

yea

noble coral
#

Damm, they really are understaffed, huh.

midnight crystal
#

Also like my class moves way too fast compared to the actual math major probability

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like you do all the normal pdf/cdf stuff but then they just start going crazy with all this linear algebra stuff using spectral theorem

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and linear algebra isnt even a prerequisite

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and then thats just a load of crap for a single unit

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and the final chapter is a bunch of signal processing stuff

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its just so much so fast and my friends who are math majors are getting to take things slow and actually learn stuff

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and on top of all of that, midterm 1 is 45% of the grade, final is 45% and homework is 10%...... and exams are take home

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so basically everyone is going to just cheat with their friends

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the entire class feels like a joke and i feel so unconfident in my probability skills

deep mango
solid snow
#

Why ryc

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What did 3b1b do

deep mango
#

Made a video about borwein integrals

violet wraith
#

I don't think I watched that

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tell me about it ryc!

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@deep mango @deep mango @deep mango @deep mango @deep mango @deep mango @deep mango @deep mango

deep mango
#

Ugh

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So

violet wraith
#

unless you don't want to

solid snow
#

...why are you being nice? dont break character...

violet wraith
#

oh actually

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I did watch the video

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it was recent

deep mango
#

The integral of sin(x)/x on the whole real line is pi/2, this is the dirichlet integral

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Oh ded

violet wraith
#

but I forgot what they were

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so you can continue

violet wraith
#

and your dog

deep mango
#

The integral of sin(x)/x * sin(3x)/(3x) is also magically the same thing

violet wraith
#

oh right I remember this now

solid snow
#

oh right i saw that video

violet wraith
#

it breaks after 15

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I forget why tho

deep mango
#

As is the integral of the product when you take the first 3 odd numbers, etc. Except when you get to 15

violet wraith
#

ryc ur slow

deep mango
#

Then it's extremely close but slightly lower than pi/2

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This happens because 1/3 + 1/5 + ... + 1/13 is below 1, but when you add 1/15 it goes above 1

violet wraith
#

oh right

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p cool

deep mango
#

Why is that important?

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It's hard to see with the integrals as they are

violet wraith
#

uhhhhhhhh

deep mango
#

But if you use the fourier transform, you can see it

violet wraith
#

pain

deep mango
#

The integral of a function is equal to its fourier transform evaluated at 0

violet wraith
#

oh shit rly

deep mango
#

The fourier transform of sin(x)/x is a step function, which is 1 in between -pi/2 and pi/2 and 0 elsewhere

violet wraith
#

makes sense

deep mango
violet wraith
#

ah ok

#

I see now

#

from what domain does that frequency come from

deep mango
violet wraith
#

doesn't the FT make everything look more steppy

deep mango
#

Showing the fourier transform of the step is sin(x)/x is a good exercise

deep mango
violet wraith
#

oh right

#

I confuse those two

#

series transform same word

deep mango
violet wraith
#

I see

deep mango
#

It turns out that the product of sin(x)/x with horizontal scalings turns into a convolution of step functions with horizontal scalings

violet wraith
#

horizontal scaling meaning scaling along the x-axis right

deep mango
#

And you can add up the horizontal scalings to see when the convolution goes below 1 at the center of the step functions, x = 0

deep mango
violet wraith
#

ok

deep mango
#

Explaining how we see that the convolution goes below 1 when the scalings add up to > 1 is kinda hard tho

violet wraith
#

understandable

deep mango
#

It has to do with the idea that convolution smudges one function by another, so we only get the biggest step function smudged down at 0 if all the smaller ones can reach from the edges (where they start smudging) all the way back to 0

#

The 3b1b video does a visualization of this which makes it much clearer

violet wraith
#

ah ok

#

I'll rewatch it when I have a chance

brittle socket
#

gmod where your very active

violet wraith
#

gone

#

bc

#

I'm not very active

#

but yeah thanks ryc

deep mango
#

Sure

#

I think it's a really cool fact

#

And i was surprised to see that it actually had useful interesting math behind it

#

Instead of being some stupid contour integral

violet wraith
#

lol

cold needle
#

Gmod did you learn laplace transforms

static loom
#

does the video also explain $$\int_{-\infty}^\infty \frac{\sin(x)}{x}dx = \int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}dx$$

fathom swallowBOT
#

mOwOsity

cold needle
#

thats a classic but i dont remember any of it

#

i think i had it as a hw problem once

deep mango
#

i think ive seen it

#

ofc

#

you can use fooyay

#

again

violet wraith
cold needle
#

Ok did i tell u about the inverse laplace transform yet

violet wraith
#

oh god

violet wraith
#

oh wait

#

that's just the F(s) function right

#

wait no nvm

cold needle
#

ordinarily you use the table to go from F(s) to f(t) right

violet wraith
#

yeah

cold needle
#

ok now what if i told you

tall badge
#

based on metals history i think hes gonna go bromwich

cold needle
#

That there was an actual formula for this

tall badge
#

so run

violet wraith
#

makes sense

cold needle
#

Do u know any contour integration

violet wraith
#

some

#

wouldn't you deal with them like line integrals

#

with parameterization n shit

cold needle
#

$f(t) = \lim_{\beta \to \infty}\frac{1}{2\pi i}\int_{\gamma - i\beta}^{\gamma + i\beta}e^{zt}F(z)\dd{z}$

fathom swallowBOT
#

cofe cube (bad kernel)

violet wraith
#

breaking them into a few parts

#

holy FUCK

cold needle
#

This is the laplace inversion integral

violet wraith
#

ah I see the 2πi there

#

cauchy

cold needle
#

yes

violet wraith
#

wait is that cauchy

#

residue theorem whatever

cold needle
#

its related u use cauchy residue theorem

violet wraith
#

yes I'm so smart

cold needle
#

We use the Bromwich contour

#

it is a mirrored D shaped contour

#

essentially

#

i will give a talk in the spring

violet wraith
#

oooo

#

so this was all just a marketing scheme

cold needle
#

i gave this talk my freshman fall over zoom

#

i will do it again this spring

violet wraith
#

that's fun

cold needle
#

it is fun

limpid pike
#

Hello

tall badge
#

metal i gave u a laplace problem but u never answered

violet wraith
#

damn

cold needle
#

its a nice example of the residue theorem that isn't annoying

violet wraith
#

ghosted

tall badge
#

u can finish it and include it in ur talk

cold needle
#

Yes

#

thats a rly good idea rokabe

#

i will do that

tall badge
#

find the inverse laplace transform by residues
$$F(s)=\frac1{s\cosh\sqrt s}$$
hint: $F$ has countably many poles, so expect an infinite series

cold needle
#

Because its an example of one i can't do with a table

fathom swallowBOT
#

Rocket Cube

cold needle
#

One of my examples is one that i can do with a table

violet wraith
cold needle
#

My camera roll is mostly pictures of chalkboards /whiteboards and pics of me and my gf

#

Or screenshots of discord

violet wraith
#

you have a gf?????

cold needle
#

yes

violet wraith
#

no longer a math major

cold needle
#

she was in ur micro class actually

violet wraith
#

oh rly

#

how do you know

cold needle
#

same prof

violet wraith
#

ohhh

#

actually yeah there's only one prof

tall badge
#

theres another problem where u can use a table to confirm ur answer from bromwich

violet wraith
#

I'm dumb

tall badge
#

or basically just take any table problem and force em to do bromwich instead and make sure u get the same thing

cold needle
#

is it pinned on bois channel rokabe

#

oh ye

#

chrew

tall badge
#

for $a>0$, find the inverse laplace transform of
$$F(s)=\frac{2a^3}{(s^2+a^2)^2}$$
to check your answer, find it again by using a table of common transforms

violet wraith
#

bois channel??

fathom swallowBOT
#

Rocket Cube

cold needle
#

is in a different server

violet wraith
#

o

cold needle
#

i was debating whether or not to do a slides talk or a chalk talk for this

#

but i think i want to keep it slides since i already have slides for it

#

ill just update it with some stuff because i remember i handwaved a few things awkwardly and now i feel confident enough to handwave it and say "ask me after"

tall badge
#

same quality of lecture, just better at hiding it!

cold needle
#

Yes exactly

violet wraith
#

I won't ask you after

tall badge
#

eg heat eqn with nice boundary/initial condition

cold needle
#

o wow okei

#

ill look into dat

tall badge
#

solve by laplace transforms
$$u_t=u_{xx},~0<x<\pi,~t>0$$
with boundary and initial conditions
$$u_x|{x=0,\pi}=0,~u|{t=0}=x^2$$

fathom swallowBOT
#

Rocket Cube

violet wraith
#

ugly

cold needle
#

this is one of the nicest pde

violet wraith
#

still ugly

tall badge
#

the gist is u can transform each side of the DE
$$\L(u_t)=\L(u_{xx})$$
and say $U(x,s)=\L(u(x,t))$, so that
$$sU-u|{t=0}=U{xx}$$

fathom swallowBOT
#

Rocket Cube

cold needle
#

ahh

tall badge
#

this gives
$$U_{xx}-sU=-x^2$$
then transforming the boundary conditions gives boundary conditions for $U$
$$U_x|_{x=0,\pi}=0$$
now solve this in $x$, its straightforward

fathom swallowBOT
#

Rocket Cube

tall badge
#

then the tedious part is the inverse transform vvShrug

bright hill
#

@exotic vigil that's rough

exotic vigil
#

what?

bright hill
#

Please don't let people's expectations of you determine your actions

#

It's only a recipe for misery

exotic vigil
#

yes i dont really care thats why ive been able to do extra studying

exotic vigil
brittle socket
#

How much time do you spend on math on average btw

exotic vigil
brittle socket
brittle socket
woven whale
#

that estimate includes chatting on this server

#

it counts as math

surreal sapphire
#

ill inform my advisor of that

bright hill
#

Hello loch

#

I feel like i haven't seen you in a bit

surreal sapphire
#

hello dark cube

torn willow
surreal sapphire
#

uh, im here all the time at least

bright hill
#

Must've been me then

exotic vigil
brittle socket
balmy maple
long matrix
lofty geyser
#

If you were writing something, and you had to talk about the following sets:

  • { f | f: A → B }
  • { x : |x| < f(x) }
    Would you stick with colon or bar, or just use both?
rocky shuttle
#

I would stick with my bar macro

lofty geyser
#

{ x | |x| < f(x) }

wild lantern
#

I'd just use colon

#

B^A is good enough notation to avoid having to write {f:f:A->B}

rocky shuttle
lofty geyser
#

{ f : f: A → B }

wild lantern
#

Or just B^A

lofty geyser
#

I do like { f | f: A → B } a bit more compared to B^A

#

But yeah bar aint so bad: { x | |x| < f(x) }

cinder zephyr
#

I use colon if there's a bar next to it (like absolute value)

wild lantern
cinder zephyr
#

but bar otherwise

wild lantern
#

Bar with lots of absolute values and divisibility can get kinda goofy

lofty geyser
#

I mean I feel like there should be nothing wrong with using multiple styles depending on whichever is suitable for the situation.

wild lantern
#

You can always just explain things in words if it gets confusing.

lofty geyser
#

I'd just say, "Whenever it's clear, I'm gonna use : or | for sets k?"

#

Like I feel it's rather silly to say "style must be consistent", compared to, "whatever is most readable"

cinder zephyr
#

So while I value consistency

#

I value readability just a little more

#

so I will be consistent unless it hampers readability

#

Weird? sure

#

But right now the stuff I write the most (homework) will be read by others

#

so I optimize for readability

lofty geyser
#

Yea I agree with that

cinder zephyr
#

Though

#

you could argue that I should use colon for everything then

#

and to that I say "old habits die hard"

rocky shuttle
#

Generally, I agree with that, too, but in this specific case with set builder notation, I don't think there is an example that is super unreadable.

long matrix
#

:

rocky shuttle
#

I use bar

fathom swallowBOT
#

Spamakin🎷

cinder zephyr
long matrix
#

?????????????????????????????

#

iooijijoiijojiojoioji

cinder zephyr
#

so many bars

rocky shuttle
#

a bit of spacing might help

cinder zephyr
#

yea true

long matrix
#

anyways, why would you use subset in set builder

rocky shuttle
#

but then the issue is not really in the set builder bar, but in ||S| imo

long matrix
#

thats just silly

cinder zephyr
long matrix
#

ic

#

i think i might prefer powerset all the same

cinder zephyr
#

but it's not a power set

#

OH nvm

#

yea I guess

#

but still I wanted to just cram as many bars as possible

long matrix
#

,,{S\in P(\bZ_{100}):2\mid\abs{S}}

cinder zephyr
#

yea

lofty geyser
#

Yeah there's always something you can do to make the situation better:
Maybe like 2 | card(S)?

fathom swallowBOT
cinder zephyr
#

this is a case where I would just say write divides

lofty geyser
#

Yeah same probably

cinder zephyr
#

no matter how you dice it, divides next to a cardinality is weird

long matrix
#

,,{S\in P(\bZ_{100}):(\exists n\in\bZ)(\abs{S} = 2n)}

cinder zephyr
#

actually this is something I struggle with teaching students at the beginning of the discrete math class I TA

fathom swallowBOT
neat frost
cinder zephyr
#

A good number of them get in their heads that like "yes this is rigourous math. I must use words" and I get symbol vomit

rocky shuttle
#

$${S\in P(\bZ_{100}),|,\exists n\in\bZ\colon\abs{S} = 2n}$$

lofty geyser
#

I'd probably do { S∈ P(ℤ₁₀₀) : ∃ n∈ ℤ(|S| = 2n) }

cinder zephyr
#

I'd just write divides or the word even

lofty geyser
#

Yeah

#

I'd probably do { S∈ P(ℤ₁₀₀) : |S| is even }

long matrix
#

i dont like using : after there exists

fathom swallowBOT
#

zan cube

long matrix
#

it just doesnt make syntactical sense when the same isnt done for forall

lofty geyser
#

Only if you think so

#

Yeah syntax can get weird

long matrix
#

I think a programmer's mindset is missing from a lot of symbol grammar

#

Which can make the symbols become ambiguous

lofty geyser
#

From a programmer mindset, the lack of standard is uncomfortable

long matrix
#

yes

#

needs to be a standard and no ambiguity

lofty geyser
#

But yeah, I like to imagine colon and exists is fine since, and just stick with no colon.

#

Though lack of standard means flexibility in thought I'd like to think. But who knows.

long matrix
#

im more annoyed by ambiguity - order of operations doesn't seem to be standardized or made clear I think?

#

,,\forall x P(x) \implies Q

fathom swallowBOT
long matrix
#

for stuff like this, as an example

#

and i think thats partially because we discourage this notation anyways until you get to logic

#

But its like you introduce these symbols, discourage them from being used in proofs, and end up with something wishy washy

lofty geyser
#

Yeah, I mean in logic we define it all more precisely, where as in math it's generally wishy washy and as long as it makes sense.

#

I think the main idea though, is that we shouldn't get so caught up in the syntax as that's not what we're studying.

#

But the ambiguity can be discomforting sometimes.

long matrix
#

I agree - the meaning is important. And I've seen a lot of places where I would've appreciated a short symbolic statement rather than 3 lines of words which mean exactly the same

#

And I've seen a lot of notes where by mistake there can be 2 meanings due to lack of brackets in words

haughty lintel
#

Just a bit curious, what prereqs are normally required for abstract algebra?

cold needle
#

comfort with writing and understanding proofs

#

Sometimes linear algebra is nice to have but like

#

for the first pass thru group theory it might not show up so it wouldnt be needed

#

but there are a number of examples involving linear algebra

#

eventually it will be required

haughty lintel
#

I see. Tysm!

violet wraith
#

I'm bored

#

what's a cool basic linear algebra concept

neat lintel
#

dual spaces

violet wraith
#

interesting

tall badge
#

any decomposition

torn willow
bleak wigeon
#

spectral theorem

rocky shuttle
#

included in any decomposition

bleak wigeon
#

for some reason my brain only associated things like LU, cholesky, and QR to decompositions lol catThin4K

cold needle
#

i think rank nullity is a very cool basic linear algebra concept

violet wraith
#

goddamn everyone's pitching in lmao

rocky shuttle
#

and dual spaces aren't that uninteresting

cold needle
#

um of course this is in the standard curriculum but lmao

violet wraith
#

lol

#

why is a dual space called that

#

what's so dual about it

#

the definition doesn't make it sound dual-y

torn willow
#

This is not a concept but any norm preserving operator on R^n is linear

deep mango
#

well

#

why wouldn't it be dual

#

like

violet wraith
#

idfk

deep mango
#

you have the perspective of functions acting on elements

torn willow
violet wraith
#

ohhhhhhh

deep mango
#

but there's a dual perspective where the functions are the elements, and the elements are the functions

violet wraith
#

ok that makes sense

deep mango
#

you evaluate an element at a function by doing function(element)

violet wraith
#

yeah

neat lintel
#

the duality comes through an identification of a vector space with its dual space through choice of an inner product

deep mango
#

it's the same thing but you view elements as being functions on the set of functions

rocky shuttle
deep mango
violet wraith
#

BIDUAL????

torn willow
#

This is a certified non FDVS moment

rocky shuttle
violet wraith
#

pain

neat lintel
#

how do you think about it?

torn willow
#

What they mean is

deep mango
# violet wraith pain

so every element in the vector space gives you an element of the double dual space (V*)*. an element of the dual is a linear functional to the base field (say, R), so and element of the double dual is a linear functional from (linear functionals) to R

torn willow
#

Think of $f_a(x)= \langle x,a \rangle$

fathom swallowBOT
deep mango
# neat lintel how do you think about it?

it induces a pairing and flips arrows. i don't think about dual vectors identified with vectors pretty much ever, even in the presence of an inner product, unless there is really convenient reason to do so

#

to me this gets too confusing

#

like

#

i'd rather keep track of what's a bra and what's a ket because they transform differently

torn willow
#

You do physics?

rocky shuttle
#

covariant and contravariant vectors sotrue

deep mango
#

this is called the "evaluation functional"

violet wraith
#

oh I see

deep mango
#

in a finite dimensional space, it turns out that EVERY element of V** is an evaluation functional

#

and that V** is actually just V again

#

but in infinite dimensions this fails

neat lintel
#

i imagine concretely like if i have a linear transformation V : R^3 -> R^2 then with the standard inner product i can identify R^3* and R^2* with R^3 and R^2 repsectively, and then think of V* as a map from R^2 -> R^3 kinda like the inverse

#

and somehow it feels like the spectral theorem tells you this is a good way to imagine things (in the sense that it gives a clear geometric intuition for the transpose)

rocky shuttle
#

in infinite dimensions, it still holds for so-called reflexive Banach spaces

rocky shuttle
jovial ember
#

Now listen up, fuckers

jovial ember
#

I’m chleepy and I’m gonna go to chmed

#

Have a great night

zealous garden
#

have a great one

rocky shuttle
neat lintel
#

gn!

zealous garden
#

gn

deep mango
#

Have a good night chocobee

dapper badge
#

goodnight chmonkey

cold needle
#

riesz rep

#

i wonder if i can give a talk to math club about it

#

hmm

#

how to speedrun dual spaces

violet wraith
#

yes

neat lintel
#

Does anyone know multiplicative inverse

eager reef
proud olive
#

Sounds advanced

radiant pagoda
#

Jesus loves yall

neat frost
#

He's not my type

#

Man needs a shave

granite barn
#

I'm going live now on twitch.tv/goofthegoof where I'm working through every question of dummit and foote. come say hi if you're interested.

neat lintel
#

please do not advertise your twitch channel here

arctic grove
#

also for the sake of your sanity dont do every question in D and F

arctic grove
neat lintel
#

enneagram type

arctic grove
neat lintel
#

__co__catThink

#

based

#

Finally understood that category theory reference 😌

arctic grove
arctic grove
#

so this is what 5w4 means

neat lintel
arctic grove
neat lintel
#

fair enough

neat lintel
arctic grove
#

icic

#

gotcha

neat lintel
#

in which 5 is my main type while the latter is my secondary one

sharp mulch
#

Omg 5w4

#

Typical math person

neat lintel
#

runs away

sharp mulch
#

Ugh infps

radiant pagoda
radiant pagoda
neat frost
neat frost
radiant pagoda
neat frost
#

There are other depictions of him

#

I wasn't referring to the westernized ones

radiant pagoda
radiant pagoda
neat lintel
#

i'm an infp, so i'm not a math person smugCatto

neat frost
#

I'm sure god wouldn't let such a petty thing as not worshipping him stop me from going to heaven 🙏

radiant pagoda
#

if you dont worship God or follow God who else would you be serving completely?

#

the devil

neat frost
#

Why? I don't serve the devil

radiant pagoda
#

if you dont serve God who else is there to serve?

neat frost
#

I don't have to serve anyone?

#

I'm my own person

radiant pagoda
#

God is good and created good so therefore by doing evil wouldnt you be serving evil?

neat frost
#

Who said I'm doing evil?

radiant pagoda
#

without faith it is impossible to please God

#

without following God there is no middle area you either serve Him or the devil

neat frost
#

That sounds pretty petty hmmCat I wouldn't get pissed at someone just because they weren't constantly worshipping me

radiant pagoda
#

He doesnt hate people who try to follow Him

neat frost
#

Yeah

#

Why would he hate people who don't though?

radiant pagoda
neat frost
#

There is other good than worshipping god?

radiant pagoda
radiant pagoda
neat frost
#

Does it really count as suffering if he's immortal? It's much more of a sacrifice for us to die without the absolute of immortality than for god to die with the knowledge that he is

arctic grove
#

coz resonate with a lot of this stuff

#

like all the weaknesses opencry

radiant pagoda
#

He came in a human body, feeling and sympathizing with our weakness and temptations (He still never sinned), and on the cross He felt a lot of pain

#

He rose from the dead cuz His Spirit is immortal cuz He's God of course but in the body He could feel everything

neat frost
#

I'm sure it's very easy to not sin if you're god, even if you are in mortal form

velvet dagger
#

The tricky thing about trying to reason about this situation is establishing which part of you is God and which part of you is mortal. Mind of God in a mortal body? etc

arctic grove
radiant pagoda
velvet dagger
#

My understanding is that basically every attempt to explain the trinity in a way that makes sense to us has been ruled some sort of heresy

radiant pagoda
arctic grove
#

law of excluded middle

radiant pagoda
radiant pagoda
velvet dagger
#

And the correct answer is basically that this shtick is pretty much beyond human understanding. If you accept the Christian faith (for whatever other reason you do) you pretty much take the trinity as a thing

#

And obv if you don't then you think it's nonsensical and its apparent inconsistency is an actual inconsistency

radiant pagoda
#

there literally is no middle

radiant pagoda
#

then where do you think He would put you

#

where you have chosen to be

arctic grove
#

as a matter of fact

#

the country im from

#

there are 33 million gods

#

try pleasing all of them opencry

velvet dagger
#

I don't think debating religions is really gonna get anywhere here lol

arctic grove
#

yea lol

#

lets debate something else

#

for example, why i am the best mathematician to ever live.

radiant pagoda
solar mauve
#

Hablan español?

radiant pagoda
#

ye ight

velvet dagger
#

Religious discussion is fine and honestly I often find them interesting

radiant pagoda
#

i agree it doesnt get anywhere\

arctic grove
#

the fuck do you mean by that

radiant pagoda
#

i mean theres 1 God

arctic grove
#

there isnt

radiant pagoda
#

why are you mad?

velvet dagger
#

But the issue is that unless you're learned scholars in a religion and can debate it properly

#

It basically becomes a bunch of no u

radiant pagoda
arctic grove
#

coz i dont like blatantly wrong bs

velvet dagger
#

And it has a lot of potential to get offensive

radiant pagoda
#

its not wrong

arctic grove
#

im not even religious but im not gonna let you shit on something you dont know anything about

velvet dagger
#

Because, let's take Christianity vs Buddhism

radiant pagoda
arctic grove
#

lets see what you know

#

go on then

velvet dagger
#

I mean really just take religion X vs religion Y that are inconsistent

#

As far as religion X is concerned

radiant pagoda
#

that is my point

velvet dagger
#

People who study religion Y are just talking shit

#

And their whole life is misguided

arctic grove
velvet dagger
#

Very heavy accusation to levy at someone

arctic grove
#

statues are a representation of the god you are worshipping

velvet dagger
#

e.g. what's happening literally right now

radiant pagoda
#

but when Jesus comes down to earth dies for us raises and says "I am God" that rlly means a lot

neat lintel
#

can someone help me with basic trigo

arctic grove
#

they arent gods themselves by any means

radiant pagoda
# velvet dagger e.g. what's happening literally right now

ye i would like to use verses but mostly it doesnt work, they dont have faith therefore they dont care to listen or believe, and also when I stop using verses they say "oh so you cant defend it" its rlly so hard to finish even talking about it

#

cuz no matter what i say ppl would get mad

neat lintel
#

nah I do not need help with sums

velvet dagger
#

You can't use verses to defend Christianity because the validity of those verses presuppose the truth of Christianity

#

There are ways to debate religion correctly

#

You simply don't know how to do it

radiant pagoda
rocky shuttle
#

you believe, so you will come up with anything

radiant pagoda
arctic grove
#

why do you assume the religion you were made to believe in since birth is the correct one

velvet dagger
#

Caleb I'm gonna put it to you straight, the problem here isn't them it's you lol

radiant pagoda
velvet dagger
#

I am not Christian and I'm fairly certain that I could defend Christianity much more effectively than you can

arctic grove
neat lintel
#

I believe hinduism

radiant pagoda
#

i wasnt taught it, i had it hidden from me in every form until someone came up to me and i get mocked even by my parents for it

velvet dagger
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I don't mean this as a flex but the problem is you can't start with saying "Oh well first if you believe the Bible than Christianity is true", you have to convince people that the Bible is what's correct

radiant pagoda
#

you literally cant cuz i cant do some miracles through the screen

arctic grove
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you can try to put up a good argument

torn willow
velvet dagger
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So then don't bother caleb

radiant pagoda
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i can tell u about some but yall prolly wont believe them

torn willow
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Like what gods do you worship

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What's your method of worship

neat lintel
radiant pagoda
velvet dagger
#

If your defense of Christianity relies on miracles that you personally witnessed, the issue is as you say, you cannot communicate them

neat lintel
torn willow
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Ok,ig you know what you are doing

radiant pagoda
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i literally came in here saying only "Jesus loves yall" and "turn to Him so you can be saved"

neat lintel
radiant pagoda
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never intended an argument

arctic grove
velvet dagger
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Yeah it should've been clear to you that this would lead to a debate, or at best being ignored by anyone who didn't care

arctic grove
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its rather fine

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the part that is gonna start the fire is the second one

radiant pagoda
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ye but i cant just leave parts out of the truth

velvet dagger
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Because "turn to Him so you can be saved" addresses people that already don't believe in Christianity

radiant pagoda
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He says He's the Way the Truth the Life

torn willow
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Well what if you knew nothing about Jesus except "magic man who came back to life"

neat lintel
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bro whom do I need to be saved from?