Imagine a world where people can't lie.
#serious-discussion
fervent notch
storm sage
That's not at all what I am saying
low spruce
Alright I'm gonna call it a day, so peace out folks!
fervent notch
Something is either true or meaningless in such a language.
fervent notch
And if you want to find out whether something is true or meaningless, you have to find out if that thing is a theorem or not. You can theoretically do that.
You can say "red is blue" in English and we say that is false. But we could very well say it is ungrammatical and thus meaningless.
alpine kindle
by "true" do you mean syntactically
fervent notch
We just don't want English to work like that.
alpine kindle
or semantically
fervent notch
There is no "real" stuff in math.
alpine kindle
like do you mean "only derivable statements are WFFs" or "only valid statements are WFFs"
fervent notch
like do you mean "only derivable statements are WFFs" or "only valid statements ...
Yes.
alpine kindle
because those aren't necessarily equivalent
fervent notch
I mean the former and there is no concept of falsehood. There are just theorems.
alpine kindle
either way
fervent notch
And now you do not need true or false.
alpine kindle
you cannot like
fervent notch
Math will be a language of "truth".
fervent notch
Just to make this point again, I am not advocating we work with such a thing. I am saying that if we did, it's an example that would not lead us to these "surprising" results.
I find our paradoxical system very convenient to use.
alpine kindle
I find our paradoxical system very convenient to use.
this is an incredibly bad system
fervent notch
It's impractical but it can prove all the results we have from our usual math.
It's impractical because you can't express a hypothesis and work with it because you don't know whether it's "math" yet since you don't know whether it's well-formed. You always have to work yourself from the ground up.
alpine kindle
can it
fervent notch
Yes.
So if I write something like a hypothesis that is say 300 symbols long I might need to brute force my axiomatic system up to all formulae of that length and see whether my hypothesis is on that list.
That's horrid. But it would work, in principle.
cloud drift
So if I write something like a hypothesis that is say 300 symbols long I might n...
I dont think this is true
fervent notch
As usual. You have your axioms and your deductive rules and then you play around with those.
fervent notch
I dont think this is true
It most definitely is. It's not easy to see why Godel's proof makes no sense if we don't allow for WFFs based purely on syntax rules that has nothing to do with truth.
cloud drift
Its a bit equivalent to what I said here
If you could just bruteforce any truth - even if it takes an infinite amount of time - reality would be computable
Or am I too dumb to understand what you're saying
fervent notch
First of all, probably shouldn't conflate reality with math. We use math to model reality; that's a thing in its own right.
alpine kindle
ok how do you prove vacuous truth
fervent notch
Its a bit equivalent to what I said here
If you could just bruteforce any truth ...
And also don't conflate Godel with Turing here. You can even more easily discard Turing if you don't allow for infinite tape.
alpine kindle
any statement of the form A → B where A is a statement false in every model
fervent notch
We don't necessarily think you could build a Turing machine in the real world. But if you want to play with infinities, which we like cause it makes reasoning simpler, then sure.
fervent notch
any statement of the form A → B where A is a statement false in every model
Remember, we did without falsehood.
alpine kindle
Remember, we did without falsehood.
false in every model of our original system
fervent notch
If A is false then talking about it is impossible. You can't say "if pigs can fly then atoms are small" because pigs can't fly, it's ungrammatical.
That doesn't take away that atoms are small, of course.
Note that vacuous truths are also a convention.
fervent notch
No, you cannot express falsehood at all. You can express 1 = 1 but never 1 = 2 since it is meangingless.
alpine kindle
this statement is true in classical logic
fervent notch
Not even false but not a WFF.
You don't need a truth predicate at all.
Since everything is true or not a WFF.
alpine kindle
Not even false but not a WFF.
then you cannot prove all results from regular mathematics
which is what you claimed
fervent notch
Is this your channel or why do you have to keep telling us you don't care about our conversation? We don't care.
We read you the first time. Go do something else.
alpine kindle
~(1 = 2) is a result from mathematics done in classical logic
fervent notch
~(1 = 2) is a result from mathematics done in classical logic
Sure but you can just say something along those lines of "if I can't express it than it's, in classical terms, false".
So in a sense, you are proving something quite equivalent.
fervent notch
In the classical construction, yes.
alpine kindle
you have moved the goalpost
fervent notch
You can't talk about literally true as if it were somehow objective.
That truth comes with that model.
If I want to, I can make it literally false.
cloud drift
Sure but you can just say something along those lines of "if I can't express it ...
Yes but the word "false" is a grammatical error in your system
fervent notch
It is indeed. We use truth and falsehood as conventions because they help us use the system in practice.
alpine kindle
If I want to, I can make it literally false.
you did however claim that your system can prove all results in usual mathematics
usual mathematics is done almost exclusively in classical logic
fervent notch
Think of "not WFF" here as the equivalent of "not WFF or false" in classical terms.
And of "WFF" as "true" in classical terms.
cloud drift
you did however claim that your system can prove all results in usual mathematic...
Assuming his system is correct, you could just bruteforce all WFFs up to 6 symbols and see that "~(1 = 2)" is not in here
fervent notch
Yes, precisely.
alpine kindle
Think of "not WFF" here as the equivalent of "not WFF or false" in classical ter...
yeah but that doesn't end up aligning with classical logic
cloud drift
But the "bruteforce" part is bugging me
fervent notch
Yes, brute force is horrible, that's why we don't do it that way.
cloud drift
Yes, brute force is horrible, that's why we don't do it that way.
Im not talking about bruteforcing that is bad but I dont see how you would bruteforce something that is intentional/not purely formal
alpine kindle
actually better question
can you properly define what a WFF is in your system
by derivable what do you mean
derivable in what system
fervent notch
I suppose it depends on how you want to define ~. But you should not be thinking in terms of emulating one thing in terms of the other but in terms of what can you take from the system, which is the same conclusions except there is no "true" vs "false" if that makes sense.
A WFF is a theorem.
alpine kindle
ok what's your deductive system
cloud drift
Damn
fervent notch
Just a set of rules to take axioms/theorems and manipulate the symbols in some way.
You get a different WFF/theorem.
alpine kindle
could you give an example of a deductive system that would satisfy your requirement of making false things inexpressible
fervent notch
Whenever you used to want to say "such-and-such is false" you now say "such-and-such is ungrammatical".
I think the issue here is that we aren't being pedantic enough and we're kind of mixing and matching between two sets of terminologies quite loosely. You mean to say false things in classical constructions not being WFFs in the new math construction.
Since there is no truth predicate, there isn't a concept of falsehood so you can't talk about it.
alpine kindle
i can prove ~(0 = 1) with the regular classical deductive logic axioms:
forall x ~(0 = s(x))
~(0 = s(0))
~(0 = 1)
fervent notch
Ok. And in the new system it's ungrammatical that 0 = 1 so you don't need to prove it at all.
fervent notch
The axioms and deductive system do not lead you there.
cloud drift
Since there is no truth predicate, there isn't a concept of falsehood so you can...
Well yes there can, you can express falsehoods with booleans
alpine kindle
Ok. And in the new system it's ungrammatical that 0 = 1 so you don't need to pro...
true
but you said that ~(0 = 1) is ungrammatical
i have very clearly proven it is not
fervent notch
No because what you're doing here when you write ~(0 = 1)
alpine kindle
that's literally a peano axiom!
fervent notch
is that you're trying to emulate the old way of doing things between the parantheses.
alpine kindle
can you define the natural numbers
please
because clearly you do not like the peano axioms
in this system
fervent notch
So the problem here is that when you say Peano you already have axioms that cling onto ideas like truth and falsehood. For example, you might want to say S(n) = 0 is always false as in there's no natural number whose successor is zero. You can define something like the Peano axioms.
storm sage
ally stop being combative in tone lol
solar hawk
Hi
fervent notch
I didn't think he was.
solar hawk
She
fervent notch
Or she.
storm sage
Oh maybe I misread
solar hawk
What’s a piano axiom
alpine kindle
ally stop being combative in tone lol
sorry i realised that last statement was kind of combative
fervent notch
Or they, since they are an albanian group, lol.
alpine kindle
Or they, since they are an albanian group, lol.
i literally have the pronoun role 
storm sage
Groups can be female #FreeGroups
fervent notch
I'm not a snowflake. It's normal to get fired up in a conversation as long as we don't start calling each other names or something.
alpine kindle
what are you talking about
storm sage
Okay anyways sorry for interrupting
cloud drift
@fervent notch your system can never be constructed, can it ?
solar hawk
Cuz he thought fired up
cloud drift
or used
fervent notch
It could be constructed and it could be used. Should it? Definitely not.
storm sage
The axioms aren't computable
cloud drift
It could be constructed and it could be used. Should it? Definitely not.
can you demonstrate how to use it ?
fervent notch
I'd have to construct some sort of system as an example... I just said no one should do that, lol.
alpine kindle
anyway @fervent notch could you give a definition of N in this system
is what i asked
cloud drift
I'd have to construct some sort of system as an example... I just said no one sh...
that what I'm asking yes. even if it's something very dumb
alpine kindle
i don't really see the problem with the peano axioms but there seems to be some moral issue
on your part
fervent notch
I mean it could be constructed using set theory but next you're going to ask me for a theory of sets.
alpine kindle
i feel like that's not the way
fervent notch
Like the usual construction where say, the number two might look like {∅, {∅}}.
alpine kindle
could you tell me why $\forall x \lnot (0 = s(x))$ is an issue to you
fathom swallowBOT
ally (albanian group)
fervent notch
Yes. The problem is that this relies on truth and falsehood. "It is not the case that" means something is false.
alpine kindle
when did i say that's what ~ means
~ is just a symbol
as is anything in maths
we give it meaning
~ is just a symbol with axioms defined that include it
fervent notch
Or perhaps you could express it. I'd need to think about it.
storm sage
I don't see how you can brute force WFFs up to length n
Like for example how would you tell if the Goldbach sentence is a WFF
fervent notch
I think the problem I am having is that 0 = s(x) part which is not supposed to be WFF.
alpine kindle
I think the problem I am having is that 0 = s(x) part which is not supposed to b...
it's not though
I've never claimed that it is
but forall x ~(0 = s(x)) is
like how T is a WFF but ~T isn't
but the other way around
fervent notch
Like for example how would you tell if the Goldbach sentence is a WFF
Can the statement be formed by a finite number of symbols?
Although, no, cause formal systems can obviously reduce the number of symbols via deduction rules and you can't know when that happens.
I suppose you just can't work with hypotheses at all.
So it's even worse than brute forcing.
storm sage
That's what I meant, there's no way to tell whether something is a WFF
fervent notch
Yes, you are right.
storm sage
which just shifts the burden to figuring out if something is or not which seems worse
fervent notch
Oh, I never claimed it was better.
I just claimed Godel would be out the door, that's how this all started.
It was just my claim that the notion is tied to the idea of having WFFs.
Then we started going on a tangent about what such a system might look like or how it could be used.
storm sage
Gödel still essentially applies here
It's just that your system/axioms aren't computable
Which the incompleteness theorem claims would happen if you had a complete and consistent formalization of arithmetic
fervent notch
Well, wait. If all your WFFs are theorems that you can't really make up sentences like "this statement is true" because it's not a theorem.
You're specifically allowing that based on syntactical rules.
storm sage
I'm saying that figuring out if something is a WFF is not computable under this system
So the same spirit of the incompleteness theorem applies
fervent notch
It's not incomplete but it's... uncomputable now. That's what euler is saying.
So in a sense, we did just shift the problem over.
And have a different one.
alpine kindle
a system G is consistent iff there is no formula f such that G entails f and G entails ~f
every theory in our system is consistent
fervent notch
Right. What they are saying is that while we don't have THAT problem, we cannot know whether something randomly scribbled somewhere is a theorem at all.
Cause we cannot brute force in fact.
storm sage
Yeah this is essentially the same as having the entire theory of N as axioms and having no deduction rules
alpine kindle
no incompleteness doesn't fail
storm sage
Then it's complete and consistent but not computable
fervent notch
(Not a finite number of axioms necessarily.)
alpine kindle
you only have to have a formula f such that you cannot prove f or ~f
fervent notch
Good point.
alpine kindle
this is independent of any sort of truth
you can still construct the gödel sentence
hm
fervent notch
Well you can but you don't know whether it's WFF and finding that out is uncomputable.
storm sage
I think the incompleteness theorem still remains very surprising to me
The natural numbers feel completely describable
fervent notch
Yeah, I guess that just goes to show that incompleteness and uncomputability are two sides of the same coin.
storm sage
Yet somehow there's always some aspect that we can't say anything about
gritty mortar
hey can anyone suggest me a place where i can get medium to hard polynomials and quadratic equation question, mainly i am looking for word problem type questions in these topics
storm sage
hey can anyone suggest me a place where i can get medium to hard polynomials and...
Maybe khan academy or ixl?
Have you tried looking up worksheets about the topic
solar hawk
Ixl 💀
gritty mortar
khan academy was basic, what is ixl ?
solar hawk
khan academy was basic, what is ixl ?
And Kahn academy has many different levels..
You can do multivariable calculus on there if you want
gritty mortar
And Kahn academy has many different levels..
idk maybe beacuse i am india it is not showing hard levels
solar hawk
idk maybe beacuse i am india it is not showing hard levels
That’s not how it works
gritty mortar
it was a 9th grade course on khanacademy for me
gritty mortar
That’s not how it works
no when i use a vpn it shows diff courses but i dont not have time for watching vids and then questions
i just need a list of questions
btw i will check ixl rn
solar hawk
Ok
gritty mortar
Have you tried looking up worksheets about the topic
i get pages from libretexts and chegg when i search that
and indian edtech platforms like toppr, byjus
no proper questions in those places, i want like strutured word problems with increasing levels in difficulty, grouped by type of problems
surreal sapphire
thank
solar hawk
Ye
alpine kindle
Well you can but you don't know whether it's WFF and finding that out is uncompu...
this is probably where gödel doesn't work
there is a long list of definitions he uses
I'm sure somewhere in there it fails
storm sage
Yeah one way to rephrase the incompleteness theorem is that if you have a complete and consistent formalization of arithmetic, then it's uncomputable
So this is just a demonstration of that
alpine kindle
I can't get the paper for free though so i wouldn't be able to tell you exactly where your system fails
fervent notch
I can't get the paper for free though so i wouldn't be able to tell you exactly ...
Again, it doesn't in the sense that it is indeed complete. But as euler pointed out, we face the same problem under a different name.
woven whale
https://tenor.com/view/simpsons-fat-discord-mod-wow-the-simpsons-predicted-discord-mods-gif-23841326
@storm sage this you?
fervent notch
Since it being complete isn't more interesting if you still cannot compute whether a formula is well-formed, which is all such a formal language would care about.
storm sage
<@531535537362829315> this you?
I'm not sure I understand the joke
jovial ember
I'm not sure I understand the joke
Lol discord mod so fat and gross haha funny
storm sage
I still don't understand the joke tbh
ocean harbor
Lol discord mod so fat and gross haha funny
sage pike
Undergraduate majors in mathematics are encouraged to study languages while at Wesleyan; majors who are considering graduate study in mathematics should note that graduate programs often require a reading knowledge of French, German and/or Russian.
found this in a uni's catalog (not mine). how true is that?
frigid timber
#math-discussion first to tell me
slow void
Is anyone here an electrical engineer or similar?
cyan goblet
there's servers for that in #old-network
sonic field
👀 yall cuttin up in here 🤣
glad phoenix
Is there anyone who also is planning to prepare for Calculus I and would want to join me so we can help each other?
sonic field
what's you guys' favorite setups for studying? I'm lookin for ideas XD
storm sage
`Undergraduate majors in mathematics are encouraged to study languages while at ...
It's becoming less true nowadays
But a lot of mathematical work is still written in those languages (which one depends on the field)
So you should be at least proficient enough to read those papers, which tbh given the amount of context clues is not that proficient
sonic field
I'll go first tho. At work, I have an office with a biggish L-shaped table. Has 3 monitors, tho i could go with 2. I've got some jazz music playing in the background, and a mug of coffee usually hot, somethin healthy to munch on and a directed led lamp so light isn't blaring in my eyes, jus shining on the paper. Got a mister in the back with peppermint going etc. Nice warm ambience helps keep me calm while I'm working math cuz I get angsty.
Wish I had this setup at home
cinder zephyr
My AG prof said he learned french by reading Serre
neat lintel
Can someone check whether my proof is correct?
Suppose that P is true. Prove that Q → ¬ (Q → ¬ P ) is true.
Given:
P
Q
Goal:
¬(Q → ¬P)
Proof by contradiction:
Assume that Q → ¬P is true.
Since we have Q and Q → ¬P, by modus ponens, we can conclude ¬P.
However, we also have P from the given statements.
This leads to a contradiction: P and ¬P cannot both be true.
Therefore, our assumption that Q → ¬P is true must be false.
Hence, ¬(Q → ¬P) is true.
ocean harbor
seems right
serene pulsar
more math, more ice cream sandwiches, and my FAFSA (financial aid) finally processed and I am eligible for maximum financial aid
it looks like I'll finally be able to go to college
ocean harbor
pog
serene pulsar
now I must get back to studying math so I can take my placement test 😎
little vine
Ah exciting
bronze jetty
sup
rocky shuttle
inf
granite flare
I went from thinking I was going to test out of calc with CLEP to taking Calc 1 & 2 Honors lmao. At least it wil be easy since I already know the majority of the concepts lol.
granite flare
L
L? That's a huge W. I get 8 Honors credits with minimal effort lol. Versus taking Honors classes that are actually hard.
slender dock
craggy yoke
vivid fable
hello can you all recommend some good math YouTube channels?
rocky shuttle
hello can you all recommend some good math YouTube channels?
the bright side of math
craggy gust
are you looking for a certain topic
brave shell
I really like Another Roof. His earlier videos focus too much on foundational stuff for my liking but recently he has a few where he just talks at length about a problem, providing enough background knowledge to follow along with each step.
craggy gust
if you go to youtube and search #SoME you will find videos that are part of the Summer of Math Exposition challenge that I think grant (3b1b) came up with
Sometimes they're tagged #SoME2 or #SoME3 (its summer 3)
vivid fable
are you looking for a certain topic
no not any certain topic, but just youtube channels to explore more of maths
ripe wyvern
hello can you all recommend some good math YouTube channels?
Jimmy woo (or something)
Red pen black pen
3 blue 1 brown
There might be better ones
toxic copper
Jimmy woo (or something)
Red pen black pen
3 blue 1 brown
There might be bette...
Eddie Woo?
tiny forge
ripe wyvern
Eddie Woo?
I knew I got it wrong
echo swift
Hey
ocean harbor
yo
forest vale
hi
serene pulsar
More studying... Still a bit sick but I want to study. I left off on logarithms. Solving the problems with the natural logarithm is really easy, but I wanted to learn a lot more about logarithms because I like them a lot. I loved learning about log tables and the history of how logarithms came to be. I think I'm ready to continue past it for now to finish studying the rest of the review.
I'm excited to finish this review exam and get to the final one that would place me in calc 1
forest vale
More studying... Still a bit sick but I want to study. I left off on logarithms....
suddenly i got a qusstion:
$$(\ln a)^{(\ln b^2)}=(\ln b)^{(\ln c^2)}$$
find the relationship between $a$ and $c$.
fathom swallowBOT
biscuityxd
forest vale
oh, i forgot to add that b≠1
real copper
!help
quasi jettyBOT
Please read #❓how-to-get-help
real copper
i need help with somthing
forest vale
i need help with somthing
!help
quasi jettyBOT
i need help with somthing
Please read #❓how-to-get-help
real copper
i need help with math
forest vale
i need help with math
!help
quasi jettyBOT
i need help with math
Please read #❓how-to-get-help
fathom swallowBOT
brandon_hu
neat lintel
Hello, is this correct?
cedar idol
j'ai crux que vous l'etudie d'apres serre mdr
long matrix
je le avais a ecole
le avais
ocean harbor
serene pulsar
Sadly did not study as much math as I wanted to today. I was too sick and had a bad mental health day. But I think it's fair that I rested since I've been studying entire days for the past week or two weeks.
I did watch an 18 minute video and logarithms and 2 numberphile videos though, I really love the history of them.
Tomorrow I hope to be back on the grind 💪
oblique beacon
Gimme a 2 digit number
oblique beacon
A 2 digit integer
static loom
Gimme a 2 digit number
11 ||in base a billion 😎 ||
oblique beacon
11 ||in base a billion 😎 ||
^
serene pulsar
^
Are you practicing mental maths tricks for squaring?
I love cool tricks like that
serene pulsar
My favorite is how 11* any two digit number is just the first digit of that number, both digits summed, and then the last (second) digit.
Like 25*11=275
It's just so satisfying
oblique beacon
Pascels triangle
oblique beacon
My favorite is how 11* any two digit number is just the first digit of that numb...
Same thing with 3 digits too, sort of
252*11 == 2772
oblique beacon
251*11 = 2761
oblique beacon
that's nice
Yep
serene pulsar
you've just doubled my fun with 11 multiplications haha
and even 4 digits it seems, 11*2345=25795
I assume this trend continues with more digits
I love it
oblique beacon
Nice
Yh 1 1 is the second row of pascels triangle
So the numbers behave like it
serene pulsar
11*54313412345=597447535795. I will never need a calculator again for 11* anything haha
thank you for showing me this
What's the trick with squares?
static loom
11*54313412345=597447535795. I will never need a calculator again for 11\* anyth...
on the flip side, do you know the trick for testing if a number is divisible by 11?
serene pulsar
don't believe so, what is it?
static loom
start reading the digits off and add, subtract, add, subtract each of them
so like 597447535795 you'd look 5-9+8-4+...
and if the end result is divisible by 11, the original number was
and you can keep chaining this as long as you want
loud snow
Prove it
static loom
kinda like the test for 3 or 9
serene pulsar
oh nice I love it
loud snow
I think I can prove that this works
static loom
when it happens to fall into the pascal triangle you can tell this will work with an even number of digits obviously, 1-3+3-1 since they "fold over" to cancel
just as a quick sanity check
loud snow
So if you let a_i be ith digit
And you start with only a_1,2
We are required that a_1-a_2=0
Maybe this can be approached inductively?
oblique beacon
oh nice I love it
10a+5| a(a+1)10^2 + 5^2 | where a is a natural number
serene pulsar
For 2 digits. It based off anything ending in 5 or 0
81^2=6561, that's pretty good
oblique beacon
10a+(5-b)| a(a+1)10^2 +2(5-b)a+ (5-b)^2 | where |5-b| <= 2
static loom
the way I like to show it is
$$\sum_{i=0}^n a_i 10^i = \sum_{i=0}^n a_i (-1)^i \mod 11$$
fathom swallowBOT
merosity
static loom
doesn't matter if you start out with subtracting or adding because whether something is 0 or not mod 11 doesn't change when you multiply by -1
oblique beacon
Basically 25^2 | 2(3) 5^2 25^2=625. 35^2 | 3(4) 5^2 35^2=1225
static loom
not if you're testing for divisibility by 11
static loom
if x is nonzero mod 11, -x is nonzero mod 11
if x is zero mod 11, -x is zero mod 11
more succinctly, -1 is not a zero divisor in Z/11Z
(more generally Z/pZ is a field for p prime)
hollow kestrel
oh wait you are right
static loom
I think I left out a step of explanation that made it a bit confusing too, that whether you start with + or - is equivalent to factoring out -1 from the sum
static loom
**merosity**
I'm referring to this, idk what "?" is asking lol
hollow kestrel
Oh
static loom
$$x=\sum_{i=0}^n a_i (-1)^i \mod 11$$
$$-x= \sum_{i=0}^n a_i (-1)^{i+1}\mod 11$$
fathom swallowBOT
merosity
static loom
idk if that helps to see
neat bluff
@ancient bone
Hello, are you available?
I’ve discussed with you regarding the star patterns
would like to talk more about it
vernal edge
an anyone give me Factorising notes and examples for a cheat sheet
forest vale
hello hru biscuit
it's a lazy day for me 😛
forest vale
an anyone give me Factorising notes and examples for a cheat sheet
I don't have to materials, but what are you looking for?
vernal edge
just examples for factoising thats its
forest vale
ohhh, the short division
yea, for numbers that are smaller or equal to 120, just check if it is divisible by 2,3,5 or 7
e.g.87
forest vale
good
vernal edge
yes?
vernal edge
wait can you give me like (3x+15) those type of factorsiing
vernal edge
4b(5a + 2c).?
forest vale
yep
vernal edge
hmm
forest vale
25abc+20ab+15bc
vernal edge
comman factor 5 ye?
vernal edge
b
forest vale
👍
vernal edge
5b(5ac + 4a + 3c)
forest vale
nice
forest vale
abc+ab+bc+b
vernal edge
b?
vernal edge
ye but all u need. to do it take b from everywherer
forest vale
that's step 1
vernal edge
whcih will be b(ac + a + c)?
forest vale
whcih will be b(ac + a + c)?
nah
vernal edge
then what?
forest vale
then what?
finish step 1 first
neat lintel
it's a lazy day for me 😛
same 😭
forest vale
next, b(ac+a + c+1)
next, b( a(c+1) + (c+1) )
vernal edge
and then?
forest vale
yea
but do you understand?
more examples, this one is tricky
-2a+4ac = -2a(1 + ?)
find ?
vernal edge
-2c?
forest vale
yes
neat lintel
i don’t know it was a feeling
ivory forge
yall are very chill... so awesome
neat lintel
trying to act like chill
gentle radish
hi
cold rivet
are there any “alternate” forms of math?
like there is noneuclidean geometry
but something in math that just feels so foreign?
loud snow
but something in math that just feels so foreign?
Yeah
neon silo
I'm not exactly sure, but this is the closet thing I can think of that might be an example of what you're looking for https://en.m.wikipedia.org/wiki/Nonstandard_analysis
cold rivet
I'm not exactly sure, but this is the closet thing I can think of that might be ...
that is… something
ill look at that
neat lintel
Why doesn't this work for numbers less than 0?
solid snow
log(x) is not defined for x < 0
woven whale
log(x) is not defined for x < 0
No
solid snow
which part are you disagreeing with
woven whale
there's only one part
mental stratus
❤️
solid snow
ok..?
rocky shuttle
the principal part
solid snow
would you like to elaborate instead of just saying "no"?
woven whale
no
solid snow
productive discussion as usual
mental stratus
is log0 defined btw?
rocky shuttle
illum probably meant the extension to complex numbers
woven whale
only in ohio
storm sage
is log0 defined btw?
No
There is no complex number z for which e^z = 0
Log of any other complex number on the other hand can be defined
I'm sure there's a number system for which you can define it 🤔
fair mural
productive discussion as usual
what did you expect from illum really
serene pulsar
still having a bad mental health day but I'm very grateful for this server to keep me motivated and for all the people that are being helpful and patient in teaching me stuff I don't understand
mental stratus
serene pulsar
thank you guys
serene pulsar
@latent edge I was able to solve 5^(5x-2)=42 thanks to you!!! It looked daunting but I did it first try using the knowledge you gave me.
and to think just a week ago I didn't even know how to subract and divide fractions
I am having a lot of fun learning
latent edge
That's a good thing to hear
serene pulsar
😄
vernal edge
has anyone done the methods entry test for year 11
neat lintel
nobody knows what this is
grand tendon
can i put links here?
neat lintel
as long as you're not posting porn or advertising something
grand tendon
as long as you're not posting porn or advertising something
thanks
tried putting the expected value formula into the 3X+1 problem and it seems to make sense
silk raven
Jesus loves you , turn to Him before its too late , He wants you in his home . 🕊 John 14:1-7
grand tendon
Jesus loves you , turn to Him before its too late , He wants you in his home . �...
i know. i turned my yard into a church about a year ago and i don't regret it
neat lintel
how much noise will ten speakers make is such a dumb question
storm sage
That's actually evil
neat lintel
the answer is obviously 0
neat lintel
5 speakers play 1 sound and the other 5 will play a sound that cancels out the sound of the others
Could someone explain me complex analysis in private,i understand nothing 😣
storm sage
I feel like you are missing the point of the question
storm sage
Could someone explain me complex analysis in private,i understand nothing 😣
Ask your question in #real-complex-analysis
neat lintel
The question is dumb
neat lintel
I'm just gonna skip
storm sage
It's a good question
It should be fairly easy if you've understand the definition of decibel
If you want, just assume "ten speakers" means that P becomes 10 times its initial amount
velvet dagger
Relevant question is, is this a math question or is this a "do you know how sound works" question?
Because if they specifically told you before that intensity is what scales linearly by number of speakers, then this is a pretty simple arithmetic question
And it's testing whether you remember that fact
But if not (e.g. if it's a math class and the unit was on logarithms, and they threw this as an example), then this is underspecified and suboptimal
sterile summit
@stark pelican
hello
what happened to the channel in which you were answering my question?
it just disappeared
stark pelican
You clicked the channel category
Make sure the arrow on the left of ⏳ MATH HELP (OCCUPIED) is pointing downwards
sterile summit
yah mb
ebon oak
anyone know how eigenvalues and eigenvectors are used with fourier transforms
storm sage
anyone know how eigenvalues and eigenvectors are used with fourier transforms
the fourier transform diagonalizes translation
that is, if you have a function f and then another function g that's just a copy of f shifted to the left or the right
and you take the fourier transforms of both
then g just becomes a multiple of f
(I have no idea if this is what you were looking for lol but it's a cool fact)
ebon oak
i'm not entirely sure how fourier transforms work. i'm trying to find an application of eigenvectors and found that eigenvectors and fourier transforms are related
storm sage
I see
Essentially Fourier transforms are like a change of basis
If you're familiar with linear algebra terminology
Some things are nicer if you work in this new basis
ebon oak
isn't it where it breaks your signal into its elementary components
storm sage
Yeah, those elementary components are your basis vectors
ebon oak
ok gotcha
so you're saying that a signal is like a matrix A
and you can find its basis vectors with eigenvectors or fourier transform?
ebon oak
Yeah, those elementary components are your basis vectors
also these "basis vectors" are cos and sin, correct?
storm sage
so you're saying that a signal is like a matrix A
A signal is a vector [x0 x1 x2 ... ] written in terms of the standard basis and then applying the fourier transform changes this to a different vector [f0 f1 f2 ... ] which is written in the basis in terms of cosine and sine (or complex exponential, if you know what that is)
The Fourier transform is basically like the change of basis matrix
ebon oak
so fourier transform is the A in Av = λv?
storm sage
so fourier transform is the A in Av = λv?
What exactly is the question that you're looking to answer? Are you just looking for any sort of connection between eigenvectors and the Fourier transform?
ebon oak
i'm trying to understand how they connect
i have an assignment for linear algebra to find an application of eigenvectors and eigenspaces
aside from that class, i'm trying to get into research dealing with black holes, and they talk about fourier transforms
so i wanted to know how fourier transforms and eigenvectors relate
1pt is essentially “write down in your own words what
wiki has to say about it”, 2pts is essentially “do something a little better but without any real
math content”, and then 3pts is “a pretty good job explaining how a specific concept from linear
algebra is used in a scientific field you are interested in.”
storm sage
ah.. I see, so does it specifically have to be about eigenvectors? or can you say anything related to linear algebra
there's a lot of interesting linear algebra involved with the fourier transform
ebon oak
no it has to be speficially eigenvectors and eigenvalues
Write a paragraph which explains how eigenvectors/eigenvalues or some other topic from the course are used in a field which interests you
oh wait
nvm
jk i can't read
storm sage
haha
ebon oak
it can be any topic
storm sage
yeah you can talk about how sine and cosine form an orthogonal basis for real-valued functions, that would be interesting
and how the fourier transform is basically the change-of-basis matrix
and how the fourier transform is applied to some topic that interests you, like black holes
that sounds like it would take at least a paragraph :)
storm sage
and how the fourier transform is basically the change-of-basis matrix
if you've learned about orthogonal projection, proj_v u = (u dot v)/(v dot v) v, then that's basically how the fourier transform works
ebon oak
oh rlly??
storm sage
You project your original signal onto each of the basis vectors
Yup! :)
And since you're taking the dot product of two functions, the "dot" product becomes an integral
(Often we call this an inner product)
ebon oak
saw this video which kinda talked about how you can take derivative and integral of the fourier equation which is just scalar multiple since you're using derivates / integrals with an e^x function
storm sage
Yup yup that's what I meant before sorry, the Fourier transform diagonalizes the derivative
It converts the derivative into something easier to work with, which is just multiplication
ebon oak
that sounds like it would take at least a paragraph :)
assignment said previous students had done like poems, slideshows, etc. so i may do a simple slideshow to make it look i put even more effort in lol
storm sage
hahaha
ebon oak
Yup yup that's what I meant before sorry, the Fourier transform diagonalizes the...
how does it "diagonalize" a function?
i know how to dialogize matrices, but not rlly functions
storm sage
So basically, the derivative is a linear transformation
And if you have a basis for your vector space, then every linear transformation is a matrix, right? (I'm ignoring here the issue that the basis is infinite so the vector space is infinite-dimensional)
What does it mean for a matrix to be diagonal? It means that it looks like
[d1 0 0 0 ...
0 d2 0 0 ...
0 0 d3 0 ...
...]
and so on
So in other words if you multiply your matrix times [1 0 0 ...] then you get [d1 0 0...] and if you multiply your matrix times [0 1 0 ...] then you get [0 d2 0 ...] and so on
ebon oak
multiplying the matrix with your vector to get the diagonal?
storm sage
Similarly, if I take the derivative of e^ix, I get i * e^ix; if I take the derivative of e^2ix, I get 2i * e^2ix, and so on, do you see the connection? I'm applying the linear transformation to the basis vectors and getting back a constant multiple
So each basis vector is actually an eigenvector of the derivative operator
That's what it means for the Fourier transform to diagonalize the derivative
It turns a complicated thing into a simple multiplication
ebon oak
Similarly, if I take the derivative of e^ix, I get i * e^ix; if I take the deri...
so would the function be basis vector?
and the derivative is just a multiple of this basis vector, hence it would be like eigenvectors
storm sage
so would the function be basis vector?
Yeah your basis vectors would just be functions of the form e^ifx exactly
storm sage
and the derivative is just a multiple of this basis vector, hence it would be li...
Yup!
ebon oak
oooh that's pretty cool!
storm sage
I know right 😍
ebon oak
but this would rlly only work with this kind of function right?
storm sage
And that enables you to use the fourier transform to solve differential equations!
storm sage
but this would rlly only work with this kind of function right?
The nice thing about exponentials is that you can actually write basically any function as an infinite linear combination of them!
This is called Fourier's theorem
You basically use the "orthogonal projection" formula I talked about before
When you take the Fourier transform, you're taking your original function, and you're decomposing it as a sum (actually an integral) of these really nice exponential functions
ebon oak
i understand this with wave signals, i'm not sure mathematically
if i could send pics, i would but here's a link of the picture
ebon oak
When you take the Fourier transform, you're taking your original function, and y...
what you're describing is the same thing as the picture right?
storm sage
Yup exactly, you're taking your original signal and breaking it up into a sum of those three sine waves (plus background noise)
Mathematicians like to use complex exponentials instead of sines/cosines because the mathematics works out a lot more cleanly
But if you remember Euler's formula e^ix = cos x + i sin x then you can switch between them
ebon oak
i do remember Euler's formula but idk if i ever completely understood it
ebon oak
When you take the Fourier transform, you're taking your original function, and y...
i'm not rlly sure how taking the projection gets you the integral of the original function
storm sage
So imma talk about Fourier series first since it's simpler, but basically if you have a function defined on [0, 1] then you can decompose it into a linear combination of functions of the form e^(2 pi inx)
The way to do that is like this
You define a "dot product" on functions like this
[f \cdot g = \int_0^1 f(x)\overline{g(x)},\dd x]
and then once you've done that, you can notice that the exponential functions are actually orthogonal by computing the integral:
[e^{2\pi imx}\cdot e^{2\pi inx} = \int_0^1 e^{2\pi i(m-n)x},\dd x = 0]
storm sage
and in fact they're orthonormal since
[e^{2\pi inx}\cdot e^{2\pi inx} = \int_0^1 1,\dd x = 1]
fathom swallowBOT
eulerERICteristic
storm sage
and so this means you can use the orthonormal projection formula!
ebon oak
**eulerERICteristic**
wouldn't it be ...(m+n)..
storm sage
**eulerERICteristic**
No because of the complex conjugate I put in the dot product here
ebon oak
**eulerERICteristic**
how did you even start with this formula?
storm sage
Sorry I forgot to include it originally
storm sage
how did you even start with this formula?
It's a generalization of the dot product for complex-valued vectors
If you recall for vectors in (\bC^n), we have that
[v \cdot w = \sum_i v_i \overline{w_i}]
fathom swallowBOT
eulerERICteristic
storm sage
If you squint a little bit, you can see that this is actually the same formula I gave above except I replaced the sum with an integral
ebon oak
yes it's the same as above
but idk how u got that either
jk it's the formula of a dot product
is the conjugate similar to transpose?
storm sage
is the conjugate similar to transpose?
No so basically, you know how we want a vector dot itself to be the length of that thing squared?
ebon oak
right
storm sage
So if you have a complex number z = a + bi, the length of it squared is a^2 + b^2 just by the pythagorean theorem
storm sage
if you do the naive thing and just take z * z, then it doesn't quite work out to be a^2 + b^2
ebon oak
so it's a^2-b^2
storm sage
On the other hand, if you take z * conjugate of z, then you get (a+bi)(a-bi) = a^2 - i^2 b^2 = a^2 + b^2
And so it does work out
Which is why when you're taking dot products involving complex numbers you always always always have to include the complex conjugate
storm sage
**eulerERICteristic**
Which explains why there is a complex conjugate in this formula
ebon oak
why is it important to get a^2 + b^2
storm sage
Because that's the length of the complex number (squared)
ebon oak
oh right dot product
storm sage
Remember you always want z dot z = |z|^2
Yup
To finish off where I was originally headed, we get that the coefficients that you get from projecting (f) onto (e^{2 \pi i n x}) are
[\frac{f \cdot e^{2\pi inx}}{e^{2\pi inx} \cdot e^{2\pi inx}} = \frac{\int_0^1 f(x)e^{-2\pi inx},\dd x}{1} = \int_0^1 f(x)e^{-2\pi inx},\dd x]
fathom swallowBOT
eulerERICteristic
storm sage
The case of the Fourier transform is very similar except you integrate from -inf to inf instead of 0 to 1 and you replace the discrete variable n with a continuous variable xi
ebon oak
what is f in this example?
storm sage
[\hat f(\xi) = \int_{-\infty}^\infty f(x)e^{-2\pi i\xi x},\dd x]
fathom swallowBOT
eulerERICteristic
storm sage
what is f in this example?
the signal that you're looking at
just some arbitrary function
storm sage
yeah we want to write it in our fourier basis exactly
so yeah that was a really fast-paced explanation of how the fourier transform relates to orthogonal projections xD
hopefully it wasn't too too confusing
storm sage
the e^(-2 pi i n x) function is our basis vector
again if you want, you can think of it in terms of sines and cosines instead
but it's the "elementary pieces" into which we're breaking up the function
ebon oak
so in summary, the projection of f onto our basis is taking our original signal and putting it into terms of cos and sin functions?
and adding them up
storm sage
yup exactly!
storm sage
have a lot of fun with it :)))) this is such a cool topic
ebon oak
agreed! i’m actually excited about it
storm sage
Hope you figure out how to tie it into black holes or whatever research you end up potentially doing in the future too!
ebon oak
Hope you figure out how to tie it into black holes or whatever research you end ...
thank you! i’d be glad to share with you when i’m done!
storm sage
sounds great!
cold needle
if this was ivory
i would have a very different response to this
I have to behave myself
small dust
i still dunno what’s happening
deep mango
i would have a very different response to this
open marsh
Does anybody know why this equation can determine even numbers from odd numbers? https://www.desmos.com/calculator/gxolxkzdqx
It is accurate from 10^(-2) to 10^21
The equation itself isnt important but knowing why it has this property is
Hopefully somebody can give their ideas before another conversation starts
jovial ember
i would have a very different response to this
neat lintel
the m in metal stands for mald
open marsh
knew it, its just gonna get buried
where is a place I can talk to a professional in math about this
neat lintel
robust pendant
Hey so kinda unrelated, but a girl from my lin alg class invited me to her birthday party. I don't really know her that well and I only see her during lin alg, but she's really sweet and I wanna have a nice icebreaker, to become better friends with her. Any wholesome, Lin alg specific pick up lines I can put in her birthday card?
long matrix
pls dont D:
solid snow
Save it for a day that isn’t her birthday
little vine
Hey so kinda unrelated, but a girl from my lin alg class invited me to her birth...
Just be yourself
long matrix
Just be yourself
what if they are a math pun person
little vine
"Let's cross products"
"Be the rank to my nullity"
"You can Cauchy my Schwarz anytime"
robust pendant
Lmao, maybe pick up line implied something else 💀💀💀. I don't wanna date her, I'm straight, I just wanna be friends with her and have a cute line in her birthday card
little vine
Sorry
long matrix
bruh wth
robust pendant
"let's cross products" 💀💀💀💀
long matrix
"pick up lines" do not mean what you want it to
robust pendant
"pick up lines" do not mean what you want it to
Ehh I like the one that r like, "if I could rearrange the alphabet I wanna put u and I together"
Like that's cute and wholesome
And doesn't imply wierd intentions
solid snow
It specifically implies that you want to be with them
cyan goblet
idk thats a pretty classic pickup line LOL
tight rock
that does imply weird intentions
solid snow
Also, why a pick up line for a birthday card?
Just make it about, you know, the birthday
cyan goblet
if their name is jordan
robust pendant
Maybe pun was a better phrasing?
cyan goblet
then youre in massive luck
because jordan canonical form would be a great one
if not, well that’s unfortunate
brave shell
Not necessarily. Maybe their name is rational.
robust pendant
that does imply weird intentions
Wdym 💀💀💀. Theres some really adorable pick up lines that don't mean anything
cyan goblet
i genuinely cannot think of a single good lin alg related pun
brave shell
Also my contribution is "I took LA so I could calculate the vector from me to you."
cyan goblet
that makes no sense 😭😭😭
robust pendant
Also my contribution is "I took LA so I could calculate the vector from me to yo...
That's adorable
It kinda does?
tight rock
"are you my multiplicative inverse as i am 1 with you"////dont use this...just came to mind
cyan goblet
“lets set aside our differences and pass to the quotient”
idk if that counts as lin alg
little vine
"Tensor?? I hardly know 'er!!"
robust pendant
"are you my multiplicative inverse as i am 1 with you"////dont use this...just c...
Bro, I needed sometime to process that 💀💀💀
raven plaza
Can you be my hom-ie? Because you're where I derive my ext-asy.
solid snow
I would wish to be vaporized on the spot if I was the recipient of these or witnessed them second hand
cyan goblet
Can you be my hom-ie? Because you're where I derive my ext-asy.
BAHAHAHAHAHAHAAAAAAA
robust pendant
Can you be my hom-ie? Because you're where I derive my ext-asy.
NAWWWWWW
raven plaza
Can you be my hom-ie? Because you're where I derive my ext-asy.
(Aluffi chapter 8 before you say this isn't Lin alg)
long matrix
cyan goblet
wow… i only thought aluffi had a chapter 0…
are you orthogonal with determinant 1? because you’re SO cool!
😭😭😭😭😭 i would lose my mind if someone said that to me
raven plaza
My passion lies in math, but you can be my SO₂
cyan goblet
😭😭😭
raven plaza
(then she says "isn't that chemistry?")
little vine
i may not be Abel but i’d commute any distance to be with you
Good one
burnt ledge
nobodys said anything about associativity
im not gonna make one up but thats just an observation
You could say becoming closer friends is associating
robust pendant
You could say becoming closer friends is associating
That's cute, but we haven't gotten to that topic yet 💀💀💀
neat lintel
Does anyone know what I'm doing wrong here?
https://leetcode.com/problems/minimum-lines-to-represent-a-line-chart/
||```rs
impl Solution {
pub fn minimum_lines(stock_prices: Vec<Vec<i32>>) -> i32 {
if stock_prices.len() < 3 { return stock_prices.len() as i32; }
stock_prices.windows(3).fold(1,|acc,window| {
let slope_one: f64 = (window[1][1] - window[0][1]) as f64 / (window[1][0] - window[0][0]) as f64;
let slope_two: f64 = (window[2][1] - window[1][1]) as f64 / (window[2][0] - window[1][0]) as f64;
acc + 1 - (slope_two == slope_one) as i32
})
}
}
I keep failing on testcase 74/82
Testcase: || [[72,98],[62,27],[32,7],[71,4],[25,19],[91,30],[52,73],[10,9],[99,71],[47,22],[19,30],[80,63],[18,15],[48,17],[77,16],[46,27],[66,87],[55,84],[65,38],[30,9],[50,42],[100,60],[75,73],[98,53],[22,80],[41,61],[37,47],[95,8],[51,81],[78,79],[57,95]]||
Expected Value: 29
Reported Value: 30Sobbing
why does it fail 74/82
f64 rounding error?
maybe
i can multiply instead of divide?
long matrix
using rust 
neat lintel
uh oh
ocean harbor
Does anyone know what I'm doing wrong here?
<https://leetcode.com/problems/minim...
what language is this?
ocean harbor
never heard of this language before lol
little vine
A rejection "I prefer to be at cross products with you and no longer associate "
fervent notch
ba dum tss 
storm sage
That's cute, but we haven't gotten to that topic yet 💀💀💀
If we were matrices we'd be in the same similarity family
little vine
Conjugate with me habibi
neat lintel
what if we had the same jordan form 
long matrix
cringe chat aint ended yet smh
storm sage
We're two blocks of the same matrix
robust pendant
We're two blocks of the same matrix
THATS SO CUTE
long matrix
storm sage
I'm determinant to be your friend
Without you I'd decompose
You're my canonical form
neat lintel
eigenvalue you 
storm sage
awwww
neat lintel
what do you think about my lie group spam eric
robust pendant
eigenvalue you <:catlove:920698762932920370>
I'm taking this
storm sage
Can you be my friend? Because eigen be yours
neat lintel
oh i looked at the exercise in lee and there's another fun corollary
serene pulsar
I'm determinant to be your friend
this the one
neat lintel
because continuous homomorphisms of a lie group are smooth, there is at most one topology smooth structure on a topological group making it into a lie group
(a topological group which cannot be made into a lie group is the rationals, for example)
storm sage
That's so neat
bright trout
Linear algebra jokes 
neat lintel
lie group actions are one of the most important things in differential geometry to understand
neat lintel
oh you probably don't know exponential map stuff yet
the argument i gave relies on it lol
storm sage
After skipping half of chapter six to catch up to the reading group
Yeah it's at the end of the book
I'll get there
neat lintel
you know of the matrix exponential?
storm sage
Yea
neat lintel
the exponential map on lie groups is a generalization
mental stratus
the exponential is just e^x who wouldn't know that? Hahahaha right? Raiiiiiiigghhhhyt??????
neat lintel
the matrix exponential maps M(n) to GL(n). in general the exponential of a lie group maps its lie algebra to the group itself
little vine
HAHAHAHAHA
neat lintel
the lie algebra of GL(n) is M(n)
with matrices it's easy to just write down the series and prove convergence. to define the exponential map in general you've gotta be a bit more careful
so the matrix exponential exp(tA) evaluates to exp(A) at t = 1. to rephrase this slightly more manifold-y, the matrix A is a tangent vector to GL(n) at the identity. now by group stuff A has an integral curve through the identity which is also a lie group homomorphism R -> GL(n). the value of this at time one is exp(A)
this is used to define the exponential on lie groups
I like to start thinking of this as detailing an initial value problem that I’d be interested in solving
wet mortar
because continuous homomorphisms of a lie group are smooth, there is at most one...
smooth structure*
storm sage
the matrix exponential maps M(n) to GL(n). in general the exponential of a lie g...
That is very neat :o
loud snow
the exponential map on lie groups is a generalization
I remember learning that matrix exponentials are supposed to make one parameter families of curves but I never understood how
Or not matrix exponentials
But the exponential map
On a lie group element
neat lintel
suppose that G is a lie group with lie algebra g. identify elements of g with left-invariant vector fields on G. then the flow of an element X of g is given by (t, h) -> h exp(tX)
loud snow
Nevermind it was part of the lie algebra
And little g is written first as frac g and second as element of lie group
neat lintel
edited for precisely that reason
loud snow
I have this commited to memory but the part I have hard time understanding is left invariant vector field. But I should be able to read and do better myself
long matrix
when u were away
violet wraith
oof
quick rapids
the lie algebra of GL(n) is M(n)
Wait a second what is GL It appeared at my exam and nevdr knew what is that
neat lintel
general linear group
quick rapids
😭 oh dam It lol If I knew at exam
neat lintel
GL(n) is the group of invertible n by n matrices over some field which is usually clear by context. the operation is multiplication
here it can only really mean R
if you wanted to specify the field F which the matrices are over then you would write GL(n, F)
quick rapids
Consider GL(3, R) of square matrix of order 3, invertible and with real coefficients. Is the subset of GL(3, R) formed by the invertible upper triangular matrices a subgroup of GL(3, R)? Reason the answer
That was my exam question
And still dont know how to make it
🤔
quick rapids
GL(n) is the group of invertible n by n matrices over some field which is usuall...
Lol
That is my exam question so
😭
neat lintel
you check that
- the identity matrix is an invertible upper triangular matrix
- the product of two invertible upper triangular matrices is an invertible upper triangular matrix
- the inverse of an invertible upper triangular matrix is an invertible upper triangular matrix
the problem tells you what GL means
quick rapids
Yea but didnt know at time :'
😭
I had 5 mins
For that exercise
For that I got a 4,9/10
And didnt pass subject
😭
neat lintel
Are there any books that teach calculus for computer science?
I know calculus 
but I need to translate that knowledge to code
echo tundra
hollow jackal
Are there any books that teach calculus for computer science?
what you're looking for is numerical calculus
try searching for book recommendations for that on math stack exchange
deft flower
I need help with maths problem, please private talk please
storm sage
I need help with maths problem, please private talk please
!help
quasi jettyBOT
I need help with maths problem, please private talk please
Please read #❓how-to-get-help
long matrix
obstruction of justice
ripe wasp
memes go in chill
hi illum
woven whale
hi
ripe wasp
hows it going
burnt ledge
About mouth related topics
ripe wasp
that's crazy
long matrix
About mouth related topics
u cant say that~
burnt ledge
why not
long matrix
u so sussy
burnt ledge
whaat
hasty peak
About mouth related topics
sally
rose tapir
do most people here really love maths
rocky shuttle
almost all
rose tapir
i wish to love maths the way i love playing guitar
i would get into like flow state during math lessons in mid and high school but now that im in uni
i dont know what happened
lol
deft flower
Need help with math
rose tapir
is that a question
if it is, no
most of what im doing is maths last days, but i cant fully concentrate for some reason
rose tapir
sure
echo tundra
Cathy about to buy some math
mental stratus
meth
rocky shuttle
@mint patio I'll have to go in half an hour, but I guess I can tell you a bit about the shape manifold of closed planar curves 
mint patio
can you recover the matrix that generates a certain eigenspace given the eigenbasis
rocky shuttle
Consider the set of smooth (C^∞) embeddings of a circle S1 in R2, denoted by Emb(S1, R2). This is an open subset of the Fréchet space C^∞(S1, R2) endowed with the smooth topology.
mint patio
<@124978310479347712> I'll have to go in half an hour, but I guess I can tell yo...
Go for it!
fathom swallowBOT
zanarcane
mint patio
Diff(S^1) is space of diffeomorphisms into S^1?
fathom swallowBOT
zanarcane
mint patio
I don’t know enough about group actions 💀 but I’m sure I can follow
fathom swallowBOT
zanarcane
neat lintel
this conversation highlights precisely why i try not to use the tex bot too much
😵💫
mint patio
**zanarcane**
Good name for it
fathom swallowBOT
zanarcane
mint patio
B is?
rocky shuttle
The shape manifold
neat lintel
indeed
mint patio
Oh okay
rocky shuttle
It is indeed an infinite-dimensional manifold modeled on Fréchet spaces.
rocky shuttle
Emb(S^1, R^2) is also the total space of a smooth principal fiber bundle with structure group Diff(S^1) and base manifold B(S^1, R^2).
mint patio
Give me a second to parse that 
storm sage
Oh... words
rocky shuttle
words 
rocky shuttle
Emb(S^1, R^2) is also the total space of a smooth principal fiber bundle with st...
Anyways, this part is not that important for now
mint patio
Thank goodness
rocky shuttle
What you can do with this shape manifold is endow it with a Riemannian metric
neat lintel
principal bundles are something you can only avoid for so long
we should put feather through kobayashi-nomizu
rocky shuttle
It turns out that in infinite-dimensions, there are two types of Riemannian metrics
A weak and a strong one
rocky shuttle
In finite dimensions, all Riemannian metrics are strong ones because the topology induced by the Riemannian metric coincides with the original manifold topology.
rocky shuttle
In the infinite-dimensional case, the only strong Riemannian manifolds are Hilbert manifolds - manifolds that are modeled on Hilbert spaces. However, if you consider smooth embeddings of S1 in R2 with the smooth topology, this cannot be made into a Hilbert space.
rocky shuttle
In finite dimensions, all Riemannian metrics are strong ones because the topolog...
This is btw due to the fact that the associated mapping of the Riemannian metric on some infinite-dimensional manifold (S) given by [G^{\flat} \colon \mathup{T}S \to \mathup{T}^*S] is injective but not surjective in general.
mint patio
Not surface?
rocky shuttle
surjective lmao
fathom swallowBOT
zanarcane
rocky shuttle
my fingers
mint patio
LMAO
rocky shuttle
Okay, so a Riemannian shape manifold is then the Cauchy completion of the shape manifold with respect to the geodesic distance induced by the chosen Riemannian metric.