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12:00 AM
@EduardoC. yeah, I'm in my second year at Unicamp.
 
@LucasHenrique Oh, cool! I graduated recently but I'm taking classes at IME-USP
I sent my application to Msc at the IMECC-Unicamp, but without hope.
 
@EduardoC. have faith!
what are your interests in math? I like the idea of economics, but I had pretty much no contact with it
(I suppose you're interested in something related to your bachelor's degree)
 
@LucasHenrique I'm putting my hope in programs that also take into account summer courses, such as UFRJ
@LucasHenrique No, I wouldn't like to work with mathematical economics, although very interesting and formal
 
12:40 AM
@love_sodam for b fixed, the inner integral is constant, so the outer integral is constant 0 in a, which implies that the inner integral must be constant 0. Thus for all b, the inner integral is 0, and thus by lebesgue's differentiation theorem (there surely is a nicer way to handle this), f(x,y) = (derivative of integral) = (derivative of constant 0) = 0 almost everywhere
 
I love it, @robjohn! The Mean Pumpkin, aka The Great Pumpkin! ;D
@TedShifrin How are you? I love the help and such you offer here!
 
heya @AmWhy. "And such"!!
:)
Happy Halloween to you.
 
@TedShifrin To you as well!
 
1:29 AM
@AminIdelhaj There's about a claim here about bounds of a convolution. Suppose $K: \mathbb{R}^n \rightarrow \mathbb{C}$ is measurable. Suppose $K$ vanished outside of $B_R(0)$ and inside of $B_{\epsilon}(0)$. Suppose
$(1)\ |K| \le A |x|^{-n}$,
$(2)$ The Hörmander condition $\int_{\mathbb{R}^n \setminus B_{2r}(0)} |K(x) - K(x - z)| dx \le A$ for all $z \in B_r(0)$.
$(3)$ The cancellation condition $\int_{B_r(0)} K(x) dx = 0$ for all $r > 0$.

One of the claims is that you could get the bound $\Big|\int_{B_{\frac{1}{|\xi|}}(0)} K(x) e^{-2 \pi i x \xi} dx \Big| \le C(n) A$, *independent of $\e
 
2:14 AM
Is there an imaginary part of $\frac{1}{\Gamma(z)}$?
why doesn't it show up on the plot on Wolfram alpha?
 
2:37 AM
Why chat doesn't support math symbols? Even small symbols would look better than latex code.
 
which small symbols would look better than latex code?
 
Even โˆ‘ looks better than \sum
 
@epic_math Check the room description.
 
not if you render it
 
Oh thanks.
Is Michael Atiyah's proof of RH verified?
I've seen tons of RH proofs on arXiv.
 
2:41 AM
are you serious?
he wasn't in his right mind when he proposed it
 
@JoeShmo Michael Atiyah says that he has solved the RH
 
yes, he was kidding
he passed away a month or so after he proposed it, you know
 
What?
 
Idk if youre trolling me
 
I am not trolling you. Sorry if it feels like that.
I sometimes get obnoxious in my talk.
 
2:45 AM
Michael Atiyah wasn't in his right mind. Many people advised him not to give that talk.
He passed away a short time later.
the RH remains unsolved.
 
It's my dream to solve RH. :)
Some people say it's funny.
 
we're all counting on you, then
 
RH?
 
Are there any conjectures on the prime zeta function defined as \sum_{p}\frac{1}{p^s} where p ranges over primes?
This function seems interesting to me.
There is a whole list of zeta functions.
 
@user1993 Riemann hypothesis.
@epic_math I have an open question on the prime zeta function: mathoverflow.net/questions/353047/…. Not (directly) related to RH, though.
Haven't looked further into generalized analytic continuation, but maybe someone has.
 
2:53 AM
@user76284 the question looks interesting to me.
 
oh okay
 
Hey, I found an interesting article. Here it is.
Do you people know any good formulas for primes?
Or approximations?
Is no one interested in primes or reading the article is taking time?
Hey this is like a rhyme.
 
our number theorists are out rn
 
What is rn?
 
3:05 AM
right now
 
I'm a number theorist.
I am not out
 
where are you doing your doctorate?
 
@JoeShmo it would sound weird, but I am smaller in age than most people on MSE.
 
I see. idk why it would sound weird.
 
Some people laugh over it.
 
3:09 AM
I don't think it's funny :)
 
Don't ask for my age I'll give an infinite sum equal to my age :)
 
I'm certainly not going to ask, then
But I can guess where you're from..
 
Guess....
 
India
 
Yes!
 
3:11 AM
:-)
I recognize the speech patterns
 
:----)
 
I'm not Indian myself, FYI, I'm just that good.
 
Hey I want to ask something. What was the first mathematical theorem, formula, etc. that was useful which you discovered or proved?
Mine is the prime number theorem.
Just joking.
@JoeShmo I knew from your name that you weren't indian
Im smort.
 
Heh, Joe Shmo is my pen name..
you can't draw conclusions from it
 
Oh... Can I ask your real name?
 
3:18 AM
for no particular reason - not at this time
not that it's a secret..
 
My name is Leonhard Carl Friedrich Bernhard Riemann Gauss Euler
 
me too.
 
@JoeShmo I understand...
 
3:33 AM
Hi, Shmo.
 
Hi Shifrin
 
๐Ÿ™„
 
Ted, for one thing, knows my true identity, @epic_math, perhaps if you find a way to bribe him, he might tell you
I only discovered that after the fact, but I actually happened to misspell Shmo
 
Nah, I don't do that. Besides, who is epic?
 
@epic_math Not to discourage you, but long back @Ted told me something that I feel to this day. It's not surprising that a lot of young kids think that number theory is the thing. There are other parts of mathematics as well, that one should explore
 
3:35 AM
It's Joe Schmoe, who knew
 
if x = 25^{99} mod(19\cdot 13) and x = a (mod 19), x = b (mod 13) are equivalent then what is the value of a and b?
I think it's related to CRT
 
Ted, do you know any probability?
I'm convinced prof is conning me, or made a mistake somewhere in his exercise, but I need a second opinion before I lay out my case
 
Clarinet is our probabilist. I taught one undergraduate course my last year. That's all I once knew.
@SayanChattopadhyay You survived my comment.
 
gotcha.. I'm looking for applications of probability to harmonic analysis @Clarinetist
 
Hmm, that would require probability on Lie groups or homogeneous spaces
i dunno.
 
3:41 AM
@TedShifrin Yeah I did. And that was very good advice at that time. All I new was that I liked math. And I was fixated on juggling numbers.
 
prof mentioned that Stein had a particularly beautiful result in harmonic analysis where he used probabilistic arguments. I'm intrigued, trying to get to the bottom of it.
 
Ask for the reference, Shmo.
 
what are you up to lately, Ted?
 
4:46 AM
@SayanChattopadhyay you are right. I explored many branches like complex analysis, non-Euclidean geometry, linear algebra but after two years I realized that my field of interest is number theory.
Happy birthday Weierstrass!
 
@amWhy I found an old gravatar, the mean pumpkin, but then I made a better one with Mathematica, the mean squash.
 
The mean pumpkin would be better for Halloween.
Sorry if I am still sounding obnoxious.
Btw don't think I am a kid... My age is (3.767)!
Problem: find the remainder when 1!+2!+...+100! is divided by 4.
Congruences will help
 
5:44 AM
What kind of distribution on $u$ minimizes $\operatorname{E}[|u \otimes u - I|_\mathrm{op}^2]$, where $|\cdot|_\mathrm{op}$ is the operator norm?
 
 
2 hours later…
7:44 AM
What are some good books for differential equations?
I want to learn them again.
 
Let $S$ be a path-connected regular surface, and $f:S\to \mathbb{R}$ a smooth function. Prove that $f$ is a constant function if and only if $df_p(v) =0$ for all $p\in S$ and $v\in T_pS$.
In the question, why path connectedness is neccessary?
 
Hi, I am trying to find practical applications for my business and I am not sure where I can use linear algebra. I don't really encounter much situations where there are many unknowns are many equations. How does one end up with equations with several unknowns anyway?
 
Simultaneous equations can be used to ensure two airplanes donโ€™t intersect at the same time. Also nearly all scientific computations involve linear algebra.
With respect to mixtures, simultaneous equations can be used for achieving a certain consistency in a resultant product.
You can also see applications of functional analysis. Linear algebra is a fundamental part of functional analysis.
 
Right. I remember reading about experimental design and linear programming and see a lot of linear algebra related stuff
 
Sometimes linear algebra is useful in cryptography (I have heard about this, don't ask me where it is used)
 
7:58 AM
I'm just trying to make use of my time wondering if I will need linear algebra anytime soon
 
Linear algebra will be very useful.
I was excited when I heard that there are some connections between number theory and linear algebra.
I am not talking about the 'trivial connections', by the way
 
Yeah things are cool when they line up
 
Proofs with unexpected fields 'lining up' are often called elegant.
 
Math is a very brute force kind of approach and lots of time and work has to be put in it indeed. Past discoveries and derivations build up to what we have today
 
Mastering mathematics in the 19th and 18th century was not hard. Today mathematics is very vast.
 
8:06 AM
I actually have a huge dataset and i'm trying to create a robust model so I can decide without having to look at charts all the time.
I web scrape data from ecommerce websites and I have some data that is probably correlated to actual performance
But hard to find conclusions with simply a scatterplot and some charts
I don't have enough variables to probably come up with a good optimization model as well so I was thinking if I should refresh on that and go back to linear algebra
 
I don't know much about linear algebra. What are some good books/sources to learn it?
 
So I was thinking of simply doing something simpler like regression so I recently reviewed my calculus
To understand things like the least squares crriterion
There are many books finding the best one is hard
 
Maybe this website should help you.
 
I was thinking maybe I just need to brush up calculus and go straight to statistics
 
So you are joining the statistics and probability gang?
It's a fierce gang.
:)
 
8:13 AM
I was just looking around different fields
To see if something sounds like it fits my needs
 
I also did that.
 
Right now line fitting and statistics is what comes to mind
 
Then I found number theory.
 
But I need something very robust
 
So I like NT.
Did you try toplogy?
 
8:14 AM
No i'm pretty sure i'd need lots of foundation for that
Linear algebra for sure
And I don't have too much time
I watch videos like poincare and terrance tao's work and some other mathematicians
It's really a full time thing
 
You can see this for linear algebra notes.
 
And serious dedication but I doubt I have enough time to do heavy maths lol i'm more of business applications
 
So you want to study applied mathematics?
 
Thanks we studied these back in college but they're so procedural I don't really practice them so I forget
 
I am like Hardy (but not as smart as him); I love only pure mathematics.
 
8:19 AM
Yeah applied mathematics for me I mix it with programming
 
CS+applied mathematics?
There is a degree called AMCS
 
I just use easy and fast languages like python and excel VBA
 
I also like python
[AMCS means Applied Mathematics and Computer Science]
 
I just self study besides my undergrad in industrial engineering
 
do you know the fundamental theorem of engineering?
 
8:22 AM
Degrees take too much time and I feel I can do more on my own than work on deadlines
 
You are right.
 
I'd rather have a tutor that is good
 
Do you know about MIT OCW?
Google it. There are notes and videos on many topics.
 
Nope not at all
 
They should help you.
It's owned by MIT.
 
8:24 AM
Thanks will take a look. I love MIT videos yeah
I understand more what goes behind the scenes than how we were taught in school here
 
They also have their youtube channel.
 
Yup mostly watch in YT
What kind of models are related to regression type?
 
I don't know about what you are asking ( I know mostly NT and analysis and some algebra). Sorry...
 
This seems interesting
:}
 
8:32 AM
That is how much sales you make as you increase your price
This is how many people buy your product depending on your price
 
Oh... Btw, I don't know applied mathematics like commerce.
 
These are one of the many charts I have made. This is only for one product line out of millions. But there's nothing conclusive about these charts and behaviors appear different depending on the product
So i'm trying to find out the best model I can use to come up with a decision and a robust one at that
I actually came up with a ratio
 
Do you use Mathematica?
It can help you in this
(I think)
 
That I can also add as a predictor so I have 2 variables so far to predict discounted price
Nope I see it a lot though
 
I recommend it
 
8:37 AM
I am looking at line fitting
But I don't know exactly how to automate it markers like R squared seem to keep going higher if I try higher degree lines maybe i'm missing something
I mean the 1st chart is most likely linear but I others aren't as simple
 
8:52 AM
I suppose i'm just over complicating things i'll just create summary tables and do some sorting/ranking. I am betting i'm at a dead end with the little variables I have. There are just some variables I can never obtain due to the scale and the methods available. Just going to have to try to find out some patterns and do things by instinct.
 
 
1 hour later…
10:04 AM
@SayanChattopadhyay one can still be interested in number theory tho!
Hello @Alessandro
 
@robjohn Is $^2C_3$ equal to 0?
Since $\frac1{(-1)!}=\frac0{0!}=0$, your answer is correct, in a sense. — robjohn ♦ Sep 1 at 18:37
 
@YouKnowMe $\binom{2}{3}$ is the coefficient of $x^3$ in $(1+x)^2$, so...
 
heya
 
Hey @Astyx
 
10:18 AM
How's it going ?
 
Not bad, semester starts on monday so just recapping
how about you?
 
Making progress in AG
 
nice :D
 
Slowly but surely getting there
 
you can teach me when I inevitably start learning it
 
10:21 AM
haha, you'll have to wait a bit before you start learning it then
 
i got time
 
10:40 AM
Can someone answer this question?
 
11:09 AM
so many people gave comments and answers already lol
 
11:22 AM
math.stackexchange.com/questions/3888587/… Could someone review this if possible?
 
@EdwardEvans Of course, I just don't want young folks going in number theory because that is the only kind of math they mostly see, its the equivalent of going into string theory because pop physics is just that.
 
@Sayan makes sense. I went into number theory because I saw a documentary about FLT and wanted to understand the proof, and now I'm in too far
 
@love_sodam do you know why this is when you consider open subsets of $\mathbb{R}$ instead of regular surfaces? the reason is the same
 
@SayanChattopadhyay I like number theory. It's not my fault that many young folks like it. Its my field of interest. (if you were talking about me)
 
(of course, connectedness suffices for this, but path-connectedness and connectedness are equivalent for regular surfaces)
 
11:34 AM
Do many people go into number theory ? IME it's quite the opposite, people go in analysis/statistics because it's more profitable
 
it's just a warning that number theory isn't the only field of mathematics that is potentially interesting, since many people see number theory on (e.g.) numberphile and somehow become obsessed :D Of course, we don't know @epic_math so shrugs $\ell$-adically
 
it seems to be a pattern
 
@Thorgott I don't get it..
 
even I was into number theory in high school lol
 
The RH attracted me to NT
 
11:36 AM
in high school I was more into analysis
 
I think there's a misconception that number theory = recreational number theory
@Lukas I was into physics in high school and then I grew up
 
@love_sodam Let $U$ be an open subset of $\mathbb{R}$ and let $f\colon U\rightarrow\mathbb{R}$ be differentiable with $f^{\prime}\equiv0$. Is $f$ necessarily constant?
 
Well... I am talking about Analytic NT
 
@EdwardEvans lmao
 
Applied math doesn't interest me
 
11:37 AM
Sure, that's fine, just don't put all your eggs in one basket if you decide to go to university lol
 
I don't think there's a lot of danger in that, because there are curricula you have to go through to get your degree
 
I am into analysis also
 
when I hear analytic NT I think of $\frac{\log X \log \log X \log \log \log \log X}{(\log \log \log X)^2}$
2
 
Don't think that I like and know only Nt
 
@Thorgott Oh I could be locallly constant
 
11:39 AM
@LukasHeger Hah I see primes
 
put all your eggs in an $(\infty,1)$-basket
 
In my case, I was attracted to math by FLT too. But that was mostly lore stuff. I became truly into math when I saw Liouville's theorem in dynamics in Classical Mech.
 
@MikeMiller I guess it depends what university you go to. My undergrad curriculum was 90% statistics and it was easy to cram for exams and then forget everything
 
@love_sodam yeah, it will be, but locally constant isn't necessarily constant, agree?
 
@Thorgott stick all ya eggs in an $L$-packet
 
11:40 AM
@Thorgott Yes got it.
 
I like modular forms and dirichlet series I guess that counts as analytic NT, but I don't really care for estimates of $\pi(x)$ and prime gaps and all that
 
I did most of the exercises in Niven when I was first getting into pure math and that was great fun
 
@Lukas I agree that analytic NT for me is synonymous with log log log log
 
Niven was scary for me, then somebody showed me group theory and modular arithmetic made much more sense
 
So many logs. Don't cut trees
 
11:41 AM
Can you define sheaves of any cocomplete category? Are sheaves in the category of sheaves a thing?
 
@Thorgott So we may conclude that in path connected space, if $f$ is not a constant function, then there is x\in X such that $f'(x)\neq 0$ right? where X is a domain
 
yeah
 
@Thorgott Thanks always :)
 
@Astyx you need some extra structure on your category, which is called a coverage (a category with a coverage is called a site)
to define sheaves, you need to know what your coverings are
 
Err... Do most of the people here don't like elementary number theory?
 
11:44 AM
cocompleteness doesn't play a role in defining sheaves
 
Its not that I hate ENT @epic_math, it's just that I could never build any intuition for it. Things seemed too hard, and never sat with it.
 
Treeeee? I am an ENT
 
@SayanChattopadhyay seems reasonable. Did you try David Burton's ENT?
 
but the category of shaves on a site is necessarily cocomplete (I think?)
 
once you build intuition for any subject, it becomes your favorite.
[my philosophy]
 
11:47 AM
Yeah lol, in my number theory days when I was obsessed with numbers coz FLT, I did go through Burton. Did not like the flavor of stuff. My question was always why should I care? Why should I care if this dude divides that dude and spits out another dude.
 
Now Burton's seems easy to me (not boasting)
 
I think I formulated that badly. I mean given a topological space X, for which category C can we define sheaves X -> C?
 
@Sayan tbf, getting into a field to understand the big questions/proofs is not so bad, but it's good to diversify your interests (even within said field)
 
@Astyx any category that has products
 
What would you choose? Analysis/NT/algebra/geometry?
 
11:51 AM
@EdwardEvans Yeah, that is actually fair. For me math was always about doing stuff about things from real life. Then I made the personal choice to call geometry as things from real life and now I sit and do random abstractions of physics lol
 
The category of sheaves on a fixed top space has product right ?
 
Euclid is smiling from heaven
 
So I could consider X->(X->C), and so on
 
I miss Euclid
 
why do you want to consider sheaves of sheaves
 
11:52 AM
@Astyx though I rarely see sheaves with values in categories outside of $\mathbf{Set},\mathbf{Ring},\mathbf{Ab}$ or maybe $R\text{-}\mathbf{Mod}$. I guess the most exotic thing I've come across is sheaves of topological rings which play a role in the theory of adic spaces
 
are you alright?
 
I'm just wondering if those exist
Perhaps taking sheaves of sheaves of sheaves ... yields something interresting
 
@Sayan nise, I obviously got interested in NT from this documentary and then going down the rabbit hole never got boring hahaha
 
Anyway it's just a thought
 
Sheaves of topological spaces are useful
 
11:54 AM
@LukasHeger ty for the answers
 
I've never seen sheaves of sheaves
 
Did you people wish Weierstass?
 
On the other hand, I don't know much about this, but sheaves taking values in simplicial sets also happens to be useful. These are exactly the simplicial object in the category of sheaves; the ambient category in which $\Bbb A^1$-homotopy theory functions is in the category of simplcial set-valued sheaves on schemes.
 
also sheaves of groupoids appear in the theory of stacks, they are closely linked to categories fibered in groupoids, I don't know too much about this
 
Given a topological space $X$, you can construct a category whose objects are inclusions $A \to X$ which are cofibrations and morphisms are inclusions (such that the triangled formed by the inclusions to $X$ already given commutes), yeah?
 
12:06 PM
Don't study topology you will end up drinking coffee in doughnuts.
Just joking
 
Let's call this category $C_X$. Then for any compactly generated Hausdorff spaces $X, Y$, $\text{Map}(-, Y)$ defines a sheaf on $C_X$ (which is like a convenient replacement of $\text{Op}(X)$).
 
Since we are talking about sheaves, I have a question. This may be extremely superficial but from whatever minimal knowledge I have about Banach algebras, the theory of Commutative Banach Algebras as developed by gelfand uses the "similar" idea of considering maximal ideals associated to points of a compact hausdorff space as we see in AG.
Is there a sheaf theoretic way to keep these two in the same footing? Or is this just random gibberish
 
You people are talking about sheaves, etc. about which I don't know much. Please suggest some sources to study topology and also algebra (not that solving equations thing lol)
 
lol
Go read Weil's Basic Number Theory
 
@SayanChattopadhyay there's the notion of the Bercovich spectrum of a normed commutative ring. That's actually a generalization of the Gelfand spectrum (so if you plug in a commutative Banach algebra, you just get the Gelfand spectrum back) and afaik there's a structure sheaf
fun fact: if you consider the Bercovich spectrum of $\Bbb Z$ with the standard absolute value, the stalk of the structure sheaf at the trivial valuation is the ring of adeles $\Bbb A_{\Bbb Q}$
 
12:15 PM
Is algebraic number theory called basic or I am an idiot?
Honestly I don't know much of algebraic NT
 
Oh @LukasHeger this is not what I was expecting. I was expecting something along the lines of Kontseivich and Connes NC Geometry. Interesting!
 
Berkovich geometry is mostly done over non-archimedean stuff
but the definitions work fine for more than that
 
After some weeks (I can learn things fast) I will be back with a dose of topology
Shame on me that I don't know what you people are talking about :-|
 
you're like 14 man, you've got a lot of time
 
Well I am... 16
 
12:20 PM
Berkovich spectra have really nice topologies, not at all like one would expect from the topology of a scheme or the totally disconnected topologies coming from a non-archimedean value
 
@EdwardEvans you just encouraged me
:-)
 
12:31 PM
Hello!
 
12:43 PM
Hey this room is almost 10.25 years old
Such a small child hears advanced mathematics
Multiply 10.25 by 4 and get a number that is a supersingular prime, a Sophie Germain prime, Newman-Shanks-Williams prime, Eisenstein prime,a Proth prime and a centered square number.
 
Hi, could someone please check out this thread? math.stackexchange.com/questions/3888587
 
Post advertising... [Just joking]
Btw, the post is interesting
 
Is that not allowed? Sorry, I thought it wasn't allowed to spam your posts here.
 
@trivialmathisdifficult sorry, it was a joke
 
It's ok to link your posts here as long as you're not spamming
AFAIK
 
12:56 PM
I will not make such bad jokes from now
 
What's $a(S\cap F)$ ?
I think they meant axiom 4
 
@Astyx This is what I was thinking. But I am unsure.
 
Applying axiom 4 twice gives the wanted result
 
I also think so. I always looked for mistakes in math books and here is one
 
typos happen
 
1:03 PM
Yes... typists are not perfect. This is comparable to the fact that all numbers aren't perfect.
 
Being a doughnut: if I've got a number $\delta > 0$ such that $1 - \delta < \lvert x \rvert < 1+\delta$ and a $\pi$ such that $\lvert \pi \rvert < 1$, and supposing that $\lvert x \rvert < 1 \implies \lvert x \rvert \leq \lvert \pi \rvert$ and $\lvert x\rvert > 1 \implies \lvert x \rvert \geq \frac{1}{\lvert \pi \rvert}$, then I gotta have $\lvert
x\rvert = 1 $ right?
I mean this means that $1 < \frac{1}{\lvert \pi \rvert} \leq \lvert x \rvert \leq \lvert \pi \rvert < 1$
ye
 
I'm confused
are you requiring those implications to hold generally?
 
no this is some specific junk that I wanted to write
 
@EdwardEvans I started doing it.
Well if $|x|=1$ then $x=-1$ since if not, then $1-\delta<1$ which implies $\delta<0$
 
I mean, a valuation $\lvert \cdot \rvert$ is called discrete if there is a $\delta > 0$ such that $1 - \delta < \lvert x \rvert < 1 + \delta implies that \lvert x \rvert = 1$. I'm just recapping some stuff from valuation theory
 
1:12 PM
do you mean absolute value by $|\cdot|$?
 
I'm not following your quantifiers
 
ergh rip
 
lol $\pi=3.14....$ is abandoned.
 
I think I know what I mean, I'm just being a mong
 
Please don't suppose $|e|<1$ :)
$e$ is banned from being used as a variable
looks like many people here like algebra
 
1:18 PM
@Thorgott yeah those implications always hold in this context, I see what you were asking lol
 
are your valuations discrete
 
Well the point is to show that the valuation is discrete
I have my field $K$, a valuation $\lvert \cdot \rvert$ on $K$, and its valuation ring $\mathcal{O}$ with maximal ideal $\mathfrak{p}$, and the point is to show that $\lvert \cdot \rvert$ is discrete iff $\mathfrak{p}$ is a principal ideal
If you assume $\mathfrak{p} = (\pi)$ then the implications from above hold
If $1 < \lvert x \rvert$ then $\lvert x^{-1 }\rvert < 1$, so $\lvert x^{-1}\rvert \leq \lvert \pi\rvert$, i.e. $\lvert x \rvert \geq \frac{1}{\lvert \pi \rvert}$. If $\lvert x \rvert < 1$ then $\lvert x \rvert \leq \lvert \pi \rvert$. So if $x$ sits in a little interval around $1$ then $\lvert x \rvert = 1$.
ergh too many verts
 
I don't know why but I don't like absolute value function and generally, the | symbol
 
but you only have one of the inequalities at each time
 
1:33 PM
yeah
I'ma watch this proof again
 
Hey did you people see my new chatroom?
 
ah, nvm, got it
you just need to choose the right delta
 
ah I got it
rofl
 
pure algebra
 
1:49 PM
pure bullshit
 
synonymous
 
weyy
Hi @Balarka
 
all math fields are beautiful
 
stfu you nerd
 
:(
 
1:52 PM
hahaha bit aggressive sorry :(
 
be gone HoTT
 
(no worries)
HoTT ?
 
Homotopy Type Theory
 
THoT
 
bad joke
 
1:53 PM
Who invited me here?
 
I didn't know the abbreviation. I got the joke though
@user21820 here? I've heard a few people here got invited in a Number theory chatroom without knowing why
Me included
 
@Astyx For a dedicated chat-room, it's easier to figure out. But here is full of people, so I have no idea who invited.
 

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