Yes because it means you answer questions and are thus a NERD

brutal

but what should I do then? accept the complex answer? put my simpler solution within my own question?

DELETE the question?

(that's the worst)

there is no noble solution here

yea, I'll put it in my own question

Tell a friend to repost the question and then immediately answer it with the new proof

Jk don't do that, maybe add it as a comment or edit your question to be like "Hey guys!"

"Every professional mathematician in the world will accept the statement "Sage told me there was only one point" as a complete and rigorous proof, particularly if you include your code in an appendix."

I enjoy this comment

@Daminark I is nerd, fight me

@ShaVuklia I'd say just post it as a separate answer, but don't accept your own answer

HAHAH o god, I'm not even sure if you can accept your own answer?

that's just insane

I guess it's possible tho

Wanna go? Best of 3 chess games

You can, I've done it a couple times I think

Come at me bro

"How to get INFINITE rep"

HAHAHAHA

StackExchangers now hate him!!

The next day a blog post goes up: "How I got b&"

Taken out of context "How to get INFINITE rep" could be the title of a YouTube video on a bodybuilding channel

Why stop at infinite: Get inaccessible rep!

:P

Cantor really put infinities into perspective

Any Australians in the house here?

I am obviously australian

For real? @Secret

(in fact in Sydney time 17:00-1:00, it explains why I am pretty much the only person in chat)

Chat has too few Sydney siders

@ShaVuklia along different lines, "Norman Wildberger hates him!"

What are your thoughts on the Steve Smith incident? (If you've been watching the cricket recently)

@Daminark I found a dank set of alg top lectures on youtube, only to find out that Norman Wildberger was the lecturer

fuuuuuu

eh, cannot comment much as I only just knew that incident exists from you (have not watched news lately due to working in my PhD)

Ahh I see

Lol I imagine that he put his finite stuff to the side for that but maybe not

There are some updates that there will be an interview, but still no comment yet: abc.net.au/news/2018-03-26/…

@Daminark I think his ideas might be useful for the reverse mathematics community in order to figure out just how many instance of infinity used in modern maths is really a shorthand for otherwise very complicated system of theorems

because it seems the evidence are piling towards we can do away (at least actual) infinity with maths in principle (except we probably won't do so because continuity is so nice to work with)

@Daminark "An here we have $\pi_1(S^1)$ to be an uhmmmm........ (stammers) non-finite cyclic group"

That said, I have yet to watch his videos that talks about the reals, and at first glance I will be quite worried about how he recover some common results of analysis that relies on the reals forming a continuum

@Perturbative ...aka the integers?

or was that the joke

That was the joke

okay then

I think if I understood correctly: finitism rejects actual infinities but have no problem with potential infinities, while ultrafinitism rejects both

Hello, guys. If $\mu$ is a "nice" measure (e.g. Radon) on a metric space $(X,d)$, is it true that $\mu(E)=\mu(\overline{E})$, for every $E\subset X$ in the Borel $\sigma$-algebra of $X$?

How much can you truly recover then? Like, how do you dodge talking about the set of real numbers?

@DarkRunner An observation: the numbers in your P(n) column are powers of 46

so 46^1 = 46, 46^2=2116, 46^3 = 97336, etc

Real matrices of order $2$ whose square is the identity. I must be doing something wrong

There's probably a simple explanation for that, but I don't know it.

@AndersonFelipeViveiros so, I'm a bit concerned

If matrix $A$ is given by $\{a,b,c,d\}$ then for $A^2=I$ we have $a^2+bc=d^2+bc=1$ and $ab+db=ac+cd=0$. Doesn't this force $a=-d$?

Should, yes.

An example which I'm not sure is Radon because my brain isn't functioning fully is if you take the arclength measure supported on the circle in R^2

Guess I forgot how to handle systems of equations

$I$ itself is a root so this is not part of the general solution :/

user21820, I, Leaky and many others are having that discussion in the logic room in the past. We concluded that the full Borel algebra is not needed to describe most of maths and only some equivalence class of Lebesgue integrals are needed. I think we only have one discussion that involves ultrafinitism, but it does not seemed to go anywhere as far I knew

ah, yeah. brain not working

But those are the equations when multiplying out $A$ by $A$

you've got $a^2=d^2$

and that can give either a=d or a=-d

Right, but what about $b(a+d)=0$?

If a=d, then a=d=0 or b=0.

Right...

The main argument is that all known physical computers have only finite memory ,thus we cannot really compute with even potential infinity

And b=0 is exactly what you'd have for the identity matrix.

O wait nvm, answering the wrong question

Ok, need to be careful keeping track of the cases

yeah, it's a bit tedious.

here's the relevant discussion (luckily Leaky have bookmarked it)

so $I_2$ has infinitely many square roots. That's annoying

We briefly discussed about imposing some largest number M in the naturals, and we showed it can recover some bounded version of Fermat's little theorem

@Corellian How are you getting to that, just to be clear?

but we have not discussed much about the context of analysis with an ultrafinite system as far I knew

@Semiclassical with the right configuration one of the non-diagonal entries can be an arbitrary real number

hmm

but I'm not bothering to make it organized right now

Suppose $a=-d$ and take $a=1$. Letting $b$ vary we can have $c=(1-a^2)/b=0$, so it's $\{1,b,0,-1\}$ whose square is always $I_2$

@Secret lol

perhaps that's something we can work with in the future now that we knew that not even potential infinity can be reliably realised

Personally however, I love infinities, which is one reason I spend a lot of time trying to find arguments for $\omega_1$

and help driven most of the discussions about infinity in here and also in logic room

$$\begin{pmatrix} 1 & b \\ 0 & -1\end{pmatrix}\begin{pmatrix} 1 & b \\ 0 & -1\end{pmatrix}=\begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix}$$

yeah, checks out

and the transpose will also do that

@Corellian oh, check out the discussion of the 2-by-2 case in this section: en.wikipedia.org/wiki/Square_root_of_a_matrix#Properties

which I guess isn't even covering all of them, since the above root isn't symmetric.

how can I solve for x in this case, lnx/x - 1/4(x^2) = -2

@Semiclassical That's interesting

I'll try directly at the equations more but there's probably a trick from higher up that quickly gives a general solution (?)

@MATHASKER your equation is this? $$\frac{\ln x}{x}-\frac{1}{4}x^2=-2$$

yes

I don't know how I can seperate the x

I don't think you can @MATHASKER

oh really lol I kinda had to make a quesiton for my class and my teacher wanted it to be kind of tough, calculator inactive and also intergretable so i just made a volume problem

damn ok then

yeah, it looks like around 0.4 and 3.1 -ish you have solutions but there's no nice way to express them exactly

(Unrelated) I wonder if there are general theorems that can tell whether the inverse function of some given function has a closed form