I was proving that $m!$ divides $\prod_{i=1}^m (n+i)$ for $n\in\bN$ and for all $m\in\bN$ where $\bN$ doesn't include zero since we are civilized. I proved this very easily by induction but I wrote this in terms of factorials and noticed that the product is equal to $m!/(n-1)!$, and when divided by $m!$ I get $1/(n-1)!$ which contradicts the induction conclusion. where did I fuck up?
#serious-discussion
violet wraith
fathom swallowBOT
please request a new nickname
dapper badge
isn't the product (m+n)!/n!
violet wraith
ohhhhhh
sorry I'm dumb
wait I don't think I can simplify that right
because (m+n)! cant be rewritten iirc
ok so I think the only way is induction
dapper badge
well, (m+n)! = m! * (m+1) * ... * (m+n) = n! * (n+1) * ... * (n+m)
violet wraith
oh I see
cunning plaza
For anyone that worked with Spivak's Calculus - I can't always tell when he wants me to be rigorous. On ch. 1 problem 4, I'm supposed all values of x for when 2^x < 8. Clearly that's x < 3, but I don't know how to go about this rigorously when he hasn't even defined numbers.
The problem says to simply find all x that satisfy the inequality. It didn't say "prove", like many of the other problems. I'm just gonna assume that means that I don't need to be fully rigorous on these problems...
(not sure where to ask this btw)
brittle socket
Why do you need him to define numbers tho? That's like a chapter of axiomatic set theory or real anal. But since he says to "find" I don't think you need to prove it anyways
storm sage
Proving it is good practice though
neat lintel
defining numbers
brittle socket
Yeah true, I like to prove stuff even when the author doesn't necessarily ask for it as well
cunning plaza
Proving it is good practice though
I tried proving what I could. I just don't know how to go about 2^x < 8 with what he's given
storm sage
Although I haven't worked with Spivak, so I don't know what his axiomatic system in particular is
Lemme look at it
cunning plaza
thank you!
brittle socket
He doesn't seem to define exponentiation
storm sage
yeah he doesn't...
storm sage
For anyone that worked with Spivak's Calculus - I can't always tell when he want...
my general advice here is to just go on if you think you understand it well enough; this sort of confusion of what the author expects is typical for the first one or two chapters of a book
if later on you realize you don't understand it well enough then go back
I don't think you could prove your answer for that question based on what he gives you in that first section though
brittle socket
Yeah
You could define exponentiation of rationals as you would normally and use some 'limits' stuff to define it for irrationals but ehh im not sure if that'll be nice or fun
storm sage
even defining it for rationals is kinda hard lol he only really gives you the tools to define exponentiation to integer powers
brittle socket
You could show that the nth root of any (positive) real number exists by showing that exponentiation to integer powers is bijective first I guess, then define
[r^{\frac{p}{q}}=\sqrt[q]{r^p}]
I guess
fathom swallowBOT
grass
brittle socket
But yeah that's a bit convoluted
cunning plaza
my general advice here is to just go on if you think you understand it well enou...
thank you! that helps a lot
I guess he gives that problem to make a person think why it's presently unsolvable
storm sage
xD yeah I dunno, considering he hasn't defined what exponentiation is
cunning plaza
You could show that the nth root of any (positive) real number exists by showing...
feels a bit premature with him not defining bijections yet 
brittle socket
Yeah he probably doesn't intent for the readers to prove that
If you get to the point where you have a definition of exponentiation/logarithms you could probably prove more generally, that logarithms preserve order
That is, x>y implies log(x)>log(y). Well, actually you can probably still prove it even if you invoke iff instead of implies since exponentiation also preserves order
storm sage
yeah all you actually need for the proof is that exponentiation is strictly increasing
but he doesn't even define exponentiation lol
amber orbit
proud olive
Hoh, glad it was not me who made that joke
If I see a possible pun i usually don't have the self control to stop myself from typing it
Man im such a comedy genius
kindred ore
🤨
coarse epoch
Hello everybody, I have 2 questions, hope this is the right place/ok (been slowly returning to pre-calculus math, haven't used it since high school, 15 years ago):
-
Anyone interested in deontic logic? Did anyone study it? I am interested in it and its "calculus".
-
Anyone can explain what the hell the Schrodinger equation means? Any books you can suggest for beginners?
chilly coral
Hello everybody, I have 2 questions, hope this is the right place/ok (been slow...
Schrodingers equation will be covered in any intro quantum mechanics textbook, but you'll need a lot more than pre-calc math for those textbooks
sharp cave
Hello everybody, I have 2 questions, hope this is the right place/ok (been slow...
Deontic logics are more philosophy than math so you should try the philosophy discords
Alternatively, I think Plato.stanford should have a page on it
alpine kindle
Hello everybody, I have 2 questions, hope this is the right place/ok (been slow...
deontic logic is a part of modal logic
a part which is, as cocat said, more philosophy than maths
coarse epoch
Alternatively, I think Plato.stanford should have a page on it
I know, just asking if in maths someone studied it thanks
coarse epoch
a part which is, as cocat said, more philosophy than maths
indeed thanks
coarse epoch
Schrodingers equation will be covered in any intro quantum mechanics textbook, b...
as I suspected, thanks
wide vector
Anyone know any good colleges with a good undergraduate program for mathematics?
velvet dagger
@wide vector what level of school are we talking?
cinder zephyr
alot of places have good undergraduate programs in math
hollow sundial
Anyone know any good colleges with a good undergraduate program for mathematics?
most are pretty expensive.
https://www.usnews.com/best-colleges/math-major-2701
neat lintel
Anyone know any good colleges with a good undergraduate program for mathematics?
MIT
Stanford
jovial ember
Most based Ohio hater
rose dock
only in ohio
wide vector
<@524244409575931907> what level of school are we talking?
College. Sorry
velvet dagger
No I mean like
I knew college I was wondering if you meant top schools, state schools, etc
hollow sundial
apply to a lot if you can get the application fee waived
hollow sundial
most are pretty expensive.
https://www.usnews.com/best-colleges/math-major-2701
like 1 every 5th group of ranking
wide vector
Yeah maybe. I'm just trying to get an undergrad so I can get a PhD. 😭
hollow sundial
10 schools, covering top 1-50 is a broad start.
wide vector
Princeton is #1?
velvet dagger
For grad I put MIT rn as the best
What's your math background actually?
Because that might influence it somewhat
For undergrad
rocky falcon
Can a ug get into a t10 school with really good math related ecs and grades in math and university courses and all that but with shifty grades in the humanities
velvet dagger
How shifty is shifty
hollow sundial
Princeton is #1?
for undergraduate, groupings of 1-5 are all about the same. you're not gonna get consensus on rankings
similarly 5-10, 11-15, ...
wide vector
Okay, that makes sense. My parents are pulling a funny and saying that I can't go to school more than 12 hours drive from my house.
Which is essentially New England and Quebec
hollow sundial
most of the top schools are in that area haha
visual roost
Quick question:
I'm having some trouble calculating somthing
I need to know how meny 16x16 Square can fit within a 1000x1000 Square
I cme up with this (1000×1000)÷(16x16) or 100^2÷16^2 but I'm not sure what to do with the output (if this is even the right equation)
static loom
Okay, that makes sense. My parents are pulling a funny and saying that I can't g...
just get a new house closer 😎
woven whale
Quick question:
I'm having some trouble calculating somthing
I need to know how...
it's the right equation
so the result is 3906.25
round that down to get 3906
so 3906 houses can fit
wide vector
just get a new house closer 😎
Just get more debt lol. Be completely drowning in debt
visual roost
@woven whale So that's 3906 chunks of 16×16 correct?
rose dock
Which is essentially New England and Quebec
just go to McGill
wide vector
Definitely not getting into McGill lol. Stuff happened this year and my math grade tanked.
woven whale
<@391270706186420224> So that's 3906 chunks of 16×16 correct?
yes
and a quarter left
where you can't put a house
rose dock
also I wouldn't place too much weight on college rankings
visual roost
Ight thx man got lost I the math appreciate the conformation
woven whale
np
rose dock
especially those rankings
since:
- I wouldn't call USNews particularly reliable/objective
- Those rankings aren't specific to mathematics, they are overall rankings, just with the list of universities filtered to schools that offer a math program
- Rankings in general aren't indicative of education quality or the amount of opportunities at a specific university
wide vector
Yeah definitely.
rose dock
Definitely not getting into McGill lol. Stuff happened this year and my math gra...
what grade are you in rn?
wide vector
11th
wide vector
Yeah, I'll try. But UMO might be my only option
frigid matrix
Quick question:
I'm having some trouble calculating somthing
I need to know how...
,w 1000%16
fathom swallowBOT
fathom swallowBOT
frigid matrix
ok im definitely off the zaza
idk how to do modulous in wolfram
in lua its %
ig i can say
,w floor(1000/16)
fathom swallowBOT
neat lintel
doesn't a mod b work in wolfram alpha?
cinder zephyr
doesn't a mod b work in wolfram alpha?
it does
neat lintel
Which is essentially New England and Quebec
Why not UoT? I heard thats the best one in Canada
rose dock
UofDepression
neat lintel
Why not UoT? I heard thats the best one in Canada
hahahahahahahahahahahahahahaha
velvet dagger
I mean is it not?
velvet dagger
uoft fucking blows
Not technically mutually exclusive with being the best in the county...... 😛
brittle socket
What's UoT 
brittle socket
I see 
neat lintel
(some) good profs though
neat lintel
getting literally anything done takes so fucking long
so many emails
so many random ass unnecessary roadblocks to everything
vivid halo
it took me 3 months to get 4 signatures on a piece of paper I needed to get my visa to come here
so many reminder emails
neat lintel
sounds about right
vivid halo
gahhh
hollow pawn
Lol
neat lintel
okay buddy
Tell me whats wrong with UofT
read the entire conversation you skipped over
Im considering to study there
solar sparrow
I'm so confused how to get research opportunities as an undergrad tbh like all the professors seem to be doing high level research in can't even begin to understand the title of their research and you expect me to email them or ask them for me to do research? Like wtf. My university is also pretty large and the professors are very well known which adds another layer of anxiety for me. Like i cant just go ask a Fields medal caliber professor to do research with him it's laughable. I feel so stupid because there are kids getting research. I'm trying to apply to an reu but apparently it's bad if the only way a professor you are trying to get a recommendation from knows you is that you took a class and did well??? Like there's 200 people in my class how tf is the professor supposed to know who tf I am? The office hours overlap with other classes so I can't even go to those I feel so stuck.
torn willow
Well I heard classes get smaller
Like 200 is only for intro classes. So getting to know profs is a more realistic goal in non intro classes ig
solar sparrow
200 is exaggeration but it's like 80 for upper div classes
The problem is I'm not the best student in the class
I'm getting As and all but I don't raise my hand or anything honestly no one does tho I feel like the only way to actually interact is by going to office hours which I can't go to
It just feels so wrong to ask a professor that probably has no idea who you are for a letter of recommendation to an reu
neat lintel
It just feels so wrong to ask a professor that probably has no idea who you are ...
it's better than not doing it
and not getting into anything because you didn't even apply
solar sparrow
But I don't want the professor to dislike me because eventually I'll be good enough to ask them for a letter of recommendation for grad school
Or so I hope
TTerra isn't it 4 am where you are?
Wtf
neat lintel
But I don't want the professor to dislike me because eventually I'll be good eno...
dude professors get asked for letters literally all the time
it's part of their job
they expect it
they're not going to dislike you for just asking for a letter lol
solar sparrow
solar sparrow
they're not going to dislike you for just asking for a letter lol
Well not dislike, per say, but they'll know me as mediocre and not worth their time vs maybe if I ask them when I'm actually cracked and do something epic they will actually care
neat lintel
i really don't think that's how that works
what if you do end up getting a letter and getting in and becoming cracked?
unless you're actually a terrible person i don't think a professor is going to brush you off as "not worth their time" for just asking for literally one letter
something something miss every shot you don't take
they're people too, by the way
neat lintel
I'm getting As and all but I don't raise my hand or anything honestly no one doe...
and if it makes you feel better, this is basically me too, and i've gotten letters with no issues before
literally just fucking talk to them lol it's part of their job
everything i say is true
unless im trolling someone
solar sparrow
The specifics of the class also make me a bit worried since I got a high grade (100%) but the class is quite easy I wouldn't be surprised if >80% of the class got close to a 100%. I'm afraid the professor is gonna be like, I can't really evaluate this kid cuz this class is pretty easy. For reference this is a 2nd course in algebra.
neat lintel
ooohhh my fucking god just ask
neat lintel
i got a 100 in my similarly easy riemannian geometry course and so did most people it seems and i still got a letter
stop being a bitch
the worst that will happen is they just say no sorry
that's it
neat lintel
i got a 100 in my similarly easy riemannian geometry course and so did most peop...
(i didn't get into the thing i was applying for, but that's their loss not mine + almost all the kids who got in had previous experience lmao)
worst that happens is u just get "no"
not everything will work out for you in life
but that doesn't mean every loss is a catastrophic failure
neat lintel
What if I get "no lol" or worse, "no LMAO"
if i were your prof sure
the REU i applied to didn't deserve me anyways
solar sparrow
TTerra so cracked
There's the fields institute reu that I have no chance of getting in 💀 maybe I will meet TTerra
neat lintel
lol that's the one i applied for
neat lintel
you won't meet me because i'm going to be leaving this university as soon as possible
and have no interest in REUs anymore
solar sparrow
Based I saw the above convo
solar sparrow
I thought utoronto was decent
neat lintel
it is. it's just got some god fucking AWFUL administration
solar sparrow
Then again my university is also dogshit they literally don't pay student employees
(UC strike reference 😱)
neat lintel
uoft math admin is probably the worst ive ever had the displeasure of dealing with
they're just too fucking slow
and it seems like all they want to do is cockblock
solar sparrow
Lmao
neat lintel
did you know undergrads aren't allowed to take more than three graduate courses in their whole ugrad?
solar sparrow
Wtf I know ppl here that did that first semester
neat lintel
did you know point set topology isn't a prerequisite for differential geometry here?
solar sparrow
What
solar sparrow
Rip
solar sparrow
Mfw I thought geometry at uoft would be good cuz coxeter
solar sparrow
WTH
neat lintel
one exhausting three hour block
solar sparrow
THATS FUCKED
neat lintel
yeah
solar sparrow
lmao that actually hilarious
neat lintel
i just leave two hours in and pray the last hour wasn't anything important
solar sparrow
We have 3 hours a week but it's 2 1.5 hr or 3 1 hr lecs
neat lintel
depends on the course/instructor
jovial ember
🐒 👨
neat lintel
for the weedout courses they're basically trying to murder you and make you fail
so like 157 257 357 457
neat lintel
calculus, multivariable calculus, real analysis, and measure theory/funcanal
those courses all seem to be made a bit harder than any others
like artificially
not just the material being hard
solar sparrow
Wait is 457 a first year grad class?
neat lintel
crosslisted as an undergrad course and a grad course
neat lintel
if you're an undergrad and you take it then it's an undergrad credit, and if you're a grad and you take it then it's a grad credit
what other bad things can i say about uoft hmm
idk nothing immediately.comes to mind pertaining to the math department
some profs suck? idk lmao
solar sparrow
Tbf some profs suck everywhere
But yeah the 3 grad class limit and 1 3 hour block seem pretty egregious
neat lintel
3 hour block is an easy way to basically kill any interest i have in something
it's just too tiring
jovial ember
3 grad class limit is the most asinine thing I’ve ever heard
solar sparrow
Wait so tterra are u actually graduate+ now or did u put that to get access to stuff
jovial ember
I remember when TTeppa first told us it exists
solar sparrow
GG
neat lintel
I remember when TTeppa first told us it exists
i was livid
i was so close to just fucking going off on the admin
neat lintel
idk
neat lintel
lemme check the email chain (long)
jovial ember
neat lintel
yeah it's not really explicitly stated but i think it's a department thing
the math admin here is really good at giving non answers
i was looking forward to like, learning a lot of differential geometry i'd gotten really excited about
and then last minute they were just like "no fuck you lol"
shouldn't have wasted one of my grad course spots on algebraic topology smh that class sucked
okay no more ranting i need to snooze
neat lintel
shouldn't have wasted one of my grad course spots on algebraic topology smh that...
can i ask what other grad courses you took
solar sparrow
Probably analysis alg top and a algebra only grad class but I'm just guessing
neat lintel
what do you even do in a grad algebra class
solar sparrow
Depends on what is covered in ugrad algebra
solar sparrow
For our uni we don't cover modules or galois theory in undergrad
solar sparrow
And polynomials isn't covered in very much detail
Actually the main thing is that the grad version is basically an accelerated undergrad class
neat lintel
fair enough
solar sparrow
Since there is a class that covers galois theory and modules as well ufd and pid stuff
But it's like 1 grad class =2 ugrad classes
neat lintel
when is measure theory usually covered?
solar sparrow
Also the grad class covers some category theory and some representation theory
neat lintel
Also the grad class covers some category theory and some representation theory
my uni doesnt have CT in undergrad
but it;s done in the fourth year
solar sparrow
We don't either. Actually I think the CT and rep theory are the important parts of the grad class
fleet oyster
is it even done at the undergrad level
sometimes
solar sparrow
We have ugrad classes that cover measure theory but not in much detail the grad class is much more in depth though
There are different "tiers" of grad classes at our university
Some are basically just accelerated ugrad
neat lintel
There are different "tiers" of grad classes at our university
can you elaborate?
solar sparrow
Some are lower level grad stuff but fairly targeted e.g. commutative algebra and some are very niche topics
solar sparrow
These are informal btw
Like they don't actually exist
It's just what it feels lkke
neat lintel
ah
solar sparrow
Based on my understanding of the course content
solar sparrow
what would be the highest tier class
Banach algebras and spectral theory, c* algebras, von Neumann algebras
Note that these are each individual classes so they go very in depth
solar sparrow
There are 2 courses on lie groups so I'm assuming that goes pretty in depth
solar sparrow
I think the less the class talks about, the more "advanced" it is in general
Ooh there's a symplectic geo course which looks pretty interesting
neat lintel
are you looking through the database?
solar sparrow
Yeah
neat lintel
holy shit are you a student at berkeley?
im applying there next year
thats my dream uni
solar sparrow
Based af
neat lintel
I literally wish to do math there
solar sparrow
Ur transferring or applying as a grad student
brave acorn
If i dont get help in #prealg-and-algebra After 15 minutes do i ping for help or not in that channel?
neat lintel
Ur transferring or applying as a grad student
uh I'm a high school student
solar sparrow
Oh
solar sparrow
Lmao I get so confused
With the roles
Cuz ppl give themselves higher roles
So it's a bit weird
brave acorn
If i dont get help in <#326138737606262786> After 15 minutes do i ping for help ...
Do you guys know?
solar sparrow
Mb
neat lintel
yeah i gave myself the undergrad role cuz im studying undergrad stuff rn
solar sparrow
Do you guys know?
Yes
solar sparrow
Ping helpers in ur help channel after 15 mins
brave acorn
Alright Thank you!
fast moat
what are some famous identities of determinants
i've collected these
the determinant of a matrix is the same as the determinant of its transpose
if a row/column is all 0, the determinant is 0
if a row/column is a multiple of another, the determinant is 0
if you switch two rows/columns, the determinant is multiplied by -1
if a row/column is multiplied by a constant, the determinant is multiplied by the same constant
if you add the determinants of two matrices which shares all rows/columns except one, the result will be the determinant of the matrix with the shared rows/columns and the sum of the different rows/columns
if a multiple of a row/column is added to another, the determinant remains the same
the determinant of a matrix is the reciprocal of the determinant of its inverse
the determinant of a triangular matrix is the product of the entries on the main diagonal
the determinant of the product of two matrices is the product of the determinants of the matrices
neat lintel
🤓
rocky shuttle
🤓
fast moat
🤓
static loom
the determinant of a matrix is the same as the determinant of its transpose
if a...
I'd try to condense these down into which ones are more important and which ones are derived from others to make it more managable. For instance det(AB)=det(A)det(B) can be used to derive det(A^-1) = det(A)^-1
another useful thing to help collapse them down is thinking of the determinant as a signed volume, then a lot of these rules look like more obvious geometric facts, like scaling a column by a constant scales the determinant by a constant
similarly, when the constant is 0, that gets you the rule you said earlier as a special case "if a row/column is all 0, the determinant is 0" so I don't know if I'd list that one
halcyon heron
what is yours mbti type?
rocky shuttle
wffl
The properties can be condensed into top-dimensional multilinear alternating form with det(I) = 1 
static loom
yeah that's exactly why I mentioned thinking about it as an oriented volume
rugged horizon
what is yours mbti type?
INTP-T
carmine barn
je crois
long matrix
meow
carmine barn
okey
alpine kindle
what is yours mbti type?
KATZ-E
rose dock
https://guide.berkeley.edu/courses/math/
omg u go to berkeley?
solar sparrow
Fuck you man
rose dock
neat lintel
you should post it here and remove personal details
maybe do it in like #advanced-lounge though
rose dock
Fuck you man
u should really take 205 next sem
untold sage
What email
solar sparrow
u should really take 205 next sem
Why tho
rose dock
it'll be so fun
solar sparrow
I need eric chen buff cuz I took his 104 too
Doesn't 205 require 185 now?
@rose dock
neat lintel
I love math like I'm so mathy like that
rose dock
Doesn't 205 require 185 now?
ye but just talk to the prof
solar sparrow
But I'm literally stupid at analysis
neat lintel
math is so hot
neat lintel
and you know what fuck the pathagorean therom the goverment can't control me
solar sparrow
imagine taking 205
Good morning -----!
velvet dagger
imagine taking 205
Couldn't be me
sage crag
How do I know if the issue I'm working on is relevant to an article?
I've been working on the solution set of polynomials in complexes and the geometry of the curve generated by the solution for example and I don't have much idea what would be interesting to investigate about it
violet wraith
I agree
hollow ginkgo
I half-agree
mint canopy
I've been working on the solution set of polynomials in complexes and the geomet...
This is complex algebraic geometry. Find any intro book on algebraic geometry and you will learn about these objects. Something you might be interested in are planar projective complex curves and their correspondence to Riemann surfaces, the genus–degree formula, and the Riemann–Roch theorem.
neat lintel
I quarterth agree
neat lintel
I quarterth agree
Quarterth ?
What should I say there
No I mean, what does quarteth agreeing mean ?
Does that also mean u disagree with the other part that isn't in quarterth?
I'm just gonna say 🤓 and leave this conversation
:((
cerulean moon
I think it's just a pun on half-agree and it's either the canteloupe or the honeydew that is half awful
which would imply half of that said consept and the whole of the other is a delice
neat lintel
I think it's just a pun on half-agree and it's either the canteloupe or the hone...
But then it's not specific enough tho, which one is it ? 1 hate towards honeydew + 1/2 hate to canteloupe = 3/4 Or vice versa or perhaps some other fraction that adds upto 0.75 which there are like infinite of
Even if u wanted to narrow down the all possible fractions that would require making hate have a quanta and be discrete
cerulean moon
not some other fraction it is specified to be a half
neat lintel
Still won't help much tho
neat lintel
not some other fraction it is specified to be a half
To get 0.75 agreement, that is 0.25 hate towards either honeydrew or cantaloupe
There are many ways to get this hate
0.1 + 0.15 = 0.25
0.01 + 0.24 = 0.25
0.001 + 0.249 = 0.25
........
And a lot more others!!!
cerulean moon
oh right
neat lintel
Like, as more as infinite amount of them
cerulean moon
I assumed the half-hatred came after the binary choice
neat lintel
It was never specified tho
cerulean moon
yeah my bad
neat lintel
I'll tell you what quarterth hate means it means nothing it was meaningless the entire time
neat lintel
yeah my bad
It's okay, we just here are doing a little bit of playing around
No need to feel bad about it 
cerulean moon
I'll tell you what quarterth hate means it means nothing it was meaningless the ...
I disagree with you a whole four quarteths
cerulean moon
It's okay, we just here are doing a little bit of playing around
No need to feel...
^v^
fathom swallowBOT
The current time for wintersavory is 03:49 AM (KST) on Sun, 08/01/2023.
vast surge
Sleep is for the weak
eager reef
sleep is for the strong
the ones able to resist the urge to stay awake and consume more media
sacred arch
Let's take a moment to appreciate the repeating decimal for 1/7th cause it's kinda underrated
Idk if there are even any analogs in other number systems
cinder zephyr
lots of numbers have repeating decimals
sacred arch
Yeah but 1/7th is interesting
sacred arch
???? Not even true?
Like, 1/9 in base 9 is just 0.1
Anyways what makes 1/7th specifically interesting
cinder zephyr
oh yea I'm dumb lol
static loom
depends on what you mean by repeating, repeating 0s counts imo
static loom
I feel like it does if you're distinguishing between rational and irrational numbers
but maybe not here, idk
I guess in this case not repeating means it shares the same prime factors as the base
sacred arch
What makes 1/7th in particular interesting is
- It goes 0.142857... Which is (almost) 27, then 47, then 87 repeating (except the last is 87+1)
- 2/7 is kind of (very informally) like a translation of 1/7th, equaling 0.285714... And all other multiples of 1/7 are the same way
Idk any other fractions that have similar properties
I think it has something to do with the fact that 7^2 = 49 = 100/2 - 1 but idk
Very underrated repeated fraction
sacred arch
Amy base
I've tried it a little but couldn't come up with anything, looks like it needs some number theory that I'm not equipped with
static loom
I guess using ${x}$ to mean fractional part of x we can write $\left{\frac{100}{7}\right} = \frac 2 7$ and maybe it's useful to think of $100$ in base $7$ as $100=2+2*7^2$ so it happens to simplify very cleanly.
fathom swallowBOT
Merosity
static loom
we could find another case this way, looks like $\left{\frac{100}{13}\right} =\left{\frac{9+7*13}{13}\right} = \frac{9}{13}$ so this means $\frac{9}{13}$ is $\frac{1}{13}$ but shifted by $2$
fathom swallowBOT
Merosity
static loom
1/13 = 0.076923...
9/13 = 0.692307...
this at least gives us a way to brute force by writing 100 in base n and looking for when the ones place is 2 if you want it to be exactly 2 that does the shift
this is nice because it also proves that there are only finitely many cases where this happens since after n>100 we always have the ones place digit as 100
a brute force search just now gives 7, 14, 49, and 98 as the solutions
for choices of n such that 2/n is the digits of 1/n shifted by 2
pari-gp code I ran to find it if you're curious, should be easy enough to implement in any other language: for(n=1, 99, if(n*frac(100/n)==2, print(n)))
fast moat
an important thing to notice is\$\left{\frac{a}{c}\right}=\left{\frac{b}{c}\right}\iff a\equiv b\pmod{c}$
fathom swallowBOT
🤓
surreal sapphire
pari-gp 
fathom swallowBOT
🤓
fathom swallowBOT
🤓
fathom swallowBOT
🤓
river moon
fast moat
this falls out as an easy corollary from lagrange theorem
yes
void tundra
kill me now I'm transferring a ton of handwritten exercises to LaTeX
there are 200 pages of handwriting to do...
jovial ember
Why…
odd brook
what on earth 
void tundra
How long will that take
I have no idea
odd brook
godspeed
odd brook
wait but like
odd brook
sorry but there are way better methods to spend your time self-studying 😭
jovial ember
Then just don’t TeX it
void tundra
\begin{proof} trivial \end{proof}
fathom swallowBOT
DerpZ
void tundra
sorry but there are way better methods to spend your time self-studying 😭
yes I did it with pen and paper
jovial ember
Go read a book or something
void tundra
to avoid LaTeXing lmao
odd brook
the transferring 200 pages to latex part
jovial ember
Theres no point to TeX it
void tundra
i didn't sleep enough last night and transferring proofs is braindead
jovial ember
Just go outside or something instead then. Go on a walk
Touch some grass. Play some video games
void tundra
we have a grass
odd brook
I went for a real nice walk today and also got stuff from whole foods
void tundra
ok you know
yall just woke me up to how
stupid it is
i must be masochistic af
jeez
jovial ember
Lyra
I made the anime AI thing look at some monkeys
It doesn’t understand what a monkey is
void tundra
thank god you stopped me ngl
i was about to transfer 200 pages of algebra exercises too
jovial ember
odd brook
It doesn’t understand what a monkey is
LOL what was it outputting
void tundra
(this is literally 4 months of self studying)
odd brook
LMAO
jovial ember
jovial ember
This one kinda goes hard tho
odd brook
Yeah the AI image looks cool in that one even if it isn't remotely a monkey
jovial ember
Okay it output 3 different things from this one image
Can you guess what created this?
void tundra
"cute anime girl with long hair in snowy weather"
brittle socket
DerpZ remind me, are you in hs or uni
jovial ember
No it wasn’t based off a text prompt, it took a picture as input
void tundra
hMm
jovial ember
The same picture made this
void tundra
also pytorch >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tensorflow
jovial ember
@odd brook
void tundra
im biased tho
brittle socket
well i graduated
Nice, what are you self-studying
void tundra
real anal and abstract algebra rn
brittle socket
Ah nice
void tundra
<@1007730440406315038>
im biased bc i contributed code to pytorch before lol
jovial ember
Why u replying to that one
odd brook
The same picture made this
LOL
jovial ember
Any ideas?
brittle socket
You
odd brook
Chmonkey umbrella
jovial ember
odd brook
MOCHA
jovial ember
This was the last one it made from the same image
Yeah
Only one of them registered as an animal
odd brook
Okay the last one isn't bad
void tundra
real talk: what nn architecture is that
jovial ember
I mean
odd brook
The same picture made this
This one is uncanny
odd brook
Also her eyes are so human there
jovial ember
This one is uncanny
Yeah this one is so funny
It just
Literally doesn’t know what a monkey is
odd brook
It's like I can sort of see it when I look at it from a distance
jovial ember
It’s so funny
bronze pelican
LOL
odd brook
She was very sleepy today
jovial ember
Is it on a stick too?
odd brook
Don't think so I'll ask her though
jovial ember
Somehow 
Isn’t that high up on my react list
I guess I just really use some emojis a lot
odd brook
Also I guess it's only recently you've been reacting w/ it LOL
Even if it has been very consistent reacting
jovial ember
bronze pelican
jovial ember
U got games on your phone?
void tundra
tfw you drop a 250g phone on your nose while lying in bed
wonder if this doi will render
nice discord doesnt
neat lintel
i wonder how in the world i could access this...
void tundra
hMm
whatever you do you definitely shouldnt use a certain website that
has a bird holding a key
neat lintel
jovial ember
Ryc-site
brittle socket
Not gonna lie the first thing I thought of was ryc holding a key
true frigate
Hi, small problem if someone can help me x)
Two people have chests, one person has 1 chests the other has 5
In each chest, there are 3 bags, each bag has a 1 in 34 chance of containing the object that people want.
Calculate the probability that each of these people will get what they want.
brittle socket
void tundra
love how many people try to get others to do their homework
small dust
i actually thought that was going to be a q from a game or smth not a hw q until the last line loll
void tundra
you can spot a homework problem by how its always like
a command
rather than a polite request
small dust
it started off as polite request tho
zinc shoal
it started off as polite request tho
Bahhh
void tundra
hii can I get help on [homework]
(pastes the hw question)
zinc shoal
こんいちわ！
void tundra
ah no no im not saying theyre being rude
zinc shoal
げんき？
void tundra
im saying the homework questions usually have a certain tone
small dust
ya the last line was very hw q tone
zinc shoal
ya the last line was very hw q tone
is this like some stereotype now
zinc shoal
since when did homework request be commanding
oh
i just watch vtubers
sora-chan and aqu-tan
small dust
since when did homework request be commanding
i didn't say that, derpz did haha
zinc shoal
i didn't say that, derpz did haha
nahhhhhhh
is it actually like that
oh wait
questions have commanding tones
it's not a stereotype
void tundra
hw questions do
small dust
idk this was just very hw looking to me:
Calculate the probability that each of these people will get what they want.
like no one talks like that with capitals and periods and commands and everything
zinc shoal
idk this was just very hw looking to me:
Calculate the probability that each of...
it's straight up a homework question
small dust
well ya that's what i'm saying lol
zinc shoal
what do yall think of montblanc pens
huh
i wanted to get this for graduation
$2.6
k
it's the glacier solitaire
neat lintel
holy shit
neat lintel
i can get a gaming pc with that
neat lintel
oh wow thats expensive
neat lintel
must be very high-end
neat lintel
ONLY??????
neat lintel
dude that will run literally anything unless u have a crypto miner or something
zinc shoal
my parents said i can't use a crypto miner
zinc shoal
they said i'll charge us more electricity
neat lintel
yeah dont
zinc shoal
and im not a cryptobro
neat lintel
it is hazardous to the environment lmao
neat lintel
uhh sorry i only accept friend requests from people i know
zinc shoal
lol I just use pilot G2
i use a pilot pen
but i want to solve a quadratic equation
using a $2.6k pen
void tundra
why
zinc shoal
because it makes me look cool
void tundra
i mean you're free to do whatever you want with your (or your parents) money
not sure why you're here
are you looking for validation or something?
void tundra
like do you want us to tell you that's a sensible purchase?
neat lintel
i dont know about quality, but i doubt any quality pen is going to need 2.6k dollars
void tundra
because it probably isn't but
zinc shoal
kk
void tundra
again its up to you (or your parents)
void tundra
feels like ur trolling
zinc shoal
wtf
zinc shoal
there are luxury mechanical pencils
void tundra
is it tho
open aspen
relative to what?
neat lintel
other pencils haha
void tundra
i want more $2 g2 pens
neat lintel
sheeeeeeeeesh
void tundra
i burn through like one of those every 2 weeks
zinc shoal
i burn through like one of those every 2 weeks
huh
void tundra
real analysis
neat lintel
i just got a drawing tablet to take notes on instead of constantly buying paper and pens haha
void tundra
funny story I have an ipad
neat lintel
i think it is cost-efficient in the long run
zinc shoal
ipad is >>
zinc shoal
i have no idea how to use latex
zinc shoal
yeah
void tundra
i mean that being said if I were in school
zinc shoal
im married to my math textbook
void tundra
is that even legal
zinc shoal
is that even legal
it is questionable
void tundra
for $2.6k I'd rather buy stonks
or rather give it to my shitty ml-based bot to lose money
ah
zinc shoal
or rather give it to my shitty ml-based bot to lose money
Nahhh
Is it an investor bot
void tundra
no it's a money losing bot
void tundra
no it simply buys cryptocurrencies (the sketchier the better)
zinc shoal
oh
void tundra
so i immediately lose all the money
(this is a joke, I do not have a money losing bot)
zinc shoal
I should make a money losing bot
It uses ML to determine the fastest way to lose money
zinc shoal
why use ML
Because it's a buzzword
zinc shoal
We use a proprietary AI-based algorithm to determine the fastest way to lose your money
void tundra
machine learning is pretty accurate
zinc shoal
People: AI will take over us
void tundra
it's not learning per se
zinc shoal
AI now:
void tundra
it's mostly just big matrices and statistics lmao
void tundra
somewhere
i study at the mathcord school of mathematics
where i mass ask for help everytime i get stuck
zinc shoal
I will send you your rejection letter
void tundra
plz do
void tundra
thnx stanfart
celest ferry
the fastest way to lose money is to throw it into the trash
or invest in logan paul
onyx pagoda
I think it'd be great to provide a channel for course recommendations
in addition to #book-recommendations
onyx pagoda
There are so many great MOOC courses available online, like https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.1x+2T2019/about and https://www.edx.org/course/introduction-to-differential-equations-2, and it would be great to have a place to share and discover these resources. Not everyone learns best from books, and having a course recommendations channel would be incredibly beneficial for people who prefer to learn through other methods. It would allow people who are interested in learning math to easily find high-quality courses that have been recommended by others. This would save people time and effort in their search for learning resources. Also, it would provide a way for people who are new to math or looking to improve their skills to find courses that are a good fit for their learning goals, and it would be particularly helpful for independent learners who are not studying in a university setting. While there are websites out there that provide lists of math courses (like https://github.com/ossu/math), having a course recommendations channel on this Discord server would still be incredibly helpful. It would provide a place for people to share and discover high-quality courses that may not be listed on that website. Plus, it would allow us to fill in any gaps in the resources available on it.
devout nacelle
There had been an attempt to store a curated list of book recommendations but the efforts have been halted due to some reason
Guess it's worth bumping it up again, and try to expand the scope to online resources as well
onyx pagoda
There are so many great MOOC courses available online, like https://openlearning...
This would save people time and effort in their search for learning resources
especially with the pin feature, it can sort of look like this
brittle socket
Careless mistakes are the bane of my existence
void tundra
i thought when I start doing real anal
turning a + into a - wont be a problem
well
brittle socket
"I shouldn't encounter stupid careless mistakes to do with basic algebraic manipulation when doing set th-"
Careless mistakes: You can run, but you can't hide
void tundra
does abstract algebra
makes careless mistake
neat lintel
Do massive integration problem
make an arithmetic mistake in the end
brittle socket
Wow there's a lotta help channels open
long matrix
noo my blue grass
brittle socket
I hid my blue 
brittle socket
"I shouldn't encounter stupid careless mistakes to do with basic algebraic manip...
I was originally gonna open a help channel to see if someone could help spot my mistake here I can't spot but it seems like im not going to lol
Asked some of my irl friends to see if they can spot it
I used wolfram to desmos to lead to more confusion
obsidian moth
tbh math was reaaly invented by physicians to calculate physics
feel free to debunk my point
devout nacelle
Physicians to calculate physics 
obsidian moth
for numbers i meant
devout nacelle
Well measurement problems were the initial driving force, so I would like to think there's a nontrivial amount of truth to it
obsidian moth
well you got the point didnt you
obsidian moth
Well measurement problems were the initial driving force, so I would like to thi...
my main argument is about calculus
if im not wrong isnt it one of the higher forms of math?
devout nacelle
Yeah, it is true that physics provided a lot of impetus to mathematics
But it's not entirely universal (at the same time, problems in the theory of equations, etc. were being considered that didn't always have physical connections)
obsidian moth
yeah thats also true
i hate math cause every single mistake i have in tests is sooo dumbb i rip the paper
not hate but
kinda do but dont
brittle socket
I used wolfram to desmos to lead to more confusion <:shiver:934961643643871332>
It turns out my answer was fucking correct
But i plugged it info wolfram wrongly
Im gonna go sleep now...
void tundra
sleep is good
neat lintel
my main argument is about calculus
Both Newton and Leibniz invented calculus Newton invented calculus for physics but I don't think Leibniz did
surreal sapphire
calculus was invented really late in the history of mathematics
the earliest societies that did something that is clearly recognizable as mathematics did so for trade, to measure land (think ancient egypt) or to observe the stars (ancient babylon)
but this quickly evolved to doing mathematics for itself or for religious reasons (again babylon watching stars and ancient greece)
rigid sun
😦 Im so lost have asked about singular solution in seperable diff equation for very long time. our singular solution is 3 and -3. and we are to supposedly to check if they are singular solution,? how do we know if it is a singular solution?
onyx pagoda
but this quickly evolved to doing mathematics for itself or for religious reason...
does this server not have a suggestions channel?
onyx pagoda
I think it'd be great to provide a channel for course recommendations
I posted a suggestion but didn't know where to send it so I just sent it here
surreal sapphire
it doesn't, but your suggestion was at least noticed
solid snow
Both Newton and Leibniz invented calculus Newton invented calculus for physics b...
The ideas for calculus have been around since longer than newton or leibniz
They were scattered albeit and newton did gather them up into a comprehensible body of work
covert portal
tbh math was reaaly invented by physicians to calculate physics
yep
wispy plover
@hasty mountain Sorry if I sounded rude, but I have good faith. You are simply doing things wrong, like objectively speaking. It's fine if you learn category theory, but you should focus on simpler mathematics that do not require fancy language so that you can sharpen your mathematical skills. It seems to me that what you are doing is simply learning a lot of definitions which are probably meaningless to you but that create a (fake) sensation of knowledge
And maybe being so direct isn't helpful because you will probably reaffirm in your position, but idk.
hasty mountain
No this is fine and I value your care.
sleek wing
Category theory, or as I like to call it: definitions
compact tartan
another point @hasty mountain is that general cases are supposed to be understood via specific cases, not the other way around
it seemed like you were trying to generalize your question as much as possible before you understood what it is you're doing
(your generalization is incorrect)
wispy plover
Concrete examples > proofs
hasty mountain
What is the correct generalization?
compact tartan
if you want to treat "the set of maps from A to B" on equal footing with A and B that means you need it to be an object, i.e. you need some sort of internal hom in your category
furthermore, your question started with the group structure on A->G for arbitrary A (not a group), but in the end you were for some reason asking about the group structure on the set of group homs G->H
hasty mountain
All true. There seem to be a handful of ways for generalization to go.
compact tartan
if you have an internal hom that participates in some sort of tensor-hom adjunction, Ax- --| hom(A, -)
then right adjoints preserve limits, and a proof that hom(A, G) is a group object is some straightforward diagram chasing
note however that this is a proof completely by structure, by unfolding definitions. It does not contain any, like, novel mathematical idea
this goes back to overzealous generalization
the cartesian product of two groups is an immensely useful concept when studying group theory, and so every book will tell you about it
the infinite case? maybe occasionally useful as well
the case of a group object in a category? the average person does not care
it complicates not even the proof but even the formulation of the idea, and what are the benefits?
in what category other than the category of sets, are you running into infinite group products?
hasty mountain
in what category other than the category of sets, are you running into infinite ...
Please forgive me but I am not ready to talk about overzealous generalization, usefulness of concepts and what people in the abstract care about. I have experienced not once being provoked to express an opinion that would put me at risk of a moderator's punitive actions. You are clearly eager to disagree with me but pursuing this discussion is in the end a fruitless and risky distraction from my studies, as well as a threat to my already frail mental health. Please accept my deepest apologies for whatever offence I may have inadvertently caused to you and please let us return to the technical aspects of the conversation.
woven whale
@untold sapphire do you do category theory for a living
untold sapphire
Category theory is my life, it is what makes life worth living. Is that what you mean?
I work in a computational biology laboratory right now. I do topological data analysis. Category theory and algebraic topology are occasionally useful. I write a lot of python code and technical documentation so that others can use our software.
bright hill
<@340405629111894016> do you do category theory for a living
What an agressive way of asking someone for their job
crystal dagger
Please forgive me but I am not ready to talk about overzealous generalization, usefulness of concepts and what people in the abstract care about. I have experienced not once being provoked to express an opinion that would put me at risk of a moderator's punitive actions. You are clearly eager to disagree with me but pursuing this discussion is in the end a fruitless and risky distraction from my studies, as well as a threat to my already frail mental health. Please accept my deepest apologies for whatever offence I may have inadvertently caused to you and please let us return to the technical aspects of the conversation.
sage crag
This is complex algebraic geometry. Find any intro book on algebraic geometry an...
thank youu, i will study about
finite marsh
Hope it’s ok to ask this here. I am not what you would call an intelligent man. Hehe. On a serious note, I was fairly good at math around middle school then fell behind and really struggled. Math doesn’t come very easily to me, but I want to engage with it more because it seems fun and a good way to keep my mind sharp. Is pre-college Math a good place to start? How do I pick up the broken pieces of my math education and make something of it?
My major in college was philosophy and I minored in CS but struggled with the Math side of it
I’m more of a language and writing person
void tundra
pre-college math can be extremely boring
If you're doing it as a hobby find some math you are interested in
finite marsh
I was thinking pre-college because I was thinking it may be easier to start engaging with, is it true you need to learn math progressing from one subject to the next or else you won’t understand it?
void tundra
Do set theory with me
I want to tbh
brittle socket
study group!
void tundra
I was thinking pre-college because I was thinking it may be easier to start enga...
I think the best way to do it is to just
again something you are interested in
brittle socket
I am only doing 2 math texts atm
Which 2 are you doing rn?
void tundra
Im doing real anal and algebra because it's what im interested in
void tundra
Which 2 are you doing rn?
algebra - gallian and anal - abbott
brittle socket
Ah i see
kindred ore
I was thinking pre-college because I was thinking it may be easier to start enga...
I’d say definitely start with brushing up on pre-college. algebra, geometry, pre-cal til u can really work with the concepts intuitively
void tundra
I mean
kindred ore
khan academy is always a great accessible way to do that
void tundra
I'm assuming you still retain your HS math knowledge
kindred ore
that way you can build up to finding something more advanced that u like like DerpZ is suggesting
zinc shoal
I love HS Math
zinc shoal
JC is wonderful
zinc shoal
I grind massive integrals for no reason
finite marsh
I think I do, but honestly not sure since I haven’t engaged with math in a long time, I took Discrete Math in college and started off ok then things went south pretty quickly
void tundra
wow that sounds like pain
zinc shoal
I grind massive integrals for no reason
That is so wonderful
kindred ore
I grind massive integrals for no reason
this is fun
zinc shoal
It brings me joy
void tundra
I think I do, but honestly not sure since I haven’t engaged with math in a long ...
Try some introductory texts
You could try some abstract algebra
#books and #book-recommendations should help
zinc shoal
I think I do, but honestly not sure since I haven’t engaged with math in a long ...
Read up on the Monstrous Moonshine conjecture
void tundra
that is very advanced group theory -.-
zinc shoal
that is very advanced group theory -.-
The Tits group is the hardest to construct
I cannot construct the Tits group
brittle socket
Linear Alg and intro real anal can be good places to start
finite marsh
I think I like Algebra if I remember correctly, maybe that is a good place
zinc shoal
Why does everyone say "anal"
zinc shoal
It sounds so weird talking to non-math people
brittle socket
Dami recs Schroder for intro anal
void tundra
zinc shoal
I love anal
void tundra
I think abbott is also very excellent
zinc shoal
I want to do an anal
void tundra
the pedagogy is unparalleled
zinc shoal
I want to do an anal with my girlfriend
zinc shoal
illegal in singapore
I want to do real anal
void tundra
w a t
void tundra
singapore government is homophobic af lmfao
void tundra
doesn't change the fact that the govt is homophobic???
zinc shoal
yeah
finite marsh
<#873809533615628308> and <#716264872018706443> should help
Thanks, I will check out those channels!
zinc shoal
yeah;
zinc shoal
that's getting into politics which is not really appropriate for this server
let's not go indepth