Mathematics

3:00 AM

Well it all boils down to my quest to try to understand everything, which caused me to reach out to areas outside of chemistry. In order:

2013: 4D visualisation, 2014: Time travel, 2016: Fine arts, 2016: Philosophy and Magic, 2017: Politics, 2018: Law, Culture, Language etc.

Ultradark

Sanity check: is $e^{s/\ln(x)}=e^{s/\ln(1-x)}$ equivalent to $x^s=(1-x)^s$.

Secret

each of these give me new ways of thinking, it is these new ways to comprehend things interested and drive me

Rithaniel

(In that case, I must simply be performing some poor arithmetic)

Holo

A big change, from 4D to politics

Secret

yeah, it just explodes and explodes

Symposium

3:03 AM

Your interests have been becoming progressively non-geeky/nerdy. You must be doing something wrong.

Rithaniel

@Ultradark Should be $\frac{1}{x^8}=\frac{1}{(1-x)^8}$, no?

Ultradark

@Secret you will never understand everything in a finite amount of time. But if there is life after death then you can continue your pursuit and learn everything in a countably infinite amount of time maybe

@Secret you should try to solve the problem of consciousness

Holo

My interest didn't change as much; computer science->physics->computer science->analysis->topology->set theory. Math was always in the back of my mind but school never taught how beautiful math really is so I start getting into only later than I would expect

Alucard

@Symposium actually everyone lives in their own world viewed through their eyes. but i don't know what i wanted to say, but great i typed it :d

Secret

Well there is a possible explanation to that: I am trying to understand nonanalytic thinking as I complained myself being too reductive and thus unable to comprehend something like emotions and gut feelings

Ultradark

3:05 AM

@Rithaniel why should it be that?

Secret

sinxe 2013

Ultradark

@secret have you ever heard of relational biology?

Rithaniel

(Wait, yeah, not that.)

Secret

probably not the term itself, but it sounds familiar, let me check

Holo

I tried to explore more things like literature, but although I love to read, I hate analysing it

Symposium

3:07 AM

I'm only interested in politics for comedic values. I had a great time for the past 2 years or so.

Alucard

politics was never my thing either..

too complex for basically "living on the same planet under some rules"

Rithaniel

Yeah, I don't think $e^\frac{8}{lnx}$ can be simplified, actually.

Holo

Basically the only things I do outside of studying is for comedy sake, like someone somewhen said "tragedy+time=comedy"

Symposium

Has anyone seen Lee-Yang theorem in a textbook?

Google books only returns books on physics (statistical mechanics).

Secret

en.wikiversity.org/wiki/Relational_biology

Ok this is very weird. Never expect seeing category theory here

Ultradark

3:13 AM

@Rithaniel no it cannot be simplified

@Secret lol

Secret

but then it's bioinformatics, so it is not surprising that level of abstraction will be involved

Holo

I should start studying category theory...

Ultradark

does anyone know if there's a database of known solvable transcendental equations

Symposium

@Secret What result in set theory surprised you the most?

Holo

But the moment I think to study something that is not set theory my motivation goes to 0...

Symposium

3:16 AM

Same question goes for @Holo as well.

Ultradark

@Rithaniel do you know what kind of object $e^\frac{1}{lnx}$ is

sorry for the multiple pings :)

Rithaniel

You're okay, but I might not respond quickly.

What do you mean "object?" Are you wanting to know the general shape of the graph?

Ultradark

I'm not sure if it's an algebraic function

or a transcendental function

Rithaniel

Ah, hmmm

That's something I've let to learn about.

Ultradark

oh okay

it has to be transcendental

Holo

3:21 AM

Hmm @Symposium , it is hard question, maybe the consistency of the existence of amorphous sets?

Ultradark

guys I'm going crzy because nobody checked my sanity check

Secret

@Symposium That $\omega_1$ is profoundly nonconstructive, to the point we can say almost nothing about its internal structure

Holo

@Ultradark what? Exp(1/ln(x)) is the best you can get I think

Ultradark

@Holo the equation $e^{s/\ln(x)}=e^{s/\ln(1-x)}$ and $x^s=(1-x)^s$

By taking the natural log of both sides and doing some algebra one can get to the equation on the right

I'm just confused

Secret

also this:

Feb 3 '17 at 13:03, by Secret

Actually, I do find it surprising that the box counting method that we learn in high school when we were taught permutations and combinations work quite well up into the infinite cardinals

Symposium

3:28 AM

Interesting @Secret and @Holo. These answers sent me through a rabbit-hole.

Ultradark

I'm confused because the first equation is comprised of setting two transcendental functions equal to each other, and after simplifying one gets an algebraic object in the form of a polynomial

Secret

Taking ln is a transcendental operation, and composition of transcendental functions need not be transcendental

Holo

@Ultradark well, this is algebra, the equations have the same solutions. What it means is that f(x)=0 implies g(x)=0, but f(x) not necessarily equal g(x)

Secret

it is the same as how binary operations between transcendental numbers can be algebraic

Ultradark

oh okay

Holo

3:31 AM

@Secret box counting method?

Secret

recall how counting combinations, you have n boxes and m objects. The first box has m choices, the second has m-1 choices and so on. Thus there are a total of $m!$ permutations

The same principle can be used to determine the largest cardinality of the image of some function given the cardinality of the domain

Holo

Never heard of this method

Actually I did in programming

But not at school

(btw, the school I went to was bad)

Secret

revisionmaths.com/advanced-level-maths-revision/statistics/… for a refresher

Ultradark

@Secret that relates to $n!$ is the number of ways one can order a set of $n$ objects

?

Secret

@Ultradark yeah, except you can have less boxes than objects, thus you need to divide by some factor

Holo

3:36 AM

Finite sets are weird...

Let's stick with infinite ones

Secret

weirdness does not confine to infinite sets

large finite sets can get pretty weird as googology and computational science showed, but they are what makes the world go round

Holo

People always takes finite sets as matter of course, but hell they are more confusing than d-infinite

@Secret do you know about large countable ordinals?

Secret

@Holo yup and simpleart taught me all about ordinal notations 2 years ago

Holo

nice, user21820 shows me how to get to Γ0 few weeks ago

Secret

simpleart show me how to get to bachmann

and beyond

Ultradark

3:43 AM

I can solve an infinite number of transcendental equations muhaha @Secret

Secret

So I guess you have a really good idea on how to prove trascendence of $e^e$?

(The fact this question is still open bothers me like there is no tomorrow for some reason, to the point every time I saw exp^{complicated} popping up I always have the instinct to plug e^e into it)

Ultradark

hmm

that is very interesting!

Holo

Hmm, @Secret I don't know this ordinal, I am guessing bachmann > Feferman–Schütte

Secret

Bachmann–Howard ordinal

In mathematics, the Bachmann–Howard ordinal (or Howard ordinal) is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such as Kripke–Platek set theory (with the axiom of infinity) and the system CZF of constructive set theory. It was introduced by Heinz Bachmann (1950) and William Alvin Howard (1972). == Definition == The Bachmann–Howard ordinal is defined using an ordinal collapsing function: εα enumerates the epsilon numbers, the ordinals ε such that ωε = ε. Ω = ω1 is the first uncountable ordinal. εΩ+1 is the first epsilon number after Ω = εΩ. ψ...

Holo

OwO

Secret

3:49 AM

It's impredicative this 21820 does not talk much about it except for one conversation with simpleart as they try to figure out how to make ordinal collapsing function predicative

Holo

I see

vzn

in MathOverflow, 4 mins ago, by vzn

hi all any collatz experts? an apparently very sharp anonymous commenter has posted what looks like some very substantial code revealing a remarkable property... am wondering if it mentioned/ known in the (rather vast) literature somewhere... https://vzn1.wordpress.com/2018/10/03/collatz-fusion/#comment-8023

Secret

Ordinal collapsing function is a way to write large ordinals by projecting down from some inaccessible ordinal

Holo

But doesn't it requir the existence of the inaccessible ordinal?

Wait ordinal, not cardinal

No, sorry I'm stupid, continue

Secret

Usually that ordinal is called $\Omega$ and it is assumed to exist (this is why it is impredicative, you cannot get that from the natural numbers)

If we only care about countable ordinals, then $\Omega$ can be $\omega_1$ or $\omega_1^{CK}$

Holo

3:58 AM

I see

Ultradark

@Secret $e^k$ for $k=1,2,3,...$ is transcendental right?

Secret

Lindemann weistrass said if the exponent x is algebraic, then e^x is transcendental

Ultradark

cool that's the lemma I need

Holo

@Ultradark Yes, suppose exp(k) is algebraic then exists P such that P(exp(k))=0, then define Q(x)=P(x^k) and you'll get Q(e)=0 which means e is algebraic

I'm too slow

Secret

hmm...

exp(e), P(exp(e))=0, Q(x)=P(x^e), Q(e)=P(e^e)=0 ??????????

Holo

4:07 AM

Your Q is not polynomial...

ooops

Lol

hello

4:24 AM

Hi chat.

user1732

4:34 AM

yo

Joe Shmo

4:53 AM

howdy

Rithaniel

5:30 AM

The empty set a subspace topology of every possible topological space, correct? Or is there some distinction to keep in mind which I have missed?

user602338

5:47 AM

Hi

user600999

Did you make progress @Ultradark?

Alessandro Codenotti

6:14 AM

@Rithaniel it is. It is even an open subspace

Rithaniel

Excellent, then my proof is valid.

user600999

@user602338 hi

Rithaniel

6:50 AM

Is any finite $T_3$ topological space automatically also $T_0$?

Secret

7:10 AM

Not just finite. Any T3 space is a subclass of T0

since any T3 must be T0 and regular

Rithaniel

Yeah, I was reading up on it, and apparently there's some mix up on the definitions we've been given. Apparently the common consensus of regularity is what I was taught $T_3$ was, and that regularity is $T_0$ and $T_3$.

Rithaniel

7:36 AM

Checking: $X/F$ is the quotient topology and $X \setminus F$ is "$X$ but not $F$," correct?

user600999

Yes

Rithaniel

(Had to struggle with that $\setminus$)

And so, if $F$ is a closed subset of $X$, then $X/F$ is $X$, but with all points in $F$ collapsed to a single point, correct?

Alessandro Codenotti

Also if $F$ isn't closed

ÍgjøgnumMeg

Mornin' all

Alessandro Codenotti

Hi @ÍgjøgnumMeg

ÍgjøgnumMeg

7:45 AM

Yoooo

How's it going?

Alessandro Codenotti

I survived the first week of lectures so pretty well :P

A couple of the courses are a bit over my level so I have some catching up to do, but that's what the weekend is for...

What about you?

ÍgjøgnumMeg

That's fair, i'd assume that's to be expected

I'm just at work, reading Fesenko's notes, complaining about the rain

It seems like now term has started some of the conversation in here has plummeted

lol

Alessandro Codenotti

I don't have internet in the dorm at the moment so I'm surely less active here now

ÍgjøgnumMeg

That sucks :(

How are the dorms?

Alessandro Codenotti

The one I'm in is pretty bad, it's a private one, not a uni one

But I'll find something else for the next semester

Silent

7:58 AM

I can't figure out how this proof of $\limsup_{n\to\infty} \frac1{x_n} = \frac1{\liminf_{n\to\infty} x_n}$ works. by pluffing $y_n=1/x_n$, I get $\frac{1}{y+\varepsilon}<x_n$ for all sufficiently large $n$ and $x_n<\frac{1}{y-\varepsilon}$ for infinitely many $n$. What should i do after that?

ÍgjøgnumMeg

@Alessandro fair enough, at least you have a roof over your head!

iBug

Another question about RSA algorithm. A computer program generates two big primes P and Q, and defines two variables such that A = (p*q)xor(p+q) and B = (p*q)xor(p-q). Now I have three numbers, A, B and E (where E=pow(M, 65537)mod(p*q), and xor and pow are bitwise exclusive OR and power). Is it possible to revert the unencrypted message M?

Silent

@LeakyNun will you please look at my question above?

iBug

If anyone can help, the numbers A, B and E are here in the HTML comment section