#serious-discussion

1 messages · Page 50 of 1

neat lintel
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I recently made an AI art joke in chill chat as well!!! Wanna hear ?

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its like nokia dying

neat lintel
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wow

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I have seen them irl tho. They make them using special 3D printers, because such products are unachievable with regular metal working techniques

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They still expensive as hell because they can only be made with 3d printing

neat lintel
# neat lintel sure

"I don't like it when artists say "Ai Is GoNnA tAKe OuR joBs AwaY" it's such a false and stupid statement.
One of the important and completely wrong thing it assumes is that artists have job, this is such a lie.
Ai isn't taking your job away, u don't even have job"

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Lol

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ye

neat lintel
neat lintel
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ye im not much of a texture artist

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i hv been doing 1 model a day for practise

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Right now it looks like its made of PVC 🤣, if you change it with a non-reflective metal texture it'd be better.

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it must be a month now

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fosure

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Well I'm currently focusing on other things

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i love this one

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I'm already enrolled into Design uni. but right now I'm still having to finish last semester of Lyceum.

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I try to follow and learn early the stuff I have to do in the first year of uni.

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But it's really stressing because of all the subjects I am taking and the big exams

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i hope i was attentive as u in college lol

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I have 11 subjects

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cool xd

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study hard

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or hv fun

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I mean Calculus is fun (sometimes)

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both maybe

neat lintel
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Well I'm taking Calc. 1\2

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The thing I hate is that it doesn't mix in with the Physics we're doing

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Cause like I learn integrals, derivatives and all shit, but we hardly have been using them for Electromagnetism or relativity topics

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cal is the worst thing

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i hate it so much

neat lintel
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i think we use to use that

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i dont remember shit

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but it use to be there

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The only thing I've seen is this where we used derivatives in Physics.

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$Q(t)=C\cdot \Delta V \cdot\left( 1-e^{\frac{-t}{RC}} \right) \
\frac{d Q}{dt}=I(t)=\frac{\Delta V}{R}\cdot e^{\frac{-t}{RC}}$

fathom swallowBOT
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北京

neat lintel
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ptsd

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wdym changes

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well I dont learn it

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I guess? I mean we learn magnetism, eletromagnetism and even maxwell equations, but the book hardly ever uses integrals or derivatives in problem. The formulas are also never explained where they come from.

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Do you know why I think it's like this? 🤣

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Because many people struggle with calculus and barely pass it.
If they also added calculus stuff into Physics twice the people would fail those

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Do you think calculus is used for basic mechanics?

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My uni. has a mechanics exam the second year.

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I actually wonder if I’ll enjoy doing mechanics math. It’s a type of math I’ve never done in my life

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No man, it’s way simpler

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It’s like structural mechanics fundamentals. It’s for basics

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Well I think it’s cool topic tho

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Cause you learn about more realistic situations of objects, that are now less oversimplified. You know in HS all objects were simplified, equilibrium was only simple cases. But the real world is complex and there can be like 6 objects connected to each other each with different weigh and properties

woven whale
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<@&268886789983436800>

wooden flax
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well someone is not a comrade...

neat lintel
hollow kettle
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Killed more people than German Fuhrer

neat lintel
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gulag

hollow kettle
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Yeah fuck stalin

neat lintel
neat lintel
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Isn't the photo somewhat faked to make stalin look good

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Stalin giga chad

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1900' photoshop

hollow kettle
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Yeah he looked good

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Until started to starve people to death

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He killed more people than Hitler

neat lintel
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but the first prize is still to lord mao

royal sail
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is there no chat channel for the vc channels

hollow kettle
surreal sapphire
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there is

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they are built-in in discord for a while now

royal sail
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oh lmfao

surreal sapphire
cinder zephyr
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Yo

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this is a bit of a weird question

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but so there's this one wireframe sphere you see in the background of alot of pictures of math professors

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and I remember reading some blog post about it

jovial ember
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Alexander horned sphere?

cinder zephyr
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anyone know what I'm talking about?

cinder zephyr
jovial ember
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Oh wait that one

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That’s oberwolfach

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Lol

cinder zephyr
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yes that's it

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tysm

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I wanna get a picture of myself at that

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I made an "academic" version of my site that's modeled after what math prof's sites look like

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And the really kicker would be a picture of myself at that lol

bronze pelican
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Oberwolfach is like the Hollywood of math academia

surreal sapphire
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for reference

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also my (old) uni has whatcanisay

cinder zephyr
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if I get into one of the European summer programs I applied to

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I'll make the pilgrimage

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and get the picture

surreal sapphire
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its in the middle of the black forest

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quite nice area

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lots of hiking opportunities

cinder zephyr
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it does looks like a pretty area

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ooo hiking

surreal sapphire
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you will have to hike to this specific area anyway

neat lintel
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quite nice imo

wooden flax
bronze pelican
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Nice beach

wooden flax
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courtesy of @cold needle

deep mango
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So pretty!

wooden flax
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very cold 🥶

deep mango
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You didn't dive in?

neat lintel
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Enjoy. They lowered rendering distance here

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Basically I breathe water

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It’s also 9C• outside

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Only in Ohio 💀☠️👽👽

wooden flax
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nvm 39

deep mango
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🐤

wooden flax
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🐦

neat lintel
violet wraith
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is there a useful idea of the derivative of a function space?

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perhaps it's just the space of the derivatives of each element?

wary wasp
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calculus of variations?

odd brook
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My instinct is to mention Sobolev spaces here - before getting into that, are you familiar with Banach and Hilbert spaces?

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I can't give a proper answer to exactly what you're asking here but there's a related idea I think

violet wraith
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I'll check those out, ty

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was just curious if this notion existed

odd brook
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not quite in the sense you're imagining I think, but oftentimes the driving force behind Sobolev spaces is that they provide a "good" context in which to study partial differential equations and their solutions

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when considering properties like smoothness and regularity of functions, the usual C^k spaces of k-times continuously differentiable functions weren't subtle enough to capture a lot of info and Sobolev spaces aim to mitigate this by admitting functions along with their "weak" derivatives in order to have complete function spaces with enough flexibility

lethal mirage
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u would have frozen

brittle socket
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Jesus, checking my earliest works, when I was less accustomed to proofs, for Enderton's Elements of Set Theory is kinda stroke inducing

jovial ember
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Lmfao

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Great news!

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It won’t go away for a long time

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I read stuff from late sophomore year and boy I was not goood

void tundra
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b r u h

void tundra
brittle socket
void tundra
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there are some which are actually rigorous and

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some just skipped like 50 steps

untold sapphire
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Thank god

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hate that guy

void tundra
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who

untold sapphire
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grassmannian

brittle socket
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I don't use twitter catKing

void tundra
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ah

untold sapphire
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no i'm just kidding. i'm joshing

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relax

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grassmannian is great

brittle socket
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Hi Clerk!

untold sapphire
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lots of fun

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hello grass

brittle socket
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Oh ok

void tundra
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grass != grassmanian

brittle socket
brittle socket
void tundra
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the grass field is real tho

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grass theory textbook when

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welp time to mute chill too

brittle socket
void tundra
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well

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if you add 1 grass blade

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and another grass blade

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you get 2 grass blades

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would multiplication just be reproduction lmao

brittle socket
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Define a grass blade whatcanisay

void tundra
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a grass blade is simply a set of grass cells

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the set is of course a finite set

brittle socket
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What are grass cells

void tundra
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i failed biology :(

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axiom 1: grass cells exist

brittle socket
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No, define it set theotically or using whatever foundations you like

brittle socket
void tundra
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LOL

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hmm

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a grass cell is just a set containing {cell wall, cell membrane, nucleus, mitochondria}

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and whatever

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and then define nucleus to be a set of chromosomes

brittle socket
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I call my sets grass cells. Simply apply ZFC. Ez Q.E.D.

void tundra
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:(

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funnily enough I think dna is isomorphic to an external direct product of cyclic groups

brittle socket
void tundra
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well atoms are just made of

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idk something

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not a physicist

brittle socket
void tundra
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meanwhile: constructs real numbers

brittle socket
void tundra
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it's just a point LMAO

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in R^3

brittle socket
void tundra
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wait that means

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grass cells are just points in R^3

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wait hold up

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no no they're

brittle socket
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lmao

void tundra
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a topological space

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its a finite topological space

brittle socket
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No buli me. I haven't learnt top sad

void tundra
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neither have i oops :(

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well there is some topology in R anal

brittle socket
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~~So much stuff to learn, so little time sad ~~

void tundra
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can they invent immortality

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so i can learn more math

brittle socket
void tundra
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munkres?

brittle socket
brittle socket
# void tundra munkres?

I want to read Lee's other two books in the same series as well so I'm planning to eventually start from the first, which is intro to top

void tundra
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ahh

brittle socket
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From what I heard munkres has quite some stuff that's not too useful, but I haven't read it so Idk

void tundra
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which books are those btw

brittle socket
void tundra
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ooh nice

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wait

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graduate texts in mathematics moment

brittle socket
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Lmao this reminds me of smt

void tundra
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LPT: When on the train, make sure to read a textbook that says "graduate texts in mathematics" to show everyone that you're a big brained genius sotrue

brittle socket
# brittle socket Lmao this reminds me of smt

The reason I got interested in Differential Geometry was because I was looking at integration by parts a long time ago and I was like hol' up. What is that du = something dx notation, that seems cursed.

void tundra
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life pro tip

brittle socket
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Oh lmao

jovial ember
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Lickmy pe

brittle socket
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Chunky boi comin in

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Hi chonk

jovial ember
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The moderators have suggested I stop this joke

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Munkres has theorems not useful for manifolds

eager reef
jovial ember
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Like separablity axioms

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Which never will be useful since everything will always be Hausdorff

eager reef
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Fuck those

void tundra
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who is grassmanian and why is he suspended

eager reef
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I hate them

jovial ember
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Lmfao

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That’s shamrock

eager reef
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Why did shamrock get suspended

jovial ember
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And in my circle he replied to me with the gay f-word

eager reef
void tundra
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suspended from this discord?

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or

jovial ember
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(He is gay)

odd brook
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Munkres insists on doing manifolds intrinsic to R^n iirc

jovial ember
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No on twitter

void tundra
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yup i saw

brittle socket
void tundra
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oh

eager reef
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Lmao

void tundra
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ironic

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doesn't twitter basically hate anyone lgbt

jovial ember
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Eh idk

eager reef
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No

odd brook
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(btw for reading about smooth manifolds first I really like Tu's book)

eager reef
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Twitter has very different sections and subcommunities

jovial ember
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You know who does hate lgbt tho? Me

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Just kidding

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Chmonkey loves all

eager reef
jovial ember
odd brook
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Thank you chmonkey

jovial ember
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Well except for some

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Who are rabble rousers

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And ruin other ppl’s day

brittle socket
jovial ember
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:(

void tundra
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hate the haters

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wait

static loom
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love urself

brittle socket
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rabble rousers?

jovial ember
void tundra
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unrestricted comprehension moment

jovial ember
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😔

brittle socket
jovial ember
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I can never tell if it’s TTerra

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Or mero

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At first glance

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Idk why

brittle socket
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lmao

static loom
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who am i

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im tterra 😎 i love beaststars

jovial ember
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You’re a gay furry

void tundra
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proof?

brittle socket
jovial ember
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He’s TTerra

void tundra
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thats gonna need a proof

jovial ember
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He died

static loom
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me on the left

odd brook
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Can't handle the gay furry beastars

brittle socket
void tundra
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oh

brittle socket
static loom
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vampysmug just did

brittle socket
jovial ember
odd brook
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her name is mocha !

eager reef
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Isn’t that uuhh

jovial ember
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🗿

eager reef
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I forgor

jovial ember
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Coffee with chocolate

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And also like, a color

eager reef
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Ah

jovial ember
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Like hot cocoa coffee

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Is a mocha

odd brook
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She's not even that color I just thought it fit 😭

jovial ember
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Lmao

void tundra
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i wanna touch grass but its raining

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we have a grass tho

brittle socket
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No

void tundra
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define touch to mean grass replied to me

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therefore i touched grass

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ez

brittle socket
neat lintel
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hello methers

amber orbit
neat lintel
tight estuary
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oh, nobody talks here for 4 hours

interesting

woven whale
neat lintel
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Hello!

woven whale
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no?

tight estuary
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really

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LMAO

neat lintel
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How does my map look so far?

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It feels kinda good, kinda bad to me, is it any good at all ?

tight estuary
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what's it about?

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why is there A and B?

bronze pelican
neat lintel
# tight estuary what's it about?

It's about how to study maths, I have been trying to make one for long time cus I want a really axiomatic, step by step approach to study maths but a lot of results I saw related this search were not axiomatic at all, people went from linear algebra to like abstract algebra without doing any foundational stuff and all
So I decided to make my own map to study maths
A is unit A, that is I soon realised I can't just say "algebra first" and do pre algebra, linear algebra, abstract algebra or just say logic and study all the logic at same time
So I divides into chunks, some algebra first, followed some geometry relating to that algebra and some basic logic and stuff until it is completed
Then I go back to logic, back to algebra, back to geometry to study some advance topics of it
That's why A and B are the units, there can be many since my map is not even close to being complete

bronze pelican
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You can start with linear algebra

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You don't need logic for linear algebra

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If you're not comfortable with proofs, you can start with a introduction to proofs book

neat lintel
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Well, but it's technically not the most step by step, axiomatic approach tho, ik I can I did do that, and it was going well but I still didn't feel like it was actually enough to understand it deeply tbh

bronze pelican
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I don't understand what you mean

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You want to derive all math from first order logic? That's stupid

neat lintel
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That has nothing to do with deriving everything with first order logic tho

bronze pelican
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What do you mean by step by step

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You don't need formal logic to do linear algebra

neat lintel
# bronze pelican What do you mean by step by step

Everything is based on logic and set theory, so I will begin with logic I won't do all of logic at once I will do basics of logic
Then I will just do some basic pre Algebra and geometry
Such step by step, things where one thing is completely built on other things which I have made sure I study

tight estuary
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I feel like it'd take you more time to create that map than to master calculus, starting with no knowledge

interesting idea though...

bronze pelican
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A lot of what you listed is highschool math topics

neat lintel
bronze pelican
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But then Godel's incompleteness theorems are graduate level math

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So it doesn't really make sense

woven whale
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@neat lintel you're worrying too much about how to learn instead of just learning

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start by reading any linear algebra book

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like right now

neat lintel
torn willow
neat lintel
# woven whale like right now

I can't, I said I have to start from February cus I have board exams in February which are really important highschool exams since they decide which uni I get, so I barely get any free time tho enough to play around with these concepts and work on things I can do after this is over lol

neat lintel
neat lintel
bronze pelican
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Honestly, my biggest recomendation to you is an intro to proofs book

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Learn how to write proofs

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Then youll be able to pick any linear algebra book and read it

split oak
# neat lintel

Hmm, so you're not taking entrance exams? Which math programs take people in through board exams?

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Or do you mean class 10 boards?

neat lintel
neat lintel
split oak
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Are you planning on taking jee?

neat lintel
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Yes

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Not sure much tho cus I wanna go into research I am just doing it cus it is often considered hard which sounds fun ^°^

split oak
neat lintel
split oak
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Ah, a man of many talents

torn willow
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Ok you sound exactly like me

neat lintel
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It's quite sad

split oak
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Damn it's like all the Indian dudes have gathered

violet wraith
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I'm not indian

neat lintel
# torn willow Ok you sound exactly like me

Do u wanna leave India cus there are no neuroscience institutes here and wanna move abroad for study but then also have this feeling of anger towards everyone cus they didn't build any that u never wanna come back like me too ? ded ded ded

violet wraith
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come to the US

split oak
violet wraith
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lol

neat lintel
# violet wraith come to the US

I do want to one day!! Wisconsin is my favorite state but I do wanna go to USA among many other beautiful countries
It's a cute country 💞💞

violet wraith
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lol I like how you call it cute

solid snow
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why wisconsin lol

neat lintel
# solid snow why wisconsin lol

I don't like big cities, they are cold and chaotic
Places like Cali, NYC or even crowded places in India feel like living among many people, yet somehow being alone cus nobody cares for each other
Compare that to Wisconsin, it's a nice cute state with a lot of extrovert people where u can make friends with ur neighbour and won't be alone much and feel like u r in a small, sweet community 💞
That's why I called America cute, sometimes Americans are very enthusiastic, energetic and outgoing people which is wonderful 💞💞💞💞

#

I mean, wouldn't u love to talk to ur friends on a sunny morning while mowing the lawn?
That's soo awesome 💖

torn willow
solid snow
neat lintel
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Also, then what would be ur first choice ?

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Most of my knowledge of Wisconsin comes from Charlie Berens' videos

solid snow
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and idk theres a lot of scenic states with smaller towns that aren't necessarily wisconsin

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with more to do as well

neat lintel
solid snow
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flawda

neat lintel
violet wraith
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that's where I live

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it's great here

tidal stag
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What would be the integral of i?

woven whale
tidal stag
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Oh

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What about complex numbers?

woven whale
tidal stag
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Yes

brittle socket
violet wraith
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too many mods

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gmod goes offline

fading moon
#

do you think there are other math servers worth joining?

chilly hull
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there are most likely some great math servers out there

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i dont know any of them but there definitely are some

odd brook
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I still don't know why q is so prevalent as an index like I still just say "dimension i" or "i-th coho group"

quasi jettyBOT
violet wraith
#

idk much about function space but I have a question or two about a pretty basic concept

the concept of f(f(x)), f(f(f(x))), etc was always acceptable imo but now I'm thinking about it a little more deeply

wlog let's use the case of f(f(x)) for simplicity. if f is from a function space F, then f takes itself and sends it elsewhere. the inner f and outer f are the same function, meaning they are from the same function space, but where I'm confused is how they can be from the same function space. the domain of the inner f is something like R for example, while the domain of the outer f is F.

does this illustrate something about how we can think of R and F as being similar in any way from some high-level perspective? also, the outer f also belongs to F, and is sending elements of that same set? I feel like this is unsettling

bronze wedge
violet wraith
#

what implications does that have?

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also how is evey vector space a function space?

bronze wedge
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Take R^n. Each vector is a function from the set {1,...,n} to R (i.e. f(i) is the ith coordinate)

violet wraith
#

mhm

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oh pk

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so we consider vectors functions

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because they are linear transformations?

bronze wedge
violet wraith
#

I see

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is there a better reason for why vectors are functions?

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or is it kind of just a definition

bronze wedge
#

Existence of a basis

violet wraith
#

ah ok

neon silo
violet wraith
violet wraith
#

perhaps I should just ask about f(f)

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or is that not a real concept

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I guess now my question is, can the domain of a function be a function space? I feel like that should be possible

bronze wedge
#

Of course it could be

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For instance the derivative takes in as input a differentiable function

violet wraith
#

ok perfect so my original question still holds

violet wraith
#

idk for me it's confusing to have a function send itself elsewhere

neon silo
#

function composition could be thought of as a "multiplication" of functions so if $f,g\in F$ are functions then $f\circ g$ is a new function in F if $\circ : F\times F\to F$

fathom swallowBOT
#

Tymelord14

violet wraith
#

right

violet wraith
#

does my confusion make sense? lol

frigid matrix
#

i don’t understand your confusion

low moon
violet wraith
#

fuck

frigid matrix
#

inner f and outer f are different sorta

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outer f depends on range of inner f

cold needle
#

this is confusing

violet wraith
#

I see, so is f(f) not really allowed

cold needle
#

so f\colon R\to F is the function

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?

violet wraith
#

yes

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wait

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oh fuck

cold needle
#

then f(f(x)) doesnt make a lot of sense

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since you want f(x) \in R

violet wraith
#

hold on lemme think

neon silo
#

The function doesn't send itself anywhere, once you specify a domain then it's fixed so if $f:X\to X$ where $X$ is some set then $f$ only takes in members of $X$ as arguments. Since function composition takes two functions and returns a function we could conceivable define a new function (which is named suggestively) $f\circ(\cdot):Fun(X,X)\to Fun(X,X),~g\mapsto f\circ g$.

fathom swallowBOT
#

Tymelord14

cold needle
#

tymelord said exactly what i was going to say

neon silo
violet wraith
#

lemme process this gimme a minute

#

oh i see

neon silo
#

$f$ and $f\circ(\cdot)$ are related but not the same function, $f\circ(\cdot)$ does what you are thinking of though

violet wraith
#

and then this can be iterated for more compositions

fathom swallowBOT
#

Tymelord14

violet wraith
#

okay makes sense

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alright tysm guys

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I appreciate the help

neon silo
#

no problemo

violet wraith
#

I do definitely want to learn more functional analysis at some point, seems fascinating

cobalt jasper
#

How do I find the number of solutions to $\sum_{i=1}^n a_i = N$ where $a_i < k$? Basically just stars-and-bars with an upper bound.

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Idk where to post the question above. Where should I?

cinder zephyr
cobalt jasper
#

Ok thanks

pastel narwhal
#

Anyone knows how to do (b)?

cold needle
brittle socket
#

Good... good

static loom
#

ryc's a mod? 😮

brittle socket
static loom
#

o ok

void tundra
#

Hitler gets confused about the topological definitions of open and closed sets. Then he totally freaks out.

There's a typo right in the beginning of the video. It should say "...and all zero of the points in the null set," so no "the" before zero. And if you're wondering what I meant by "close points," they are Wikipedia calls "limit points" of...

▶ Play video
#

why have i not seen this

brittle socket
#

Even though I don't know topology that was still funny

void tundra
#

I seriously have to be a masochist my god

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when I saw that the empty set and \bR are both open and closed

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I was like "ah this is fine"

ripe wasp
#

when open and closed are not mutually exclusive devastation

void tundra
#

english moment

fading zealot
#

Third installment to unintentionally found / learn about shapes series:
The Carolingian Cross is a cross made from four trefoil knots.

neat lintel
#

@fading zealot Are you a design or art student as well?

#

I really like this geometry and I plan to implement it in some of my Design since that's what I do

fading zealot
neat lintel
brittle socket
odd brook
#

Mostly techno as of late but I've been into electronica for a while so my tastes shift back and forth

#

A lot of dnb as well which I got into through like, old youtube channels and some artists I still follow

#

and a bunch of more ambient-oriented electronic like stars of the lid, tangerine dream, etc

#

that's awesome

#

what other artists are you into !

#

oh hell yeah

#

half of my music listening at one point consisted of regis, burial, basic channel, and a couple others LMAO

#

like portishead, sweet trip, probably cocteau twins and tim hecker as well

#

yeah I can't listen to them anymore

#

but at one time they were my absolute favorites

#

yeah, harmony in ultraviolet especially is super important to me

#

mirages is lovely

#

I think my first was virgins? but I remember I got into him circa releasing konoyo

#

LOL

#

if I had to pick a second fav it'd be ravedeath tbh

#

I was going to ask if you happened to have rym LMAO

#

here's mine one sec

#

a lot of mine is outdated and I slap 4/5s on everything because I use it more to catalog than anything and I don't believe in assigning numbers in general

#

also a bunch of my ratings are singles it's honestly a mess but I think my 5s summarize my taste pretty well

#

mm that makes sense

#

that also makes a lot of sense

#

I don't strongly differentiate between 4.5 and 5 anyway I just like having exactly 50 because that's two clean pages

#

ooh awesome will do !!

#

wowww nice to see block control EP in their favorites ahaha that one is so old I love it

#

skimming this tracklist now these are exceptional picks

#

nice to see gyrofield :D

#

I've known her for a bit she's awesome

#

I remember hearing superheat for the first time and I was like

#

god please release this

#

ridiculously good tune

#

billain is amazing

#

this reminds me I still need to check out that recent vision comp

#

I've only heard the monuman tune which I loved

#

preamble is crazy

#

ultra and inflict are incredible as well

ripe wasp
#

is the lagrangian in the context of lagrange multipliers $\mathcal{L}(x,\lambda_1,\ldots, \lambda_n)=f(x)+\sum \lambda_i g_i(x)$ or $\mathcal{L}(x,\lambda_1,\ldots,\lambda_n)=f(x)-\sum \lambda_i g_i(x)$?

fathom swallowBOT
ripe wasp
#

i see both being used

#

i.e in boyd it says

#

wikipedia says

river moon
#

if the problem involves inequality constraint the sign absolutely does matter (although not that significantly), if there's only equality constraints then it doesn't matter

ripe wasp
#

oh okay

#

thanks that's very helpful

river moon
#

I write with the plus because the commonly accepted standard form problem is that you have f_i(x) <= 0 and h_i(x) = 0, then lambda*f_i would have to be zero by complementarity and lambda >=0, the sign of the multiplier on the equality constraint doesn't matter so the plus just looks nicer

#

if you were to write -lambda * f_i(x) when f_i(x) <=0 that would imply lambda <= 0

ripe wasp
#

ah that's fair

#

thanks for the insight

neat lintel
#

This calculus book is pretty nice.

#

It starts the Integrals chapter by definind Riemann sums, then definite integrals

gusty star
neat frost
#

This one?

#

Did you just add \quad or something?

#

Anyway yeah ig it doesn't really make much sense for them to restrict you to only 2

#

Would've been pretty easy to change this I think

#

Yeah makes sense

#

All alignment environments are pretty much related

woven lichen
#

mathematics = magic

#

change my mind

woven whale
#

mathemagic

violet wraith
#

I has quostion

#

so we can represent operations as functions, like + as +:R×R→R

#

what about the union

#

what's the domain of the union

#

there isn't a set of all sets

#

would I just define a specific collection of sets

#

would it be our "universe"?

storm sage
#

I don't think taking the union is a function for the reason you said

violet wraith
#

oh

#

then what is it

#

isn't it an operator?

#

because operators are basically functions

storm sage
#

I guess it's just the set whose existence is guaranteed by the axiom of union

violet wraith
#

oh I see

brittle socket
#

`Yeah the union is not a function or relation

#

The union axiom basically tells you that given a set A, U A exists

#

You should join me and read Enderton's Elements of Set Theory sotrue

#

jk

violet wraith
brittle socket
#

Practically none

violet wraith
#

hmmm

#

might be an interesting offer

brittle socket
#

You just need to be determined to sit through it, as with any math textbook

violet wraith
#

I haven't read an entire math textbook all the way through

brittle socket
#

I meant it in the sense that some theorems and exercises will take some time

violet wraith
#

I see

brittle socket
#

Lol its actually my first real math book

violet wraith
#

oh there are pdfs online

brittle socket
#

Yeah

violet wraith
#

have you read a lot of it already?

tall badge
violet wraith
#

pain

brittle socket
brittle socket
violet wraith
#

oh you're over halfway lol

#

well I can still give it a shot

brittle socket
violet wraith
#

ah ok

brittle socket
violet wraith
#

😄

brittle socket
#

Come join my suffering

violet wraith
#

why does discord convert my emoticons into emojis smh

brittle socket
violet wraith
brittle socket
violet wraith
#

:D

#

oh there we go

brittle socket
#

Yeah catthumbsup

violet wraith
#

ty

brittle socket
#

np :)

neat lintel
#

It's in settings

violet wraith
#

I remembered that but couldn't find it on mobile

#

pain

neat lintel
#

It's only in pc & web

violet wraith
#

pain

brittle socket
violet wraith
#

fixed

storm sage
tall badge
#

to fix this i propose a middle ground noone will like, using chinese characters eg 中

brittle socket
odd brook
#

One time my friend used a hieroglyph for a variable

hybrid quest
#

Bushels of weat

gaunt swallow
#

Is this a good map for studying math [ Arithmetic, Pre algebra, Algebra I, Algebra II, Algebra III integrated, Geometry/trigonometry, Pre calculus, Calculus I Calculus II Calculus III]

#

any recommendation Tweaks

#

pre requisites

solid snow
#

what is algebra 3 integrated

#

everything here is a repeat

#

pretty much

gaunt swallow
#

But algebra is esssential

#

to master

#

all the practice

#

will help

#

later on.

#

At least so I hope

brittle socket
#

You might wanna learn some LA first depending on how deep your calc III class goes

brittle socket
#

linear algebra

brittle socket
#

When you guys self-study math, do you normally check your work (i.e. answers and proofs) afterwards like one or a couple chapters later?

green sparrow
proud olive
brittle socket
#

Im checking all my work again right now after a couple chapters but it kinda is boring lol, so I wanted to see if you guys' think its worth the effort in your experience

brittle socket
#

hehe boi

#

Will we get 0 mods? kekw

violet wraith
#

unfortunate

#

3 mods rn

#

I shall remain offline

proud olive
#

Soon SCWhehehehehe

neat frost
deep mango
#

Why don't I count

woven whale
deep mango
neat frost
#

Exactly

deep mango
#

I don't know what that means

brittle socket
#

cope

proud olive
#

It means ur too scared to mute grass

#

obvs

long matrix
#

ryc antagonization. yayy

deep mango
#

Have fun

harsh lion
#

pandaScreams 😠 pandacop

#

ryc is a mod

analog hedge
#

hi

violet wraith
#

ryc should just sit there and be cute, he shouldn't be mod

#

what type of object is a differential? is it its own thing? from what set does it come from? what's it's definition?

wild ravine
#

abstract object

violet wraith
#

isn't it a sort of operator too? since it operates on functions and variables

vivid halo
#

e.g. dx

violet wraith
#

yes

vivid halo
#

in general if you have a smooth manifold X and f is a smooth function on X then df is a section of the cotangent bundle T*X of X

#

T*X is the bundle of 1-forms on X, df is an example of a 1-form

violet wraith
#

I know everything except cotangent bundles

vivid halo
#

dual of tangent bundle

violet wraith
#

idk anything about bundles

#

is this a diff geo concept

vivid halo
#

do you know about the tangent space at a point

#

and yeah this is diff geo

violet wraith
#

a bit

vivid halo
#

if X is a smooth manifold and x is a point then you have the tangent space T_xX of X at x

#

this is literally the vector space of tangent vectors to that point

violet wraith
#

oh I see

vivid halo
#

as the point varies you can glue these together smoothly

#

and get a bundle TX->X

#

whose fiber over a point x of X is T_xX

violet wraith
#

alright

vivid halo
#

the cotangent bundle is what you get if you do the same thing but gluing together the dual spaces of these tangent spaces

violet wraith
#

alright makes sense

vivid halo
#

so a section to the cotangent bundle gives you an assignment of points of X to functionals on tangent vectors

#

the way you would evaluate this is like

#

e.g. if you had the 1-form dx on R^2, you can evaluate this at 0 on a basis of tangent vectors d/dx and d/dy say at the origin, then dx(d/dx)=1 and dx(d/dy)=0

violet wraith
#

d/dx is a tangent vector?

vivid halo
#

yeah

violet wraith
#

how so

vivid halo
#

there are several equivalent definitions of a tangent vector

#

one of those definitions is in terms of literal tangent vectors to curves going through a given point

#

another is in terms of differential operators or derivations on the algebra of smooth functions

violet wraith
#

oh ok

#

so is d/dx a tangent vetor basically by definition

vivid halo
#

if you're taking derivations to be the definition of tangent vector then yeah

violet wraith
#

makes sense

vivid halo
#

otherwise you just have to do a little work to see how you can go back and forth between these two definitions

#

basically the point is such a thing gives you a notion of directional derivative

violet wraith
#

oh yeah this concept is familiar

#

how this stuff gives rise to directional derivatives

vivid halo
#

if you have a tangent vector in the literal sense then this is telling you in which direction you are differentiating, but if you have some notion of directional derivative then this had better be a differential operator or a derivation

violet wraith
#

I learned some diff forms

#

I'll be back one minute

#

so pretty much df can be thought of as an operator that maps the fuction to a section of T*X

#

is this a correct summary? @vivid halo

vivid halo
#

err d does this

#

it sends the function f to this section df of T*X

violet wraith
#

ok cool

vivid halo
#

if we suggestively write \Omega^0(X) for functions on X and \Omega^1(X) for 1-forms on X

#

then you get a map d:\Omega^0(X)->\Omega^1(X)

#

in general you get maps like d:\Omega^i(X)->\Omega^{i+1}(X)

#

with dd=0

violet wraith
#

what operations can we do with them? I'm aware that you can add them, multiply them together, and multiply them by other functions; anything else?

vivid halo
#

yeah so \Omega^1(X) becomes a module over \Omega^0(X) so you can add 1-forms together and multiply them by functions

violet wraith
#

we cant really divide differentials so how do they turn into derivatives

vivid halo
#

the way they turn into derivatives is by pairing them with tangent vectors

#

so like the way we paired dx with d/dx or d/dy

#

like in general if you write down what this pairing of vectors and covectors is doing in some choice of basis

#

the coefficients in the expression will involve derivatives in the usual sense

violet wraith
#

I see

#

that's cool

#

i find strong interest in this kind of stuff

#

if I had more time I'd love to pick up a book on diff forms or diff geo

#

thanks for your help :)

dark wharf
#

Anyone know website design really well? I’m having issues with my domain causing a “not secure” message to pop up on certain browsers encouraging the user not to enter any sensitive information including payment cards… which is the whole point of my site…

merry hedge
#

Hacer hacer

eager reef
#

that's probably not design related

#

but certificate

dark wharf
#

Well i’m using square space and it should already have an SSL certificate but for some reason it isn’t???

#

yea that’s what’s weird lol. I’m trying to contact their customer support rn

woven whale
dark wharf
#

???

woven whale
#

why are you making your own payment site

dark wharf
#

I’m not

woven whale
#

what?

#

squarespace is just a website builder

dreamy cloud
#

hey yo peeps

woven whale
#

lmao then

neat lintel
# dark wharf Well i’m using square space and it should already have an SSL certificate but fo...

That's nice ^°^ good luck on ur website
https://support.squarespace.com/hc/en-us/articles/205815898-Understanding-SSL-certificates
Square space does have an article on it you can read on, good luck on ur website stev ^°^

dreamy cloud
#

joined up in here to help some peeps

dark wharf
neat lintel
dark wharf
#

Thanks all!

woven whale
#

@topaz swift are you V.Ch.?

jaunty raft
#

how do I answer this ?

chilly hull
vast surge
#

I'm seriously afraid that I'm not going to be able to graduate

#

Just due to stupid bullshit

violet wraith
#

like what

vast surge
#

My advisor's placed a hold on me registering for classes until I declare a minor

violet wraith
#

then declare a minor

vast surge
#

But to declare a minor I need to pick a professor to be my minor advisor

#

And the only CS professor I know retired, and wasn't taking on new advisees

violet wraith
#

oh

vast surge
#

I'll be in a few CS classes next semester if I can register, which would let me meet new CS professors and pick one to choose to declare my minor with

#

But I can't do that if this hold on my ability to register isn't lifted

violet wraith
#

wait so your school requires you to have a minor? and you have advisors for your minor?

vast surge
#

Yes

violet wraith
vast surge
#

And that's just one of, like, 3 situations like that that I'm in where cycles of administrative bullshit are getting in my way

violet wraith
#

great!

vast surge
#

So anyway I'm continuing to apply for PhDs anyway even though I might be fucked and not able to even take classes next semester let alone graduate

#

(well in theory that's what I'm doing, in practice my executive functioning is so bad that I'm not actually doing that)

#

Because I basically need adderall in order to have decent executive functioning but I need an adhd diagnosis to get adderall but I need better executive functioning to get around to setting up an appointment...

violet wraith
#

you can't set up an appointment?

vast surge
#

Well I tried sending an email to set up an appointment a few days ago and haven't heard back yet, but that's exceptional; I normally write an email and panic over making it perfect and then it sits in my drafts folder and then I forget

jovial ember
#

Bruh

vast surge
#

Is my life the plot of a college au catch-22 fanfic? Maybe.

undone wren
#

Why did you do adderall when your brain was fine?

vast surge
# undone wren Why did you do adderall when your brain was fine?

It well and truly was not. I was barely functioning, and a friend suggested I try it, and so when I had access to a dealer I was able to do well, but my dealer is super fucking sketchy and scares the shit out of me so I want to get a proper diagnosis, and we're not in touch anymore

undone wren
#

Are you from america? That's the only place i can think of where it's soo easy getting drugs

vast surge
#

I'm currently in America, yes.

#

But there's way easier places to get drugs than America

undone wren
#

How was your productivity studying before and after taking adderall?

vast surge
topaz swift
violet wraith
vast surge
#

It varies a lot day-by-day and based on mood, though, which when I was on adderall was very much not the case.

#

When I was productive I was very productive though.

#

But then the slightest distraction could ruin my concentration for like 2 days

violet wraith
#

what the fuck

#

that's severely bad

#

can't you call someone to set up an appt if emailing gives you trouble

#

^

vast surge
violet wraith
#

no fucking way

undone wren
#

I had a similar issue when i was younger but the issue is was that i wasted all my mental energy in dumb stuff like videogames, dronning in youtube watching random videos, etc. Once i quit all that i was reasonable consisten with my studies, studying about 2 hours every day

vast surge
#

But I think that might be more of an autism thing

violet wraith
#

do you live with anyone?

vast surge
vast surge
violet wraith
undone wren
#

Don't you get bored when that happens or you think you are working?

vast surge
#

Eliminating distractions doesn't make me more productive. At best it makes me turn to other distractions, at worst it just means that I do nothing.

violet wraith
#

you need motivation

#

you need to find things that motivate you to work

vast surge
violet wraith
#

oh

#

it's just distractionsn

vast surge
#

Like, I want to do my PhD applications

violet wraith
#

maybe work with a friend

#

who can keep you in check

vast surge
violet wraith
#

well then idk

undone wren
#

I'm very slow when it comes to studying, sometimes i spend an hour or two just trying to understand a page of some book

vast surge
#

That's a typical pace

#

If it's a sufficiently advanced math book

#

If you're actively working on it

#

My problem is I'll have it out in front of me and often not be actively working on it

#

It will just be there and I will be completely unable to concentrate

undone wren
#

Yeah i gotta work every exercise even when they are not exercises given by the autor to solve, it's just a thing i have

#

When i'm unable to solve some exercise i have it for days in my mind

vast surge
#

That's not a problem nor is it being slow. That's just doing extra work, more than is required of you.

#

That's me on a good day

undone wren
#

Anyways, i know some people that do modafinil instead of adderall, i'm not recommending it but maybe it works for you

vast surge
#

I looked it up, you also need a prescription from a doctor to get it

undone wren
#

Ah, right

#

I take a lot of caffeine too when studying but in the form of mate which is some tea from south america

#

Some people smoke but i don't think smoking will give you the spark you need

vast surge
#

Weed doesn't help me, and I already go through a pack of cigarettes maybe once a week. It helps me sober up if I've had too much to drink, but otherwise has no real effect on me.

#

Also helps me if I get the shakes, actually

woven whale
undone wren
#

Are you shaking uncontrollably as well? Brutal

vast surge
#

Not often but I do sometimes get anxiety attacks

topaz swift
undone wren
#

Is it stress or has it always been like that?

topaz swift
#

Or did you just randomly happen upon it?

woven whale
#

I randomly stumbled upon a post and knew it was you

topaz swift
#

Interesting. Was it because I posted part of the same question in the algebra channel recently?

woven whale
#

yes

vast surge
topaz swift
# woven whale yes

To be expected. We actually have something in common, I also study in Germany. However I am not a schoolchild, as I understand you are. Which uni are you taking your courses at?

vast surge
#

Actually I get the shakes mostly when I have a crush

vast surge
#

Love is an anxiety disorder

undone wren
#

A crush? As in when you think of someone you like?

topaz swift
woven whale
#

I'm in 10th grade

topaz swift
#

Bah, even better.

#

I hear Scholze was the same.

#

How's RUB? I'm thinking about potential master's unis.

woven whale
#

the mathematics building is being renovated

#

so math stuff is spread across other buildings

topaz swift
woven whale
#

such as the engineering ones

#

and physics/chemistry

undone wren
#

Never had a crush in uni, everybody in my course are autistic men (i'm probably one) and one or two women with personality disorders

topaz swift
vast surge
undone wren
#

Ah, right

woven whale
#

I'm not that involved in those things

undone wren
#

@topaz swift what's iktf?

topaz swift
#

How many courses do you take, do you manage well with your schoolwork?

vast surge
topaz swift
undone wren
#

Ah, right

#

@vast surge most people in computer science are like that

#

In math and physics they are more social

topaz swift
#

Seriously, it's a fucking blight (at my uni at least), all the courses I've taken have been sausage parties. If there are any girls, they all study Lehramt, i.e. to be certified gymnasium teachers.

topaz swift
vast surge
#

My school's CS department is more neurotypical than the math department. At least we get our fair share of "women with personality disorders" as you eloquently put it; the CS department are just... The opposite of the math/CS stereotype, basically.

undone wren
#

Weird

vast surge
#

My school just doesn't have those stereotypical nerds, I think

topaz swift
#

@vast surge two questions:

  1. The cover of what book is your avatar? I remember it was a French CA textbook, but I don't remember the title. There is no English translation afaik, right?
  2. What kind of fantasy lit do you read?
undone wren
#

Herr we have a bit of everything but that's because the uni i go to is the biggest in the country, probably top 3 in size in the continent

vast surge
vast surge
topaz swift
vast surge
#

I also read the first couple of Weiss and Hickman's Deathgate Cycle recently, but I'm not sure if I'll finish it.

#

Yeah, Elric is amazing

#

The writing style can be... Difficult, at times, but the story itself and the ideas in it are incredible

topaz swift
#

I had a big fantasy phase couple of years ago when I first got into the genre, having only read HP and LotR as a kid. I've kind of slowed down recently and nothing has been able to keep my attention, which is why I've been reading Conan stories recently (the bite-sized chunks are a positive).

vast surge
#

Before you ask, no, I don't have a crush on your mother, she's just an easy shag.

topaz swift
vast surge
#

A fair warning about Elric, it's super hard to find the books, and the reading order is also hard to figure out.

topaz swift
vast surge
#

It's not weird to sleep with your mom, everyone's doing it

topaz swift
#

Have you read First Law? Big fan of that.

vast surge
#

Not yet. I've heard mixed things though.

#

Some say that it's really, really good, but some say that it's like a lot of later grimdark in that it's edgy just to be edgy and would be better if it was toned down.

topaz swift
#

It gets a little repetitive sometimes, but the writer is very self-aware in a good, non-Deadpooly way.

vast surge
#

Honestly I read more fantasy before I started college. I just haven't had the time these past few years.

topaz swift
#

He knows what he's writing and how to deliver to the audience. I don't think it's edgy for edginess sake at all, just ebcause the story if violent.

vast surge
#

Rothfuss' The Name of the Wind is really good though. When I read it I think I read it in like two or three days, so it's also good if you don't have much going on

topaz swift
vast surge
#

Oh, I've also recently read all the Hellboy and B.P.R.D. and Abe Sapien comics

topaz swift
#

I liked the University setting, even if it was a little of Hogwarts ripoff.

vast surge
#

It was better than Hogwarts, in my opinion, but I'm also just not a big Harry Potter fan so maybe that's just me

#

HP fanfiction tends to be better than the HP books themselves, and lots of HP fanfiction just sucks

topaz swift
#

And I really like the concepts of sympathetic and naming magic, the story's framing device and its overall theme of semiotics and historiography.

#

But Kvothe is a fucking obnoxious protagonist.

#

And don't get me started on the Della romance.

#

And how book 2 goes completely off the rails.

#

With thick ninja mommy gf's and faerie sex goddesses.

topaz swift
vast surge
#

Book 2 is a little bizarre at times, yeah.

topaz swift
vast surge
#

But I actually kind of like Kvothe as a protagonist (though not as a person), and the Della romance was... Well, it wasn't good per se, but it certainly wasn't unrealistic.

topaz swift
vast surge
#

Like, Kvothe is an interesting protagonist to follow and character to read about, but I'd kind of hate the guy if I interacted with him.

topaz swift
vast surge
vast surge
topaz swift
#

I do like punished older Kvothe.

vast surge
topaz swift
#

It's a meme on /lit/.

#

Jesus, this image was huge.

#

I thought the server choked on it.

vast surge
#

Yeah, I remember this. As I said, it's not a particularly healthy romance, but it's well-written and realistic. Like, Kvothe's an obnoxious jealous sadboy about it, but I like it.

topaz swift
#

Have you read any John Gwynne? Was thinking of trying that too.

#

Or Gene Wolfe.

vast surge
#

I've not heard of John Gwynne, but I've been meaning to read Gene Wolfe.

#

Oh the absolute best fantasy series of all time by the way

#

Memory, Sorrow and Thorn by Tad Williams

#

It might be absolute perfection.

tribal jay
#

Il y a un français

topaz swift
#

Do check out First Law, the first trilogy is universally acknowledged to be very good.

#

And Prince of Nothing, if you want the A Serbian Film equivalent of fantasy.

vast surge
#

Nominated for an Arthur C Clarke award, with a blurb by N. K. Jemison, and near-universal acclaim on goodreads.

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And it has that cover, and that title, and is about aliens who are romantically obsessed with humans

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I found out about it the other day and it's quickly jumped near the top of my to-read list

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I feel like that would have just tipped it too far into absurdity where it's obvious the cover is bad on purpose

rapid fjord
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what is that 😭

vast surge
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As it is I can't tell if it's just a bad cover or an intentionally bad cover.

vast surge
rapid fjord
topaz swift
vast surge
rapid fjord
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explain

vast surge
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So there are aliens

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And someone had a camera

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And took a photo of them for the cover of this book

topaz swift
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You'd be surprised, but not everything is CGI.

rapid fjord
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i just can't imagine living in a world with actual extraterrestrial activity

topaz swift
vast surge
rapid fjord
vast surge
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They also have some cameras and telescopes

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And a metal plaque

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With naked people on it and a map of where to find Earth

rapid fjord
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that just threw all that science shit out the window

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but it's a good theory though

vast surge
topaz swift
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@vast surge bro did you find the ComAlg textbook?