This is the Realm of Simply Beautiful Art

12:01 AM

@SimplyBeautifulArt I didn't mean that facetiously, really. This is a very productive chat room, and I'm "tickled pink" that it is!

Simply Beautiful Art

Hehe, as do I very often

12

A: Visually stunning math concepts which are easy to explain

Divergent Series can be visual: from the Wikipedia showing that $(1-1+1-1+\dots)^2=1-2+3-4+\dots$

Lol, it appears my answers here have received upvotes? XD I wonder how much traffic that question gets per day

Trumpoon Baffoon

@SimplyBeautifulArt That was a "neat" and visually instructive post, indeed. I just got another upvote (they come every so often) here.

Simply Beautiful Art

:-( Sadly, I can't understand such symbols

Trumpoon Baffoon

12:20 AM

@SimplyBeautifulArt I think with your mind, learning propositional, and quantifier&predicate logic will only require learning the syntax, since you are already, in many ways, using the logical reasoning in many of your arguments. For some reason, I became passionate about logic when I learned it, because it enables a depth in expressing what one wants to express in math. I learned it fairly early in my education, while in high school, when I was able to take college math courses.

By the way, @SimplyBeautifulArt. I still feel the pain of one of my first interactions with you, when I sort of belittled you in terms of a logical statement, not meaning to, but because, given your strong showing in math, assumed you must have known some "basics" in college-level logic. You replied to me saying that you were in high-school, and hadn't encountered college level logic yet.

At any rate, I apologize again, because, as they say, when I assume, I make an "ass" out of "u" and "me".

Trumpoon Baffoon

12:45 AM

@SimplyBeautifulArt are you there? Or are you taking in some nutrition? I don't even know if you remember the encounter I speak of. But ultimately, it was a compliment, when all is said and done. Because I assumed you were a upper level undergrad, given what I had seen you do.

Simply Beautiful Art

@TrumpoonBaffoon I was washing dishes lol

Trumpoon Baffoon

You wanna come over and wash my dishes! lol

Simply Beautiful Art

And no worries (I don't remember that specific event, but I get put under the same assumptions all the time due to the things I do lol

No thanks XD. Not unless you feed me :D

Trumpoon Baffoon

@SimplyBeautifulArt :-D

Simply Beautiful Art

I wonder how many people don't believe I'm still in high school

Trumpoon Baffoon

12:59 AM

@SimplyBeautifulArt Don't know that...but I am hoping you've forgiven me for my assumption "way back when."

Simply Beautiful Art

:P I forgive all who belittle me

Trumpoon Baffoon

I don't even know if you remember our initial interaction.

Simply Beautiful Art

@Ramanujan good morning

Meh, it is of no importance

@TrumpoonBaffoon I used to get yelled at for using $x$ in complex analysis scenarios

Trumpoon Baffoon

I'm really curious how far I can go with this TrumpoonBaffoon thing! Perhaps, after I go to bed tonight, I'll wake up to with a suspension, especially if the TSIA (Trump-sanctioned Intelligence Agency) gets wind of my username, profile, and Trumpinian Blasphemy!

Simply Beautiful Art

Łøł

Hm, I'm stuck on a problem trying to find the second derivative of the zeta function at $x=2$.

In closed form ofc

Simply Beautiful Art

1:56 AM

@TrumpoonBaffoon Good lord, I highly recommend against figuring out the second derivative of the Riemann zeta function

Simply Beautiful Art

2:16 AM

This is equivalent to finding $\zeta''(-1)$, since$$\zeta''(2)=\frac{\pi^2}6\left[\frac{\pi^2}{12}-12\zeta''(-1)-(1-12\ln(A))^2+1+(12\ln(A)-\gamma-\ln(2\pi))^2\right]$$ — Simply Beautiful Art 1 min ago

Ugh that's ugly

Brevan Ellefsen

3:21 AM

@TrumpoonBaffoon I'm generally pleased when people presume I'm not in high school anymore and point out "simple" errors in my posts. I find that I learn best through trial and error, which is largely why I am on MSE in the first place. While some of the statements against me could be construed as condescending, I generally appreciate the criticisms, as they patch any holes my self-study approach might have missed (which are evidently great in number from the amount of criticisms I get daily XD)

@SimplyBeautifulArt I like how you comment on how you've been yelled at for using $x$ in complex analysis scenarios and then use $x$ for the Riemann Zeta function XD given, you are calculating along the positive real axis for which the function is naively defined, and so you dont have to bring complex analysis in, but I laughed for too long anyway

@TrumpoonBaffoon I really need to see you sacrifice some reputation points in order to fully utilize your new stance. It's time for some mock rants everywhere. Post legitimate answers and then write a psuedo-tweet at the end just for the kicks and giggles

Sometimes I wish we were back in the days of the mathematician Cardano, and I could challenge people in my school to a math duel to claim fame and honor. Curse this newfound belief that mathematics must be applied to science and is not a worthy discipline in its own regard like art or philosophy. Sigh.

Ya know

I think I use this chat mostly for raging now. A worthy use if you ask me - gotta rage somewhere I suppose XD not that my raging is too extreme. Now that I think of it, I really want to see my angsts written as Trump Tweets, with all my problems replaced with the word "Hillary"... and then have Mark Hamill read them in his best Joker voice. His voiceovers so far have been hilarious.

But that is enough ranting for now. Au Revoir my compadres.

Starfall

3:48 AM

noo

@BrevanEllefsen why did i miss a rant

Brevan Ellefsen

4:00 AM

@Starfall I'm sorry. I'm all ranted out now :'(

perhaps next time

I'll shoot you a notice

Starfall

yay

S.C.B.

6:04 AM

@Starfall What time is it there?

You are on this chat room, no?

Starfall

@S.C.B. yes

it is 09:05 am

S.C.B.

Hm. It is 3:08 pm where I am at.

Do you like arguing?

Starfall

depends on what you mean by arguing

i don't like yelling over people to tell them they are wrong and i am right

it's fun to do it to troll people sometimes, though

but i am ardently opposed to the notion that some things should not be discussed because "there's no right and wrong"

S.C.B.

Do you find them amusing?

Starfall

trolling people or arguments?

S.C.B.

6:10 AM

I mean, there is no clearly sensible conclusion IMO

Arguments.

Starfall

the purpose of an argument is not always to convince the other person to change their mind

you can't always do that

it's to understand the real root of your disagreement

what, exactly, is different about our ways of thinking that is leading to different opinions?

perhaps one of us is misinformed, perhaps we value different things, perhaps we are speculating differently on incomplete data

without talking with someone extensively, it's hard to pin down the source of a disagreement

S.C.B.

Then we disagree on the purpose of an argument. IIt's purpose is to activate at a compromise.

If you are trying to understand

Starfall

sure, arguments can also lead to compromises

that's not why you argue with someone, though

rephrasing

that's not why i argue with someone

S.C.B.

That should be called a discussion, not a argument, although I may refer to the Oxford dictionary on that one.

Oh, the dictionary seems to corroborate your claim.

Damn, typing on mobile

So many typos and because of auto correct.

Starfall

see, we were not actually disagreeing about anything, we were just working with different definitions

yes, i am correcting them myself to the best of my abilities when reading them

that's something that occurs quite frequently

S.C.B.

6:16 AM

Do you live in Eastern Europe?

Starfall

i live in turkey

S.C.B.

It seems it is UTC+3

Starfall

which is sort of like eastern europe, but not really

S.C.B.

Oh, Turkey

The country that helped us during the war?

Starfall

yes

S.C.B.

6:17 AM

Korean War

Starfall

indeed

S.C.B.

Many Koreans like Turkey for that reason I think

Starfall

that's nice

turkey is not very well liked nowadays, especially in europe

due to, well, circumstances

i suppose south korea doesn't really care about any of that

S.C.B.

m.koreatimes.co.kr/phone/news/view.jsp?req_newsidx=4062

Starfall

yes

S.C.B.

6:20 AM

Though I myself do not actually like any country.

Including my own.

A nations purpose, first and foremost is the benefit of its denizens.

That is what I think.

Starfall

wouldn't you like a country which does that job very well, then

is it just that such a utopian country has not graced the surface of this planet, in your opinion?

S.C.B.

Well, that means I respect the country for doing its job. Not that I like it.

For example, Steve Jobs

The idle businessman IMO

I hate him but he is IMO one of the most brilliant people in the 21st century.

That is what I think of countries that do their job.

So countries I respect are

Germany and China and Japan.

Starfall

only three?

i wonder why you pick those countries in particular

S.C.B.

No. These were what came to mind in particular.

Starfall

i see

S.C.B.

6:24 AM

Scandinavian countries and Canaada are probably on there.

Though I like none of these countries

I would like our country to be more like, say, Swiss.

Utopia cannot exist.

It is just human nature.

The mean average human happiness is constant over time.

An unfortunate but true statement IMO

I am doing my homework ahead of time right now.

Starfall

why

S.C.B.

So I don't have to do it at home

I do it at school.

It co

nserves time.

Starfall

i see

S.C.B.

Do you have many friends?

Starfall

no, not many

i have some

i am content with not having many friends

S.C.B.

6:34 AM

I also have some friends.

But the fact of the matter is

Society behaves cruelly to those who do not have friends.

They give you the least privileges.

Like giving you the worst portion.

So though I am content with my number of friends I am discontent with society.

Starfall

i wonder why you are so cynical about this

you sound like someone who has seen someone being handed the worst portion because they had no friends

S.C.B.

No I speak from experience.

I have gone through with it.

Starfall

seeing yourself also counts

i have never had such an experience

S.C.B.

So your statement is true is What I am saying.

I think it is an aspect of Korean

Culture.

Starfall

i see

korean culture sounds quite horrible

S.C.B.

6:42 AM

Generally, it can be generalized to mean that my society is conformist. You have to match the norm of having at least nine or more friends in any given environment which you jave occupied for at least 3 months time. So in total, you should have around 20 or 25.

Which is why

I want to immigrate.

Starfall

i see

S.C.B.

I shall proceed to vacate this site as of now until 5 hours later.

Starfall

fair enough

Brevan Ellefsen

7:54 AM

@Starfall XD you got your rant from S.C.B I see... I hope you enjoyed it!

@S.C.B. Holy cow. The cynicism got intense in this chat. Out of curiosity, where would you prefer to immigrate to?

Simply Beautiful Art

12:22 PM

@user21820 welcome to my realm! It's usually not this intense and always tangently related to mathematics.

@BrevanEllefsen @Starfall @S.C.B. I usually have lots of friends I suppose. Usually female, preferably smart. At least relatively smart

@BrevanEllefsen probably America. If Trump doesn't stop me and I get rich, maybe I'll make dreams happen.

Hehehe, I see your fun has ended @amWhy

amWhy

@SimplyBeautifulArt Yeah... I didn't want to take it too far lol

Simply Beautiful Art

Lol, safe

Simply Beautiful Art

1:06 PM

proofwiki.org/wiki/ProofWiki:Jokes/Mathematicians%27_Party

user21820

@SimplyBeautifulArt: Hello! I came here because I saw some scheduled "big number" thing..

But didn't see anything. Though if it was going to be a "who can name the bigger number" then honestly it's no point haha..

@amWhy: I noticed your changed username and then went to your profile to make sure, and then couldn't help but do a google search to convince myself that you were joking there...

@amWhy: It's hard to tell the truth nowadays.. it's really strange!

@SimplyBeautifulArt: But if there are 100% precise rules such that there are finitely many valid candidates, then it would be interesting!

Simply Beautiful Art

@user21820 lemme go find the rules then

in Mathematics, Feb 6 at 12:59, by Simply Beautiful Art

If anyone is interested, I'm hosting a big number contest. Code your number in any language (no experience needed), maximum of 256 characters, not including spaces, and try to reach the largest number you can. First submissions due Saturday. :-) http://chat.stackexchange.com/rooms/51337/this-is-the-realm-of-simply-beautiful-‌art

repl.it

^ feel free to use the given link to code @user21820

Any experience with coding?

Feb 5 at 2:24, by Simply Beautiful Art

If you haven't much experience, the above code in Ruby is a good starting point

user21820

1:30 PM

@SimplyBeautifulArt: It's not precise enough. Someone could just invent a new language that has the BB function.

Secondly, just being able to write a program in a mainstream language does not mean it will ever finish computing.

So what are the exact rules? Are programs interpreted to run as if they will never run out of memory?

Also, your code snippet does not compute a number. You still need one more line to call f.

Simply Beautiful Art

1:56 PM

@user21820 well, I don't expect anyone to do something like the busy beaver function

It does however, have to finish in a finite amount of time, but it has infinite memory to run on

You can't call in large constants like the current time.

I mean, this is all for fun @user21820

And yeah, I didn't show the rest of the image because I had other things before I called that function

Also, don't worry about whether or not we can judge which number is larger than which

chat.stackexchange.com/transcript/51337/2017/2/9/…

user21820

@SimplyBeautifulArt: Why don't you just list the acceptable programming languages?

I know this is for fun, but without clear enough rules it's not as interesting anymore.

=)

Simply Beautiful Art

Lol

Well I don't know enough languages

But Ruby, Python, Java, and maybe C and common variants of C (e.g. C++)

user21820

You can simply say anything on this list can be used. =D

And then cry when someone gives you a program in a language you can't read.

=P

Simply Beautiful Art

If you think that's too much, just do Ruby or python. That's what everyone has been doing

Lol

user21820

I myself probably know fewer languages than you. And yea it seems the best bet is Python-like languages with inbuilt arbitrary precision arithmetic.

Simply Beautiful Art

2:09 PM

Disqualified if I can't read it and you can't explain it in math

user21820

Hahaha.

Ok I'll try to come up with a Python program that computes a very large number.

Simply Beautiful Art

@user21820 haha, and one more thing. We're not running the programs XD

user21820

Clearly Ackermann is just a small fry.

Obviously.

Simply Beautiful Art

Clearly

:P

If you plan on beating me, you'll need to call Graham 's number small fry

user21820

Ok let's see.

Right now I'm busy doing something else.

Simply Beautiful Art

2:11 PM

Same

Simply Beautiful Art

2:39 PM

@Ramanujan good morning

or good night or whatever you know

Ramanujan

Good morning to you @SimplyBeautifulArt

I need some help

Simply Beautiful Art

ok

Ramanujan

@SimplyBeautifulArt

7

Q: Find the limit $\lim_\limits{x\to 0^+}{\left( e^{\frac{1}{\sin x}}-e^{\frac{1}{x}}\right)}$

Find the limit: $$\lim_\limits{x\to 0^+}{\left( e^{\frac{1}{\sin x}}-e^{\frac{1}{x}}\right)}$$ Using graph inspection, I have found the limit to be $+\infty$, but I cannot prove this in any way (I tried factorizing, using DLH)... Can anyone give a hint about that? The limit should be done ...

limits

I don't understand accepted answer to this question

Simply Beautiful Art

Ah, ok

Around where does your understanding fall apart?

Ramanujan

How in second step it is equals to 1?

Simply Beautiful Art

2:41 PM

The 1/sin(x) - 1/x become 0

Ramanujan

Yes

Second step?

Simply Beautiful Art

so we can replace them with anything that goes to 0

replace them with x

now we have

$\lim_{x\to0}\frac{e^x-1}x=1$

which is the limit definition of the derivative

Ramanujan

Haha，nice!

Simply Beautiful Art

Do you get the next step now?

Ramanujan

Yes,replace X with 1/sinx - 1/x

Oops,I didn't understand next step @SimplyBeautifulArt

Simply Beautiful Art

2:45 PM

the part after "Now write..."

he just did some algebra manipulations

Do you see which parts cancel and stuff?

@xihocipi Hello!

Ramanujan

Give a Second

xihocipi

@SimplyBeautifulArt I'm just looking at what is this, after being recommended here math.stackexchange.com/questions/2138168/…

Simply Beautiful Art

:)

xihocipi

but I'm working now. No time to chat

Simply Beautiful Art

Yeah, ofc

aren't we all busy?

(very busy :D)

@xihocipi if you are interested, I'm hosting a coding competition.

it's interesting and related to math

Ramanujan

2:54 PM

@SimplyBeautifulArt I didn't get from here : Continuing the computation, this last limit is equal to…

How it got 1/6?

Simply Beautiful Art

Ok, so we have some things happening

they got the 1/6 from the limit involving sin(x)

If you want to prove that, you have to use either L'Hospital's rule, Taylor's theorem, or a lot of trig

Ramanujan

Lhopitals is best as of now

Simply Beautiful Art

see you in about 5 minutes.

Yup

I prefer Taylor's because I think it is more intuitive.

Ramanujan

@SimplyBeautifulArt so iam slow ?

Simply Beautiful Art

Nah

You are fine

S.C.B.

3:23 PM

Hello.

Simply Beautiful Art

@S.C.B. Did you see my newest answer?

S.C.B.

No.

Did you try my exam question?

Simply Beautiful Art

@W.R.P.S Hello! Welcome to my realm :D

2

Q: Is my proof correct? (Limits)

I tried to prove $$\lim_{x\to \infty}\frac 1x = 0$$ I started as thus $$\lim_{x\to \infty}\frac 1x=\lim_{x\to \infty}\frac x{x^2}$$ Applying L'Hospital's Rule $$\lim_{x\to \infty}\frac 1x=\lim_{x\to \infty}\frac x{x^2}=\lim_{x\to \infty}\frac 1{2x}=\frac12\lim_{x\to \infty}\frac 1x$$ Thus, $$\fra...

proof-verification

@S.C.B. No, its very hard

S.C.B.

Yeah, the thing took me 15 minutes of concentration during the test, and I was the only one who got it right, I believe. Mainly consisting of calculations (the answer is not a nice, integer value).

Simply Beautiful Art

Jesus

Well, good job man

S.C.B.

3:33 PM

@amWhy changed her profile pic again.

Simply Beautiful Art

Hehe I know

that was the original image

S.C.B.

Yeah, I had seen her some time before as well as the original image.

Though it was only now I realized they were identical.

I did nearly nothing on MSE today.

Simply Beautiful Art

Yup

I noticed

W.R.P.S

@SimplyBeautifulArt Hello ,Thanks :)

S.C.B.

Highschool OT today.

Which was I wasn't able to do anything.

Simply Beautiful Art

3:38 PM

@S.C.B. Ok

@W.R.P.S Btw, we have a coding competition going on

amWhy

@S.C.B. Yeah, I asked the user "Boot Scootin' Pootton" to get Trumpoon Baffoon "out of here!" (here being my profile page!)

S.C.B.

lol, I know one person who named there account Trumplestilskin on some website.

Simply Beautiful Art

XD

amWhy

It worked, and so when I woke up early this morning, I got rid of the stench that the Baffoon left on my profile page! The nerve!

S.C.B.

Short answers are always popular.

3

A: Given $\Delta ABC$ acute. prove that $\cot A + \cot B + \cot C \ge \sqrt{3}$

We have that, since $\cot x $ is a convex function on $\left(0, \frac{\pi}{2} \right)$, and $A,B,C \in \left( 0, \frac{\pi}{2} \right)$ that $$\cot A + \cot B + \cot C \ge 3 \cot \left( \frac{A+B+C}{3} \right) =\sqrt{3}$$ Following from Jensen's Inequality. We are done! Inequalities involving...

Simply Beautiful Art

3:48 PM

Yup

S.C.B.

If this had been longer, it wouldn't have recieved 3 upvotes as quickly as it did.

amWhy

Most recent post to Mod's Chat: "Good to see that Trumpoon Baffoon is gone from the site. He hijacked my account and committed vandalism to my profile page, out of spite for me. Thank goodness Boot Scootin' Pootton was around, 'cuz I asked him to come Scootin' so he can boot the Trumpoonian Baffoon "OUT of here!"

Simply Beautiful Art

Lol

XD

Uh... Why so many people in here!?

Brevan Ellefsen

@S.C.B. What is this exam question you speak of?

Simply Beautiful Art

XD I know you guys are regulars, but goodness, I never expected such... Things!

Brevan Ellefsen

3:54 PM

@SimplyBeautifulArt this is the new main chat. But classier.

@SimplyBeautifulArt plus, the rants in this chat are comedy gold

Simply Beautiful Art

Lmao, too true

amWhy

@SimplyBeautifulArt From Mr. Rogers: "Because we like you!" (cough, cough).

Brevan Ellefsen

@SimplyBeautifulArt also, this is a chat that doesn't judge me for having a deep understanding of real analysis and decent understanding of complex analysis but almost no intuition for abstract algebra XD

Simply Beautiful Art

Aw... Thank you guys. Hopefully I love you too!

Brevan Ellefsen

❤️

Does MathJax have a heart? That emoticon might not render on all devices.

Maybe \heart?

Simply Beautiful Art

3:57 PM

$$\huge\color{red}{\heartsuit}$$

Brevan Ellefsen

That's what I'm talking about

S.C.B.

Perhaps you are looking for $$(x^2+y^2-1)^3=x^2y^3$$!

@S.C.B. -_-

Graph this.

:-)

3:59 PM

All the equations in algebraic Geometry still confuse the heck out of me

When you go up to even just all the cubic forms

S.C.B.

desmos.com/calculator/qxpkxpf6cm

Simply Beautiful Art

^

amWhy

See WA

S.C.B.

Perhaps if I find someon I like, I will send her $$(x^2+y^2-1)^3=x^2y^3$$ See if she understands.

Simply Beautiful Art

@NicolásVilches welcome to my realm!

S.C.B.

4:01 PM

Lol, so many people.

Simply Beautiful Art

Lmao

Brevan Ellefsen

Quadratic are scary enough alone $a+bx+cy+dx^2 + ey^2 + fxy + gx^2y +hy^2x + jx^2y^2$

@S.C.B. I must say, I've always enjoyed it. Anyone got a link to that famous question about different heart curves that post is from?

Fun fact. I spent more time on MSE last night than I did sleeping.

All during time I should have been sleeping

I don't recommend it

Simply Beautiful Art

@BrevanEllefsen fun fact, that's my life

Every day

Brevan Ellefsen

@SimplyBeautifulArt XD I can't run off of 3 hours of sleep for very long though.

@SimplyBeautifulArt I clearly haven't mastered the art of sleeplessness as you have

Simply Beautiful Art

Oh no, I'm just on MSE all day

I try to get sleep when possible

Does anyone else like responding to "is my proof correct?" with "I tried the same thing..."

@S.Ramanujan hi and welcome to my realm

(How to make it auto say that?)

S.C.B.

4:15 PM

I don't know, but I don't think MSE likes these kinds of questions @BrevanEllefsen.

Brevan Ellefsen

@S.C.B. Are you referring to your essay question? Feel free to post the important part of it here if you are and it was frowned upon elsewhere. If it's not closed I'll just take a link to it

S.C.B.

No, I solved the exam question by myself.

I meant the one about Heart Curves.

Brevan Ellefsen

@S.C.B. Oh, OK. Makes more sense.

S.C.B.

416

Q: Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?

geometry algebra-precalculus graphing-functions plane-curves

Has 161 downvotes.

The most downvoted question on this site.

Brevan Ellefsen

Nononono. That question.

Simply Beautiful Art

4:20 PM

XD

S.C.B.

@SimplyBeautifulArt Can you prove there are infinitely many such $n$ that $n!+1$ is not an square?

Question made by me. An original question.

Simply Beautiful Art

Hm

S.C.B.

I asked a question related to this, so the answer is in my profile.

Simply Beautiful Art

Nah, I must solve myself

Brevan Ellefsen

@S.C.B. I'll try to solve it without looking it up as well. Isn't that related to Bernard's Conjecture?

S.C.B.

4:29 PM

Brocard's Problem.

Brocard's conjecture is completely different.

Bernard's Conjecture?

W.R.P.S

@SimplyBeautifulArt Thanks for your invitation but i'm not experienced enough with coding yet sorry.

S.C.B.

You probably mean Bernard's Postulate.

@W.R.P.S I have a weeks experience in coding but I am trying to participate here.

Brevan Ellefsen

And that should actually be Bertrands Postulate

S.C.B.

Yeah.

Simply Beautiful Art

@W.R.P.S and by the way, @S.C.B. is probably in second place

@S.C.B. can I prove by contradiction?

S.C.B.

4:31 PM

Of course.

However, both methods I know (one by me, theo other by Alon Amit) does not involve contradiction.

Brevan Ellefsen

@S.C.B. Yeah. I think I could nuke this with Bertrands

S.C.B.

You mean Brocards.

Brevan Ellefsen

@S.C.B. With a little work

S.C.B.

Brocards is an unproven conjecture.

Brevan Ellefsen

I meant Bertrands

S.C.B.

4:34 PM

Brocard's Problem".

Brevan Ellefsen

I looked up both

S.C.B.

You mean Bertrand's Postulate?

Really?

Brevan Ellefsen

Yeah

S.C.B.

That seems truly unapplicable, but I'd like to see you try.

No one I know has ever proven it that way before.

Brevan Ellefsen

I think I could apply it since you ask for infinitely many examples and don't ask me to construct them

So I'm trying to think of a creative non-constructive proof

Simply Beautiful Art

4:35 PM

Well, can you prove there are infinite n such that it is a square?

Brevan Ellefsen

I'll get back to you if it works XD gtg for now.

S.C.B.

Yeah, then do so. Construct a proof. I can see it work if it was $n!$, but $n!+1$?

Simply Beautiful Art

@S.C.B. @BrevanEllefsen

S.C.B.

@SimplyBeautifulArt Those numbers

Such that $n!+1$ is a square

are called Brown Numbers.

Simply Beautiful Art

Yup

Hm, cool

S.C.B.

4:36 PM

It's conjecture, but it is said that $n=4,5,7$ are the only Brown Numbers.

It has proven it holds for $n<10^{6}$ I believe.

I can compute by hand that $$n=2 \times 10^{6}$$

Is not a brown number.

Although it involves seeing the prime list.

Wolframalpha cannot do it.

Starfall knows the answer.

Simply Beautiful Art

Lol

Ok

S.C.B.

I leave this case to you.

Simply Beautiful Art

Yup

I wish me good luck

S. Ramanujan

5:09 PM

Hello @SimplyBeautifulArt

Hello @amWhy

Simply Beautiful Art

5:31 PM

@S.Ramanujan hello and how do you do?

Zach Gershkoff

5:57 PM

I'd like to change my entry repl.it/FeQo/2

Transcript for

$Mathematics$ This is the Realm of Simply Beautiful…