/SQT/ - ask your math/science questions

[Anonymous No.8821825]

How do you show a=1 given x^a = x using logs? I forgot how to do this and reduced a math proof to this algebra step.

[Anonymous No.8821829]

x=x^1 so if x^1=x^a then log(x^1)=log(x^a) or equivalently 1logx=alogx or equivalently 1=a

[Anonymous No.8821841]

>>8821829
Thanks: I totally forgot you could rewrite log_{x}(x^1) as 1 log_{x}(x). That totally makes sense. Thank you!

[Anonymous No.8821849]

>>8821825

I'd rather show this using patterns:

x^4 = x*x*x*x
x^3 = x*x*x
x^2 = x*x
x^1 = x

You need x^1 = x in order to keep the pattern consistent.

Then, define a as the exponent to get the general case:

x^a = x*x*x*...*x [where the number of x's is a]

This way, you don't need to introduce the concept of "log" to see it -- so the result is immediately understandable and more intuitive.

[Anonymous No.8821854]

>>8821849
that only works if a is a natural number though...

[Anonymous No.8821862]

A resistor reduces the amount of Q that flows every second, it reduces the current. So it wouldn't lower the voltage right? Because the amount of energy every Q has, will maintain.

Why does the voltage get lower after flowing through the resistor in pic related?

[Anonymous No.8821870]

>>8821825

Ass Crack Man Did /Nothing/ Wrong.

[Anonymous No.8821879]

I'm reading up Strang's Linear Algebra and appiication to learn about linear algebar as a step to stop being a brainlet
How long (approximately) should I take to finish the topic? and is there anything I should take be aware of while learning Linear Algebra?

[Anonymous No.8821888]

>>8821879
visualise things in three dimensions in your head

[Anonymous No.8821895]

>>8821849
jesus fuck delete your post and your life

[Anonymous No.8821940]

>>8821862
Because a current flowing through resistive material requires a voltage drop. If there is no voltage drop, then no current is flowing because both points would have the same potential.

[Anonymous No.8821946]

how would i go about solving this problem?

[Anonymous No.8821973]

>>8821849
>the result is immediately understandable and more intuitive
and entirely useless unless [math] a \in \mathbb{N} [/math]

[Anonymous No.8821983]

>>8821946
Once you open the switch no current flows between the left and right loop. Then what you're solving is LdI/dt+IR=0 in the right loop with the initial condition for I that you found

[Anonymous No.8822053]

>>8821973
>entirely useless unless a∈N

That reminds me: complicated numbers like 3, 42, and 696969696969 can be made much simpler by defining them as a sequence of marks:

4 = ||||
3 = |||
2 = ||
1 = |

This way you don't need to introduce redundant alien symbols like "9", so equations like
|||||||| * (||||| - ||) = ||||||||||||||||||||||||
become immediately understandable and more intuitive.

[Anonymous No.8822304]

If I'm driving a car at a constant speed does the amount of force the engine is applying depend in any way on the mass of the car or is it just the air resistance?

If I'm cruising in a vacuum at constant speed then I don't need to use the engine at all, right?

[Anonymous No.8822314]

>>8822053
everyone learns the addition / subtraction / multiplication / division algorithms for base 10 very early on, so that's pointless

[Anonymous No.8822318]

does anybody have the /sci/-approved guide to computer science textbooks?

[Anonymous No.8822332]

>>8822304
mechanical resistance likely depends on the mass of the car

[Anonymous No.8822344]

>>8822318
did you miss the sticky brainlet?

[Anonymous No.8822366]

>>8822344
shut the fuck up you retarded newfag, the sticky is shit

[Anonymous No.8822370]

>>8822366
if the /sci/-approved guide in the sticky is shit why did you ask for it brainlet?
also i've been here longer than you

[Anonymous No.8822376]

>>8822332
>mechanical resistance
As in the friction of the tires angainst the road and whatnot? Yeah, I guess that might be a different story.

[Anonymous No.8822382]

>>8822370
if you had been here longer than 5 minutes then you would know that the guide in the sticky is NOT /sci/ approved you tremendous liar faggot

a group of people made a new guide several months ago, and it has several bad things but it's still decent. on the other hand the one up there right now is COMPLETE SHIT and it has always been complete shit.

fucking baboon

[Anonymous No.8822396]

>fell for the CS meme
jokes aside, I have a question that's really making me mad as fuck
apparently the following answers about Virtual Machines are wrong, anyone know why?

a. Virtual machines can be easily transferred from one computer to another TRUE
b. Processes running on a virtual machine run more slowly TRUE
c. Virtual machines allow one operating system to be ran on top of another TRUE
d. Servers running on different VMs cannot communicate with each other TRUE
e. It is safe to run untrusted executables inside a virtual machine FALSE
f. Virtual machines can be used to restrict processes' memory usage. TRUE
---------------------------------------------------------------------------------------------------------------
The following is a UTF8-encoded Unicode string. Each group of 8 binary digits represents one byte of the string. 01000001 11110001 10110000 10110110 10001010 00110110 01110010
Answer: 4 characters. three ASCII, 1-byte chars + one 4-byte character = 4

[Anonymous No.8822400]

>>8822382
i've been here since the first day this board opened

the sticky is the only /sci/ approved list

whatever other 'guide' you're referring to is probably made by someone as brainlet as you

[Anonymous No.8822406]

>>8822396
they should be correct.


VMs can be easily transferred, no need to explain this simple fact

Processes running on the VM run more slowly, obviously, even with VT-X there's a MEASURABLE delay, it's mathematically true for fuck's sake

VM allow one OS to be ran on top of another, true, because the host OS runs on top of the VM

Servers running on different VMs cannot communicate with eachother, FALSE (sorry, I made a mistake in the previous post, it's not true), communciation is possible since internet connection is possible through a VM

safe to run untrusted executables, TRUE, because that's what the lecturer said, but if I were to be fully correct here I'd say it was false because exploits have been found for VMs too that allow you to go outside of it

VM can be used to restrict processes memory usage, TRUE, one of the most basic shit you can do in a VM is set a RAM, storage and core limit to the OS, any babby knows this

[Anonymous No.8822408]

>>8822400
you're either a liar or SO FUCKING RETARDED that you don't realize how ABYSMAL that fucking piece of shit up there in the sticky is. every /sci/ regular knows it's absolute shit

[Anonymous No.8822412]

>>8822396
>d. Servers running on different VMs cannot communicate with each other TRUE
Well, I knot for a fact that's not true because I've personally done that. I don't really know how that works though, it's just an option you set in VirtualBox.
>e. It is safe to run untrusted executables inside a virtual machine FALSE
Not safe to the VM, but otherwise what could happen?

[Anonymous No.8822418]

>>8822408
what's wrong with it? you already admitted whatever this other ""guide"" you're talking about has 'several bad things' on it

[Anonymous No.8822429]

>>8822412
sorry about that, i said in the next post that I switched them around by mistake

so D is actually false, I agree with you
and E is true, so I agree with you on that as well

is anything else wrong, besides that? apparently I lost some points on it but I don't see where

also, breaking free from a VM is possible: https://arstechnica.com/security/2017/03/hack-that-escapes-vm-by-exploiting-edge-browser-fetches-105000-at-pwn2own/

[Anonymous No.8822452]

>>8822418
yeah I told them they were idiots for several small things I personally hated but god, their guide was really good in general

so I have already posted about this several times, let me be short and on point.

specific to math:
the famous guide posted by "an anon" is clearly shit for anyone who knows any math. good calculus book, good book for intro to proofs, then suddenly a TERRIBLE book for independent study of real analysis (rudin is good for lecturing but SHIT for studying alone) and all of a sudden it jumps to graduate analysis. what the fuck? no mention of literally all other math. there's a second good calculus book for some reason.
the "guide more like notes" thing is a very short comment that can be very easy to misinterpret. the calculus - linear algebra - diff eq is the standard engineering "math" sequence and you don't need me to comment on this

both math and computer science:
then there's a huge assortment of tons of shit that hasn't even been sorted by someone who knows what they're doing. some of the resources are SHIT, some of the resources are good, some of them are for highschool, some of them are graduate level, some of them are meant for lecturing, some of them are encyclopedic references, some of them are study textbooks, it's just a clusterfuck.

in math there are some charts done by a 5 year old who doesn't know what math is and a list of random math topics around too, why?

I haven't checked the other fields very closely (I have seen these two so many times it hurts) but I assume they're shit too

[Anonymous No.8822457]

how do i change the cursor in mathematica from horizontal to vertical

how do i keep it from changing from vertical to horizontal

[Anonymous No.8822468]

I'm stuck on a question

>Your friend wants to test your understanding of waves. She weaves together one end of two different ropes (one with greater mass density than the other, but each with the same radius and length) to make a single rope. You are blindfolded and asked to hold the other end of the stretched rope. Your friend expects you to determine not only which end you are holding (the heavier or lighter rope), but also whether your friend used a fixed or free method of attachment to the pole. You think for a minute, then laugh and declare that you can even estimate the ratio of the lenear mass densities! While she is speechless, you create a single wave pulse with your hand.

I've concluded that I can find whether a fixed or free method is being used by checking to see if the reflected pulse is inverted or not respectively, though I am having trouble finding out which end I would be holding and what the ratio of linear mass densities would be. Any advice?

[Anonymous No.8822484]

>>8822468
>You think for a minute, then laugh and declare that you can even estimate the ratio of the lenear mass densities!
I love it when science questions really get into the roleplay.

[Anonymous No.8822519]

if x and y are integers, how do i prove that x=+-1 and y=+-1 are the only solutions to xy=1

[Anonymous No.8822520]

>>8822519
fundamental theorem of arithmetic

[Anonymous No.8822523]

>>8822519
divide both sides by either x or y

[Anonymous No.8822531]

>>8822468
Trick question, no one answering this has any female friends.

[Anonymous No.8822650]

Is there a term for when a mathematical advancement is made because somebody shoved a number where it didn't belong?

[Anonymous No.8822688]

>>8822650
serendipity?

[Anonymous No.8822704]

>>8822519
Oh, I was given this as an exercise last year when we were constructing the naturals and then again when doing the integers.

A simple way of seeing it:
You are working in the integers, a ring with multiplication. So

xy=1 if and only if x is the inverse of y and vice versa.

But 1 and -1 are the only invertible integers, therefore the only pair of solutions is 1 and the inverse of 1 (which happens to be 1) and -1 and the inverse of -1 (which happens to be -1).

But here you are using algebra and you are assuming that you already know that only 1 and -1 are invertible. So I give you a more elementary approach using only the properties of the order of the integers:

Suppose there exists another pair of solutions ab for the equation ab=1

By the way multiplication works, we have that either both a and b are positive, or both are negative. Lets assume first that both are positive.

Note that a cannot be equal to 1 becuase if it is then we have b*1 = 1, so b=1 which yields the solution pair (1,1) and we are assuming that (a,b) is a distinct pair.
By the same reason, b can't be 1.

Then, by the order of the integers we have that

1 < a and 1 < b
and a < ab and b < ab
but then we have
but ab = 1 so we have
1 < a < 1
Which is a clear contradiction. No such number can exist, therefore no such pair (a,b) can exist.

Now that you got the idea, I'll let you figure out the case when both a and b are negative.

[Anonymous No.8822705]

>>8822457
please this is driving me nuts

the last time i could find it on google but now it's ungoogleable

[Anonymous No.8822821]

>>8821849
Lmfao you should probably end it all by now

[Anonymous No.8823021]

I have a question about brown sugar. Why don't they sell the raw syrup that still contains the molases, instead of adding molases to already refined sugar? Wouldn't it be cheaper and more nutritious?

[Anonymous No.8823082]

If I've already taken two semesters of Calculus, should I go back over a textbook like Apostol or just keep rolling?

[Anonymous No.8823093]

>>8823082
No, don't waste your time learning calculus over and over again.

[Anonymous No.8823310]

I went to a gifted highschool program, and straight up failed out and been a depressed mess sitting at home since.
I'm now considering doing an iq test to figure out if i'm actually a dumbass or if I just wasn't applying myself, and if I'm not a dumbass I'm going to give the sciences another shot, and if I am a dumbass I'll figure out what to do with my life from there.
Is this a good idea or no?
I've never done an iq test, are these things reliable?

[Anonymous No.8823314]

>>8823082
"learning calculus right all over again" is what analysis is about

[Anonymous No.8823327]

>>8823310
IQ tests are shit and will be useless for your purpose

were you fucking applying yourself or not? be honest to yourself and there's your answer, no need to jump around the issue. go study and stop feeling sorry for yourself if you want to be someone

you can literally do anything you want if you get off your ass and work hard

[Anonymous No.8823343]

>>8823310
you're obviously not applying yourself. you're a dumbass not because of a lack of genetic potential but for your failure to grow up and become a responsible adult

[Anonymous No.8823387]

>>8823327
i wasn't applying myself, that's the issue
what I don't know is what would have happened had I applied myself
>you can literally do anything you want if you get off your ass and work hard
that's not true mate. it's very possible that I could push myself to my highest capabilities and still not be a successful physicist/mathematician/etc. It's also possible that I push myself and can be one of those things, but I'm just wondering what's the best way to figure out if I'm cut out for it or not for fear of pursuing something I'm not quite qualified for and only realizing that fact years later.
and just as a sidenote I'm no longer depressed. Just trying to figure out what's a viable career to pursue.

>>8823343
this desu

[Anonymous No.8823391]

How should I take notes and study a book like Lang's Algebra that has 1000 pages and still remember everything I studied?

[Anonymous No.8823398]

>>8823387
> it's very possible that I could push myself to my highest capabilities and still not be a successful physicist/mathematician/etc.
No. Seriously. Dumb people who work hard can go the long way in math. Intuition is something you train if it doesnt come naturally. I dont know if youll believe me, lets just say I'm qualified to give this advice

[Anonymous No.8823412]

>>8823398
i mean
i don't really believe u
lol
what's your qualifications

[Anonymous No.8823417]

>>8823398
i didn't even realize intuition was a math thing bro

[Anonymous No.8823512]

Is there anything significant about the set of numbers that can be produced by raising a prime number to the power of another prime number?
4, 8, 9, 25, 27, 32, 49, 121, 125, 128, 243, 343, 1331, 2048, 2187, 3125,...

[Anonymous No.8823522]

>>8821841
Log base x isn't a thing, dummy.

x^a can be rewritten as e^{aln(x)}, so you get aln(x)=ln(x).

This only works for nonzero x btw.

[Anonymous No.8823531]

>>8823512
not really.

here's a pretty nifty site for questions like this:
https://oeis.org/

[Anonymous No.8823535]

>>8823531
I knew about that site, but for some reason didn't think it would have a search function that worked like that. brb, drinking bleach.

[Anonymous No.8823615]

>>8823535
no worries anon. now you know!

[Anonymous No.8823707]

>>8823310
>Is this a good idea or no?
Judging your own self worth based on a number is a horrible idea.

Whatever the result will be it will be negative for you.

If it is high you are a failure because despite your intelligence you achieved nothing.
If it is low you are a natural failure and destined to fail at everything.

No result of an IQ test is ever good.


What you should do is find a goal and work towards it.
If you really want to make it in the sciences nothing is stopping you.
Working hard is a lot more important then being intelligent.

[Anonymous No.8823797]

Does this function have a closed form?
f(a,b)=f(a-1,b)+f(a,b-1)
f(a,0)=f(0,b)=1
It's something really simple so I would be astounded if it didn't have a closed form.

[Anonymous No.8823809]

>>8823797
https://en.wikipedia.org/wiki/Pascal's_triangle

[Anonymous No.8823812]

>>8823809
>>8823797
i.e. f(a,b)=(a+b choose a)=(a+b)!/[a!b!]

[Anonymous No.8823837]

>>8823797
>>8823809
>>8823812
I'm pretty sure it's f(a,b) = (a choose b)

[Anonymous No.8823844]

>>8823837
it's not a choose b, its first sign that's wrong is that the definition of f is symmetry in a and b while (a choose b) is not equal to (b choose a)

also (2 choose 1)=2

and f(2,1)=f(1,1)+f(2,0)=f(1,0)+f(0,1)+f(2,0)=1+1+1=3

[Anonymous No.8823896]

Why the fuck do I need LaPlace transform when it's just as long as variation of parameter?

[Anonymous No.8823905]

Brainlet here, how do you go about solving basic calc problems like Optimization and related rates? To be more specific, how do you see/know what equations you must make and which ones u need to use? For example, i was doing an optimization problem and i needed to have used some geometry concepts that i had no idea about untill i looked at the solution key. How do u "see"/"realize" this?

[Anonymous No.8824087]

>missed a single lecture on differential equations
>turns out it was an introduction to the Laplace transformation
>can't understand shit now

Any tips?

[Anonymous No.8824090]

>>8823896
Try solving the differential equation with variation of parameters and you tell then why we need the Laplace transform

[Anonymous No.8824101]

>>8824087
Read this guy's example. >>8823896
He laid it out pretty well.

[Anonymous No.8824184]

>>8824087
...read a textbook.

[Anonymous No.8824222]

>>8821825
I'm trying to derive Jeimenkos equations, I'm told to use the retarded Greens' function of the form: [eqn] G = \frac { \delta \left ( t - | x | / c \right ) } { 4 \pi c |x| } [/eqn]However when I use that I end up with an erroneous factor of c in the denominator. So I checked his solutions and he uses a Greens' function that looks like [eqn] G = \frac { \delta \left ( t - | x | / c \right ) } { 4 \pi |x| } [/eqn]Notice the absence of c here. This works, but when I check the lecture notes he consistently uses the first function. Have I missed something here?

[Anonymous No.8824242]

>>8824222
Nevermind, figured it out.

[Anonymous No.8824261]

>>8823809
So it seems that pascal's triangle describes the number of short paths that follow a grid between two points on that grid.

[Anonymous No.8824277]

>>8823809
what is the use of pascal's triangle? what is pixar using it for?

[Anonymous No.8824292]

Which was that page to bypass journals paywalls?

[Anonymous No.8824436]

Anyone know if there's a function built into MATLAB to round down a number to an integer? So e.g. it would round any number on [0,1) to 0. Will I have to write that myself? All I can find is a function that rounds to the nearest integer.

[Anonymous No.8824437]

>>8824436
does MATLAB not have a floor function...?

[Anonymous No.8824440]

>>8824437
Thanks, I'm retarded.

[Anonymous No.8824444]

>>8823905
You gain intuition with practice.

[Anonymous No.8824449]

>>8824292
scihub

[Anonymous No.8824455]

>>8823905
Step 1: Understand the problem

Draw a picture, label what the problem tells you, then label what the problem doesn't tell you with appropriate notation (V for volume, h for height, etc.). Usually these problems boil down to "Given dv/dt is some constant, and given dh/dt is some other constant find dx/dt when x is some constant"

Step 2: Find the relationship

Find a relationship between your variables (usually similar triangles, pythagorus, sometimes a little more unfamiliar like sine or cos law)

Step 3: Differentiate the relationship

Take the relationship you found in step 2 and differentiate it

Step 4: Plug in and solve

Plug in the knowns and solve the equation algebraically, you're done now.

[Anonymous No.8824457]

>>8824087
Read one of the numerous DE textbooks available in your library/the internet?

[Anonymous No.8824615]

>>8823707
>If it is high you are a failure because despite your intelligence you achieved nothing.
>If it is low you are destined to fail.

Dude one implies I'm a failure for life, the other implies I've failed to achieve to my full capabilities. That's a pretty important distinction (that I don't fully agree with, but that's more or less irrelevant for the purpose of this conversation), and if an iq test can really tell me that info then sign me up right now. The only thing I'm concerned with is if an iq test can even give me that info in the first place.

I also disagree with the hardwork thing. Pls no debate. I started to write out why I disagree but then I realized that would just lead to a lengthy debate.

[Anonymous No.8824619]

>>8824436
Same retard again, how do I plot a function of multiple variables on just one variable with constants plugged in for the others?

[Anonymous No.8824629]

is the mapping from lnx to x regular?im trying to imagine it in my head and the plane has to transform continously in a non regular way for it to make any sense.

[Anonymous No.8824645]

>>8824619
you could just compute the constant*variable on paper and do it that way.

[Anonymous No.8824683]

>>8824645
It's not that kind of function. Specifically I'm trying to do Euler's method and I can get it to approximate a function at a certain point but I can't figure out how to get it to plot the approximation given a certain step size, initial value, and function of that initial value.

[Anonymous No.8824685]

>>8821849

[Anonymous No.8824689]

>>8824683
post the code

[Anonymous No.8824692]

>>8823896
Suppose your RHS is a Dirac delta function

[Anonymous No.8824713]

x^a=x
a=log(x)x
a=logx/logx
a=1

[Anonymous No.8824740]

>>8822053
Wildberger please go

[Anonymous No.8824752]

>>8824689
I just realized this won't work when q is negative, but that shouldn't be hard to fix. Also I realized that the inputs in line 1 spell "hoax." Anyway here. I want to plot f(x) for a certain initial value and etc.

[Anonymous No.8824753]

>>8823905
raise your power level

[Anonymous No.8824787]

>>8821825
>a board of supposed intellectuals need to use the log function to prove something as elementary as x^a = 1

Lol at you faggots. Consider suicide.

[Anonymous No.8824807]

>>8824787
>x^a = 1
Nobody wanted to prove that though

[Anonymous No.8824815]

>>8824787
It's not obvious, and it's not even true for complex numbers.

[Anonymous No.8824818]

>>8821825
CS or med school? Given that money isn't an issue.

[Anonymous No.8824822]

>>8824787
>bullying people for asking stupid questions in a stupid questions thread

[Anonymous No.8824888]

Any Algebraic Geometry people here?

What the heck is this question asking? I understand the math notation, I think, but the question seems retarded.

[Anonymous No.8824891]

>>8824888
it's just asking for two different Q(T) points on E, and whether the rational pairs have intersection or not

[Anonymous No.8824893]

Reviewing for diff exam. My brains farting. To solve a homogeneous equation you use the substiution:

y=ux which becomes dy=xdu+udx

My brains blanking on this obvious thing, how did they do this step I forgot.

[Anonymous No.8824896]

>>8824888
Ok, I think I understand now. It should say
P1 = (x1,y1) and P2=(x2,y2) are distinct solutions, and you want to know if there is some point t in Q such that (x1(t),y1(t)) = (x2(t),y2(t)).

Is that right?

[Anonymous No.8824900]

>>8824891
Gracias.

[Anonymous No.8824902]

>>8824896
yes

[Anonymous No.8824920]

>>8824900
did you find two points? there's two that aren't too hard to write down

[Anonymous No.8825122]

>>8821825

/sci/ I need help

I don't remember shit about geometric dimensioning and tolerancing, and I don't have a book on it anymore. Any suggestions of online resources to review this topic as well as reading engineering drawings?

Also, I'm not mechanically inclined... Any suggestions on how to work on this?

[Anonymous No.8825174]

[math]d+\dfrac{a}{(2-P)^{\frac{bx}{c}}}=x[/math]

I'm trying to create an equation for balancing the costs of abilities with random components in video games. "a" is the cost of the random component of the ability, "P" is the probability of the random component working, "b" is an arbitrary value that represents how detrimental randomness would be in a situation, "c" is the upper bound on a "recoverable" cost to pay, "d" is the cost of the non-random components of the ability, and x is the balanced cost of the ability. The idea behind "b" scaling with the ratio of "x" to "c" is because you're risking more if that ratio is higher.

Does this make sense? If an ability has TWO random components, then the equation becomes.
[math]d+\dfrac{a_1}{(2-P_1)^{\frac{bx}{c}}}+\dfrac{a_2}{(2-P_2)^{\frac{bx}{c}}}=x[/math]

[Anonymous No.8825259]

I know that the average value of a given function is

[math] \int_{a}^{b} x \cdot f(x)[/math]

and I sort of understand the notion behind it (giving a 'weight' for the x's but I dont know how to necessarily prove this? Like how did they arrive at this equation in the first place?

Same thing with variance.

[Anonymous No.8825400]

>>8824920
No haven't tried yet. Did you just play around with it til you got it, or is there a better way?

[Anonymous No.8825410]

>>8824920
Oh yes, by inspection x=T and x=T^2 work.

[Anonymous No.8825414]

>>8825259
That's the average by definition. You can try another definition and see why they match.

[Anonymous No.8825531]

>>8825414

Alright, i can accept that. I thought there's some underlying calculus i've been missing. I tried to think of what "average" means for a function and couldn't get anywhere. This is a clever one indeed, cheers.

[Anonymous No.8825543]

>>8821825
Is it known if the digits of pi and e differ in infinitely many places or not?

[Anonymous No.8825598]

>find the expression for velocity and acceration of A, considering that the round body(?) has a constant angular velocity

I can do it with ropes and pulleys (finding an equation for the rope's lenght and derivating it), but don't know even when to start with exercises such as this one. Can you guys give me a tip?

[Anonymous No.8825616]

>>8825543
No since that would imply that pi - e is rational, but don't know that (though we know Pi - e and pi*e, at least one is irrational)

[Anonymous No.8825657]

>>8825616
would it? for example, the digits of pi and 0 differ in infinitely many places, but pi-0 is not rational.

interesting about pi-e and pi*e, didn't know that.

[Anonymous No.8825662]

>>8825616
>>8825657
nvm, i think i misinterpreted your post. if they DON'T differ in infinitely many places, then the difference is rational, which is presumably what you meant.

[Anonymous No.8825671]

>>8825662
I'm not that guy but your discussion has prompted a stupid question from me:

Since it's still open if pi-e is irrational, and I assume that plenty of people have tried to tackle this problem, what are some of the interesting implications that result from assuming that it is rational (i.e. that there are natural numbers M,N such that M/N = pi-e)?

[Anonymous No.8825693]

>>8825671
I don't think there are very many. It's more of a challenge/provocation. "We think we know so much about e and pi, but we can't even prove something as simple as THIS!" Although I'd love to be proven wrong by someone who knows more about number theory.

[Anonymous No.8825698]

Is it worth it to join air force after bachelor's, or perhaps before transferring from community college, to increase odds of working for nsa/nasa?

[Anonymous No.8825701]

How the fuck does mathematical "proof" work

Like how can you "prove" something about how some sequence will continue off into infinity when you can't possibly demonstrate/check

[Anonymous No.8825808]

If you have charge density (x) for an infinitely long sheet (within a range, a and b, infinitely long in the other direction), and you're asked to find the expression for the electric field, you would use the charge from many infinitely long lines

My question is, would the charge density for the lines be the same as the charge density for the sheet?

[Anonymous No.8825929]

considering all knowledge I have is high school math, what should I study to become a master in diff geometry?

[Anonymous No.8825952]

>>8825701
Do you want an example?

[math]\sum_{i=1}^{\infty}\frac{1}{i}[/math]

Is an example for a diverging series, because it will become arbitrarily large as you got to infinity.

The proof:

You can write out the series without the summation sign as
[math]1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+...[/math]

Now we group them:

[math]1+(\frac{1}{2})+(\frac{1}{3}+\frac{1}{4})+(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8})+...[/math]

You can now see that if you evaluate every bracket I put there it will always be greater or equal to 1/2.

We also know that we can continue this process placing brackets always 2*n steps further.

This means, as we go along this series we can always add another 1/2 to the series by just going far enough.

Obviously then the series can not diverge.

Proofs for convergence often have a similar Idea, finding something taht converges that is always smaller then what you have.

There are also other properties about the real numbers we can use.

[Anonymous No.8826127]

How is this equal? What the hell happened?

[Anonymous No.8826134]

>>8826127
Multiply both sides with [math] \sqrt{1-x^2} [/math]

[Anonymous No.8826136]

>>8826127
>a^2-b^2=(a+b)(a-b)
How can you not know this

[Anonymous No.8826139]

Consider the recurrence relation C:N->N where C(n+1) = largest odd number divisible by 1+3*C(n)

Is C known to be bounded for all starting values C(0)?
In other words, is it true that for every value of C(0) there is a number M such that C(n) < M for all n?

[Anonymous No.8826142]

>>8826134
>>8826136

It's not an equation to solve for x. It's part of a bigger problem. I'm asking what operation was done to get the left part of the equality look like the right part of equality.

And yes, I'm completely dumb about this.

[Anonymous No.8826150]

>>8826142
[math]1-x^4 = (1+x^2)(1-x^2)[/math]

[Anonymous No.8826151]

>>8826150

Thanks.

[Anonymous No.8826153]

>>8826142
[math]\sqrt{ab} = \sqrt{a}\sqrt{b}[/math] and [math]a^2-b^2 = (a+b)(a-b)[/math]

[Anonymous No.8826161]

>>8826127
Put [math] y=x^2 [/math] then [eqn] \sqrt { 1 - x^4 } = \sqrt { 1 - y^2 } = \sqrt { 1^2 - y^2 } [/eqn] then use this>>8826136 to get [eqn] \sqrt { (1-y)(1+y) } = \sqrt { 1 -y } \sqrt { 1+ y } [/eqn] then just substitute x back in and simplify.

[Anonymous No.8826457]

Alright so I have a project where I ask people some questions using a Likert scale, and when dealing with the F-test I've come across an impasse. The means of the same independent variable (i.e. testing the same factor) have different means on different questions. What does that mean?

[Anonymous No.8826466]

What undergrad course typically teaches differential forms?

[Anonymous No.8826468]

>>8826457
>What does that mean?
It means you're unclear about the difference in meaning between the sample mean and population mean.

Imagine an experiment where you flip a coin n times and count heads=1, tails=0. If the coin is fair then the population mean = 1/2 (the population is the set of all possible outcomes of the coin flip, and exactly half of them are outcomes where the coin is heads) but the sample mean will depend on your luck at the moment and is generally not equal to 1/2.

[Anonymous No.8826474]

>>8826139
>C(n+1) = largest odd number divisible by 1+3*C(n)

This isn't defined for any value of C(n), let alone any starting value.

[Anonymous No.8826482]

>>8826466
there might be an appendix about them in a book on multivariable calculus if you're lucky

otherwise, differential geometry

[Anonymous No.8826484]

>>8826474
>This isn't defined for any value of C(n), let alone any starting value.
Well shit, that's what happens when you write p | n so often that you forget which way around the word "divisible" means in standard English.

Naturally I meant to say that C(n+1) is the largest odd number that divides 1+3*C(n).

[Anonymous No.8826487]

>>8826484
isn't that just the collatz conjecture? obviously not known to be bounded if so

[Anonymous No.8826492]

>>8826466
>>8826482
also a calculus on manifolds or differential topology class i guess

[Anonymous No.8826506]

>>8826468
So it's just a matter of interpretation. Thanks m8, appreciate it.

[Anonymous No.8826507]

>>8826487
>isn't that just the collatz conjecture?
It's the Collatz recurrence (the 'C' was probably a bit of a giveaway) but being bounded is weaker than converging to 1 since it doesn't rule out the possibility of cycles [math]C(0) \to C(1) \to \ldots \to C(n) \to C(0) [/math].
Can we rule out the case of unbounded sequences with a limit inferior of [math]\infty[/math] at least?

[Anonymous No.8826518]

>>8821862
>the amount of energy every Q has will maintain
why do you think less Q flow? the charge doesn't get lost so it must lose kinetic energy (speed) that is reflected in the potential drop

[Anonymous No.8826525]

>>8826507
>>8826507
>Can we rule out the case of unbounded sequences with a limit inferior of ∞ at least?
i don't think so, i think the current state of the art on the collatz problem still says nothing about whether
a) there are loops other than 1-2-4-1
b) there exists numbers that fly off to infinity

there's a good book called 'the ultimate challenge: the 3x+1 problem' that contains the bulk of knowledge about the problem

[Anonymous No.8826560]

What's galois group of x^n-1 over Q and over arbitrary field of characteristic 0?

[Anonymous No.8826565]

>>8826560
literally look at the first result on google when you search 'galois group of x^n-1 over Q'

[Anonymous No.8826580]

>>8826525
Thanks for the reference. Unfortunately the book doesn't seem to be available via the usual channels, but the author does seem to have an annotated bibliography of partial results on arXiv
(https://arxiv.org/pdf/math/0309224.pdf)), and I suppose I'll have more luck finding the individual papers and their corresponding proofs.

[Anonymous No.8826587]

>>8826580
>Thanks for the reference.
np, it's an open problem that's certainly begging to be solved. the proof should be interesting and will probably have to be something powerful enough that it'll involve techniques applicable to new problems

[Anonymous No.8826669]

>>8825122
halp

[Anonymous No.8826811]

Does genetics count as science? I was just hoping someone could explain why humans are considered one race with no real difference, yet for other species categorizing them is fine.
Is it all a moral thing, where we don't want to put down any human as being less? I heard someone say something about how if we were dogs we would all be the same species or something like that, but I have a hard time understanding it.
I've always felt like it's really hard to read about things like this, because everyone seems so biased. I don't know who to trust.

To make it clear, from personal experience of interacting with people I haven't really noticed any difference, than wasn't already present in different individuals of the same race. It just feels weird to me that for example IQ wouldn't at least somewhat be part of your race, with so many other aspects seeming to be so.

[Anonymous No.8826840]

>>8826811
Short answer is that humans are too genetically similar to justify splitting them into separate species. In fact, humans are unusual in how narrow our genetic variation is.

[Anonymous No.8826903]

>>8825701
You know how you can take an algebraic formula and reduce it to a simpler formula that remains equivalent? Mathematical proofs reduce problems to axioms, using methods that have been proven to preserve equivalence. Since those methods need their own proofs, big mathematical proofs are very complicated because they draw on dozens of other proofs, so you need to climb down very far before you get back to the axioms.

[Anonymous No.8826913]

What prevents the Collatz Conjecture from being the Halting Problem?

[Anonymous No.8827088]

>>8826127
this is why i hate the square root symbol. it makes it looks like everything is inside is untouchable. the solution would be easier to see if it was just a parentheses with a 1/2 exponent.

[Anonymous No.8827093]

>>8825598
The position of A depends on the position of P. For start, try doing it with beta=0. Then the position will simply be b sin(theta) + whatever the length of that rod is. Beta complicates it a little but not that much

[Anonymous No.8827172]

>>8827088
>parentheses with a 1/2 exponent.
>not using the Z of power and reciprocal symbol to generalize this relation

[Anonymous No.8827210]

>>8826161

I remember seeing this and hating myself so much for not seeing [math] (x^2)^2 [/math]. It's so simple yet so hard to notice the first time.

[Anonymous No.8827245]

Not a math or science question, but figured /adv/ wouldn't really know:
Should I take applied electrodynamics or discrete time signals? I'm a comp e major, and need to fill out my schedule for summer. Not sure which would be more useful.
I've already taken a 300-level e&m physics class, but that only covered electrostatics (first part of a three series, I won't be taking those other classes). And right now I'm taking a continuous time signals class.

[Anonymous No.8827262]

https://www.youtube.com/watch?v=bG7cCXqcJag

wtf are they talking about? they don't explain what they mean by "exchange"

[Anonymous No.8827264]

and wtf is she wearing jesus christ

[Anonymous No.8827267]

so 4 mins in and now they've explained it

she has the charisma of a brick

[Anonymous No.8827285]

>>8827264
>>8827267
fuck off, I think she's cute

[Anonymous No.8827291]

>>8827285
at least talk about an interesting subject not just this retarded girly shit

[Anonymous No.8827296]

>>8827262
timestamp?

[Anonymous No.8827305]

>>8827296
nvm they're just talking about swapping digits so if you have 1.23 and 1.51 you can make 1.53 and 1.21 etc

[Anonymous No.8827396]

whats the answer to this? been bugging me for days

[Anonymous No.8827457]

>>8827396
I strongly suspect it's #3. but I ain't got a good explanation for why just yet.

[Anonymous No.8827505]

What the hell does <M, <M>> mean> It's a tuple that contains M and the tuple <M> that contains M. What the hell does it mean? What does it mean to run H on a tuple that contains a turing machine (any kind) and the same machine inside another tuple?

Why?

There's no explanation for this in the slides. Holy shit.

[Anonymous No.8827509]

>>8827396
i'm stumped. usually in these tests there is a fairly easy/elegant trick like XOR or figuring out how the dots move or something to do with counting the dots. but i'm not seeing it here.

[Anonymous No.8827552]

>>8827396
>>8827509
>>8827457
what about this:
use OR instead of XOR
I'm interpreting the drawing as this:
first column: normal rotation, normal being the last cube's rotation.
second column we have the squares that are rotated 45deg to the left, we can turn them back to "normal" by rotating them by 45deg to the right
3rd column is normal too
now, it seems to me that it should alternate, since in the 3rd column it returns to the same angle as the 1st col and the "normal" angle is the same as the last one's

now we normalize the squares, turn the angles to normal (rotate the "diamonds")
-----------------------
first column: logical OR where black dots = 1 and blank = 0.
we get
11
01
second row:
OR them together, we get:
11
00
3rd column, OR them together, we get:
11
01

now in the 4th one (second to last), we OR the previous cubes and get:
11
01
we rotate it 45 deg to the left, we get the last cube rotated to the left a little

last step, we rotate the cube to the right by 45deg, it becomes "normal" again

[Anonymous No.8827567]

>>8827552
Except there is no precedent set for ORing the previous cubes.

I instead believe we have two different operations, one for rotating clockwise 45, and one for rotating counter-clockwise 45. 4th step must be reached by performing an operation (not necessarily the same one) for the two cubes previous two it, that achieves the same result. Then the fifth one is reached by performing an operation determined by rotation on the 4th one.

I've been experimenting with using adding a dot to a location of a previous dot, as well as moving dots for the other operation, unfortunately it doesn't give an answer that matches.

Assuming CW for +1 gives a contradiction, and assuming CCW for +1 also contradicts.

[Anonymous No.8827583]

>>8827567
I kinda went with the idea that usually in these tests you can many times omit some steps or ignore some parts of the figure and try to look at some other, inner patterns that need to be respected

what about pic related

if you were to look at the figures as if they were pixellated graphs that display graphs of linear equations

[Anonymous No.8827596]

>>8827583
Assuming your linear equation idea would mean that A in your picture doesn't make any sense. I'm not convinced.

[Anonymous No.8827606]

I have this idea for an encryption algorithm, and I was wondering if something like this already exists.
Basically, you have a message, a key, and the encrypted message.
The message is known to you, and you know what you want to encrypt it TO. You then calculate the key to make this possible.
For example: you have the string "Meet me Friday night." and you want to create the output "Can I borrow your lecture notes?"
The idea is that someone intercepting the note wouldn't be able to tell that it was encrypted in the first place. They would just assume you are asking for lecture notes, when you're actually asking them to meet you in secret.
I calculated this example through.
original = "Meet me Friday night"
encrypted = "Can I borrow your lecture notes"
the original string has less letters than the encrypted one, so you fill it up with z's.
Now the key calculates to [16, 22, 9, 15, 15, 10, 12, 0, 6, 19, 24, 16, 7, 9, 5, 23, 9, 20, 21, 18, 5, 14, 15, 20, 5] or as string: qwjppkmagtyqhjfxjuvsfopuf

If the recepient has the message "Can I borrow your lecture notes" and the key, they can get back the original message "meetmefridaynightzzzzzzzz"
it's a bit ugly, but 100% human readable.

Does something like this already exist?

[Anonymous No.8827614]

>>8827596
>>8827583
>>8827567
Holy fuck I think I figured it out, gimme a sec to write it out.

[Anonymous No.8827616]

>>8827614
let's see

[Anonymous No.8827636]

>>8827505
<M> is the Gödel number of the turing machine M.

[Anonymous No.8827641]

>>8827616
OK, this solution is not elegant, but it works.

We're not ORing or XORing anything, instead each dot has a value of 1.

The diamond represents two different "potential cubes, one rotated 45 CCW, and one 45 CW.

To get the next "normal" cube, we simply add the numbers in each respective corner to each other. This is where, in my opinion, the weakest part of argument comes. A dot will appear on the next one on any value except 1.

This would mean for the top row, we have.
1 0
0 0
+
1 1
0 0
+
1 0
1 0
Which gives us,
3 1
1 0.

By the rule of 1's not being dots, we get the next "normal" cube.

The same is true for the bottom row:
0 1
0 1
+
1 1
0 0
+
1 0
1 0
Which gives:
2 2
1 1
the next "normal" cube.

The answer would thus be 4, since it would give us for the top row:
1 0
0 1
+
0 1
1 1
+
1 1
0 1
=
2 2
1 3

and for the bottom row:
1 1
0 0
+
0 1
1 1
+
1 1
0 1
=
2 3
1 2

Which is the last "normal" cube.

[Anonymous No.8827723]

>>8827396
this is what i was thinking of...

is it possible the last two boxes were printed upside down??? fucking hell i cant sleep

[Anonymous No.8827727]

>>8827723
sorry, i meant top box is counter clock rotation, and the bottom box would be clockwise rotation. im assuming they're rotating into each other

[Anonymous No.8827739]

>>8827723
I had that idea too, but none of the given answers fit. I still believe my idea is correct:
>>8827641

[Anonymous No.8827767]

>>8827641
hey im having trouble following your solution. in the top row, why would the 3rd box be
1 0
1 0
instead of
1 0
0 1
(this would be the same no matter how you're rotating)

in the bottom you're rotating CCW right?
then im seeing:
0 1
0 1
and
1 0
1 0
and
1 1
0 0

[Anonymous No.8827789]

>>8827767
Here, I made an image. Only showed the top row though, to not multiply work, but the same is true for the bottom row as well.

[Anonymous No.8827805]

>>8827396
look at bottom row. it rotates counter clockwise and p(1,2) in config 0 stays still while the other one swaps between (2,2) and (1,1) every rotation.

Therefore the answer is either 2 or 3

In the final configuration, p(1,1) and p(1,2) come from the bottom row.
Only one point, p(2,2) comes from the top row.
Therefore, by reversing the pattern (rotating counterclockwise (or clockwise, it doesn't matter))

it is answer number Two.

[Anonymous No.8827810]

>>8827805
i know this answer assumes that theres only 1 point in the final config coming from top row.
But i dont Fucking care.

[Anonymous No.8827819]

>>8827789
that works out with answer 4. is it likely that the person who made this question was thinking of the same solution though? i think probably not given the rest of the quiz

impressive answer though what gave you that idea?

[Anonymous No.8827825]

>>8827819
Yeah, answer 4 like I stated here:
>>8827641

However, yes, I do believe I am in danger of simply having constructed a solution that specifically fits the question.

>what gave you that idea
I started off with the idea of different rotations applying different operations. Like adding a dot for CW, and flipping, like:
>>8827805
thought of here, for CCW, or vice versa. However that didn't work out. By the way, his solution doesn't work either, since it has no explanation for how #2 would become the final configuration.

ORing or XORing was my next idea, but obviously that didn't work.

Finally I just thought that maybe instead of the diamonds rotating in just one direction or the other, they could perhaps be rotating in both, and after that it was quite easy to establish my solution.

One important facet is that the distance between the top and bottom row is shrinking, which implies that the same operation needs to be applied to both the 3rd item in the top row, and the bottom row, to produce the same result, and then that operation must be applied to #4, to achieve #5. Just adding the bottom and the top won't work, since we only have one item in #4.

[Anonymous No.8827828]

a=b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
2b = b
2 = 1

Prove me wrong fagets

[Anonymous No.8827830]

>>8827828
you divided by 0 going from the 4th to 5th line

[Anonymous No.8827833]

>>8827828
>dividing by zero
Between steps 4 and 5. Cmon son.

[Anonymous No.8827836]

>My coworkers know I really like math.
>Sometimes I say shit without really thinking about it.
>Have friend with aspergers at work and invite him along to help him learn math.
>His algebra is probably pretty shit so I think I just agreed to tutor this guy in algebra for free.
>I've never tutored before, so I'm trying to look at this as an experiment in whether I enjoy tutoring or not.
>Also feel a little bit stupid for agreeing to do this as peers (i.e., not as a paid tutor)
Am I an idiot or a pretty cool dude for agreeing to do this?

[Anonymous No.8827839]

>>8827836
A fucking idiot

Tutors can make up to $30 an hour

[Anonymous No.8827840]

>>8827836
I used to work as a tutor.

It's hell.

[Anonymous No.8827844]

>>8827839
>>8827840
I just said, hey, here's this really cool calculus book and my plans for the summer are to teach myself all that I can out of it. I asked if he thought that was something he'd like to do. He said sure, of course.
So now I'm like...kinda fucked. The good news is I can be "busy" if it doesn't work out since it's no formal agreement.

[Anonymous No.8827847]

>>8821825
But x^a=x for any a is true for any idempotent element in your ring.

[Anonymous No.8827848]

>>8827606
Take any bijection from [math]A^{25} \to A^{25}[/math] to itself, where the alphabet A = {a,b,c,...,z} so [math]A^{25}[/math] is the set of all strings with 25 letters.

The only constraint you want is that "meetmefridaynightzzzzzzzz" maps to "caniborrowyourlecturenotes", so a trivial example of a key that satisfies this is the following:
(a) "meetmefridaynightzzzzzzzz" encrypts to "caniborrowyourlecturenotes"
(b) "caniborrowyourlecturenotes" encrypts to "meetmefridaynightzzzzzzzz"
(c) every other 25-letter string encrypts to itself

If you find this too trivial you can replace (c) with a cleverer encoding, like mapping each string to its reverse or something (you'll have to adjust (a) and (b) accordingly though).

[Anonymous No.8827866]

>>8827583
Is this one an answer choice?

[Anonymous No.8827875]

>>8827866
If the coloured squares are dots, then no. For the third time in this thread, one of the dots staying while the other flips, and similar things, do NOT work.

[Anonymous No.8827879]

>>8827847
>assuming a is natural
kys brainlet

[Anonymous No.8827892]

>>8827866
>>8827396

this >>8827641 is the only answer that is consistent with the pattern of both rows, and works with answer #4. might not be the intended solution, but works out. i suspect this is unlikely to be the intended solution, the answer is right from some sort of mathematical entanglement

[Anonymous No.8827939]

>>8827892
I'm going to bed, but if anyone wants to keep going with this that'd be fun.

Another idea I had is that it might have something to do with mirroring. Notice how in the top row the rotated square can be an x-mirror or y-mirror, and the last one (before unknown) is diagonal mirror.

I'm too tired to work it out completely, but I suspect this is closer to the intended solution.

[Anonymous No.8827981]

>>8827396
im starting to think whoever made this question just didn't make it very well. it also includes some other box questions that nothing like this
>>8827789 would work

[Anonymous No.8827988]

I have two time-series statistics questions, if someone wouldn't mind helping me.

If I am estimating a VAR model, how do I know how many lags are appropriate?

and how do I get the impulse response function from my regression estimates?

[Anonymous No.8827990]

>>8825259
Anon is right this is sort of a base definition but I like thinking of it like this. Think of taking averages in the first place. Adding everything then dividing by the size of the sample in total, right? So
[eqn]\frac{X_{1}+...+X_{n}}{n}=\frac{X_{1}}{n}+...+\frac{X_{n}}{n}=X_{1}(\frac{1}{n})+...+X_{n}(\frac{1}{n})=X_{1}Pr(X_{1})+...+X_{n}Pr(X_{n}) [/eqn]
So if some of those values are equal, then surely you'd just add their probabilities together to be multiplied by the value. Wherein we get a weighting.
I.e. sample 1, 1, 2, 2, 5, avg is
[eqn]\frac{1+1+2+2+5}{5}=\frac{1}{5}+\frac{1}{5}+\frac{2}{5}+\frac{2}{5}+\frac{5}{5}=(1)(\frac{2}{5})+(2)(\frac{2}{5})+(5)(\frac{1}{5})[/eqn]
f(x) is the continuous probability of x, which must be non-negative and integrate over the support out to 1. x*f(x) is each value multiplied by it's corresponding weighting, so we integrate x*f(x) over the support to find the average.

[eqn]E(X)=\int_{-\infty}^\infty xf(x)dx[/eqn]
And integrating over the reals does work, since most of the time, especially in real application there's finite support, and the rest of the function in question is 'zero elsewhere.'

[Anonymous No.8827996]

>>8825259
Anon is right this is sort of a base definition but I like thinking of it like this. Think of taking averages in the first place. Adding everything then dividing by the size of the sample in total, right? So
[eqn]\frac{X_{1}+...+X_{n}}{n}=\frac{X_{1}}{n}+...+\frac{X_{n}}{n}=X_{1}(\frac{1}{n})+...+X_{n}(\frac{1}{n})=X_{1}Pr(X_{1})+...+X_{n}Pr(X_{n}) [/eqn]
So if some of those values are equal, then surely you'd just add their probabilities together to be multiplied by the value. Wherein we get a weighting.
I.e. sample 1, 1, 2, 2, 5, avg is
[eqn]\frac{1+1+2+2+5}{5}=\frac{1}{5}+\frac{1}{5}+\frac{2}{5}+\frac{2}{5}+\frac{5}{5}=(1)(\frac{2}{5})+(2)(\frac{2}{5})+(5)(\frac{1}{5})[/eqn]

f(x) is the continuous probability of x, which must be non-negative and integrate over the support out to 1. x*f(x) is each value multiplied by it's corresponding weighting, so we integrate x*f(x) over the support to find the average.

[eqn]E(X)=\int_{-\infty}^\infty xf(x)dx[/eqn]

And integrating over the reals does work, since most of the time, especially in real application there's finite support, and the rest of the function in question is 'zero elsewhere.'

[Anonymous No.8828003]

>>8825259
Anon is right this is sort of a base definition but I like thinking of it like this. Think of taking averages in the first place. Adding everything then dividing by the size of the sample in total, right? So
[eqn]\frac{X_{1}+...+X_{n}}{n}=\frac{X_{1}}{n}+...+\frac{X_{n}}{n}=X_{1}(\frac{1}{n})+...+X_{n}(\frac{1}{n})=X_{1}Pr(X_{1})+...+X_{n}Pr(X_{n}) [/eqn]
So if some of those values are equal, then surely you'd just add their probabilities together to be multiplied by the value. Wherein we get a weighting.
I.e. sample 1, 1, 2, 2, 5, avg is
[eqn]\frac{1+1+2+2+5}{5}=\frac{1}{5}+\frac{1}{5}+\frac{2}{5}+\frac{2}{5}+\frac{5}{5}=(1)(\frac{2}{5})+(2)(\frac{2}{5})+(5)(\frac{1}{5}) [/eqn]
f(x) is the continuous probability of x, which must be non-negative and integrate over the support out to 1. x*f(x) is each value multiplied by it's corresponding weighting, so we integrate x*f(x) over the support to find the average. Works for
[eqn]E(g(X))=\int_{-\infty}^\infty g(x)f(x)dx[/eqn]
And integrating over infinity does work, since most of the time, especially in real application there's finite support, and the rest of the function in question is 'zero elsewhere.'

[Anonymous No.8828269]

Can someone please explain to me how the top thing turned into the bottom thing? No skipping steps I tried to understand it but wtf..

[Anonymous No.8828283]

Can someone please explain to me how you get the top result from the last result? Show all working... I cant figure it out for my life

[Anonymous No.8828293]

>>8827505
H takes a pair <M, x>, with M a turing machine and tells you whether M halts on input x. So running H on <M, <M>> tells you whether M will halt when you input M itself.

[Anonymous No.8828307]

It's not funny when you nerds already solved the question.

[Anonymous No.8828308]

I think that there should be two different sqt threads, one for maths, and the other one for science. Opinions?

[Anonymous No.8828313]

>>8828283
Multiply everything with (1-p), you get n/p-n in the first part, the -n cancels out with the other -n and you're left with n/p= the sum

[Anonymous No.8828314]

>>8826811
humans indeed have different biological races, but there are no different political races

[Anonymous No.8828319]

>>8828313
wtf... please draw this I dont understand just typing

[Anonymous No.8828328]

>>8828319
Rereading your question i'm not exactly sure what you're interested in. Is it how you get the last equation after therefore?

[Anonymous No.8828331]

>>8828328
I don't know how they simplified the n/p - sum/(1-p)

to get p = n/(sum xi)

I tried so many times but I cant get it for some reason...

[Anonymous No.8828334]

>>8827805
Used the exact same thinking
As you have mentioned the only prerequisite this assumes is that the two dots start at the same place in picture 1, which isn't uncommon in these types of puzzles.

[Anonymous No.8828335]

>>8828331

It's really not that hard anon
[eqn]\frac{n}{p}(1-p)-(\Sigma x_i -n)=0 [/eqn]
[eqn]\frac{n}{p}-n -(\Sigma x_i -n)=0 [/eqn]
[eqn]\frac{n}{p}=\Sigma x_i [/eqn]

[Anonymous No.8828339]

>>8828335
Ok right here, how did the 2nd step go to the 3rd step? thats what I don't understand

[Anonymous No.8828344]

>>8828339
-n-(-n) is zero and you switch the sum to the other side. I assume that n in the brackets is outside of the sum cause there's no point in adding n to itself a bunch of times they would just write that as n^2.

[Anonymous No.8828345]

>>8828344
THe full thing is in pic related

Is the n in the brackets really supposed to be outside of the sum? If thats the case im going to fucking kill myself please confirm..

[Anonymous No.8828351]

>>8828345
Yes it comes from the definition of L(p). When you multiply all of those (1-p) together you get a sum of their exponents in the exponent. The sum is [math] \Sigma(x_i -1)[/math] from 1 to n and adding all the 1's together gives you n outside the sum.

It's frustrating but missing stupid shit like this happens

[Anonymous No.8828359]

>>8828351
holy fuck......thanks for pointing this out, I had not thought about it and just kept staring at the brackets so assumed it was part of the sum, tried for hours to make it work doing all kinds of fucked up shit

jesus christ.

[Anonymous No.8828449]

I'm reading up on Fourier series.

In an example where they calculate what the complex coefficient c_{m}, they simplify the result as shown in pic related.

Does anyone have any idea how the heck they go from the first expression to the last?

I'm guessing Eulers identity is used to get a sinusoid term in there?

[Anonymous No.8828462]

>>8828449
Pull exp( -j m pi/3) out of the
[exp(-j m 2 pi/3)-1] on the top to get
a difference of exp()'s inside the [].

Then use (exp(i t) - exp(-i t))/(2 i) = sin(t)

[Anonymous No.8828471]

>>8828293
You're correct but what does it mean to run M on M itself? Does it check the syntax of ! And treat it as a string, or what? Can't figure this out. I know this is a high level explanation of Turing's proof.

[Anonymous No.8828472]

>>8828462
Thanks !

[Anonymous No.8828474]

>>8828449
It's simpler to use the sine formula:
[eqn]\sin x=\frac{e^{ ix}-e^{-ix}}{2i}[/eqn]
If you factor [math]e^{-jm\pi/3}[/math] out of the numerator you should get something in that form

[Anonymous No.8828479]

Is there any reason to believe that Geoengineering won't be necessary in the next 20-30 years?

Is there any reason pumping sulfur into the stratosphere won't work?

[Anonymous No.8828706]

> Vector Calculus
> System of ODE's (general solutions and phase portraits)
> Laplace transforms
> Series and Sequences
> Fourier Transforms
> Second order PDE's

Is this syllabus easier or harder than calc 3? My university doesn't call it calc 3, instead they call it "engineering mathematics". Just trying to get an idea of the level I'm studying at.

[Anonymous No.8828713]

>>8828706
vector calc on its own is usually calc 3 at most places, so if all those are in one course that should be easier since you won't be able to go very in depth in any of the topics

[Anonymous No.8828743]

>>8828706
it's engineering differential equations. it's usual to do this somewhere in the calculus sequence

[Anonymous No.8828813]

>>8827636
>Gödel number
I kind of get it now. So is it just a number, a kind of ID that is used for a later argument that I'm not seeing in the lecture slides?

is it used for a diagonalization proof in turing's paper?

[Anonymous No.8829210]

>>8827988
Anybody mind helping? Sorry if this is the wrong place to ask about statistics.

[Anonymous No.8829309]

If a car is going 1 m/s with a dynamic acceleration of 100% of its speed then after 1 sec, the car will be going e km/s right?

[Anonymous No.8829465]

In Logic, is an argument only valid when it's a tautology?

[Anonymous No.8829614]

I'm having a total brain freeze right now

We roll a dice twice, and take X to be the larger value from the two rolls. What is the pmf of this?

I know I can just manually figure this out, but what is the intelligent way of computing this?

[Anonymous No.8829660]

what does the co in coordinates signify? Something about belonging to the ordinates/ordered numbers?

is coordinates to ordinates as coroutine is to routine or cooperation is to operation?

[Anonymous No.8829901]

What type of problems are the least google-able?

[Anonymous No.8829997]

What operations do I need in order to be able to turn one planar graph into any other planar graph without creating any intermediary graphs that are not planar? An operation means something like removing edges, adding vertices to the middle of edges, splitting a vertex into two vertices such that each one has all the edges of the original, and fusing two vertices such that the resulting one has all the edges of both the components combined. Are using just these operations enough to do what I said?

[Anonymous No.8830046]

>>8829901
something about the thing you are trying to find being a more obscure version of what most people would search for

I used to have one or two examples but I can not remember them right now

maybe something like say you wanted a sample of a virus but all the results are for virus removal or antivirus or virus scanners and tons of synonyms

you could of course search for like virus sample download or something like that but the idea is the same. The thing you are searching for is a subset of what most the results are off, so you have to negate all the "scanner, removal, anti"-stuff rather than be more specific.

also stuff that requires perception like whether a hard drive noise is supposed to happen

[Anonymous No.8830051]

>>8826811
>To make it clear, from personal experience of interacting with people I haven't really noticed any difference, than wasn't already present in different individuals of the same race.

You are comparing individual variance with group variance, which is a logical fallacy.

[Anonymous No.8830092]

>>8829901
things that only the bogdanoffs know the answer to

[Anonymous No.8830103]

>>8821849
This is the retard who complains that the teaching of math isn't intuitive enough.

[Anonymous No.8830169]

Why do log graphs extend in the negative x-axis? I thought its domain was all real x-values above its vertical asymptote?

I ignored it until i learned that the derivative of ln(x) is 1/x and now I don't understand. pls help

[Anonymous No.8830201]

So in the graphs of the equations x^x^x^-x and x/(x^x^x^-x), each has a trough that seems to occur at a really arbitrary value. The first equation trough is at x=0.529467581 -> y=0.770266162 and the second equation trough is at x=1.87176288 -> y=0.87446512.

What is so special about these numbers?

[Anonymous No.8830267]

>>8830169
its probably log|x|

[Anonymous No.8830288]

>>8830267
then what about the derivative ln(x)? 1/x looks like the derivative of ln|x| but not ln(x).

Or does this particular derivative have a restriction of x > 0?

[Anonymous No.8830291]

>>8830288
D(ln|x|)=1/x
D(ln(x))=1/x fox x>0 because the ln function isnt defined for x<=0

[Anonymous No.8830293]

>>8821829
This. Everyone in this thread going off about patterns is a faggot

[Anonymous No.8830297]

>>8830291
ah true. thanks.

[Anonymous No.8830301]

The thread
>>>8828773
presents a one-line proof that uses the sine function to conclude that there infinitely many primes (it links https://www.johndcook.com/blog/2016/10/30/a-short-unusual-proof-that-there-are-infinitely-many-primes/
which reproduces the proof and elaborates in more detail).
However, I suspect that the reasoning is circular in that at least one of the steps
>definition of pi
>definition of sine
>concluding that the sine of an integer multiple of pi is equal to 0
cannot be done without assuming, a priori, that there are infinitely many primes.

Am I wrong?

[Anonymous No.8830346]

>>8830301
Where in the definition of pi, or the definition of the sine function, do we assume that there are infinitely many primes?

[Anonymous No.8830366]

>>8830301
i don't think it's circular, but at its heart it's just a needless complication of euclid's proof.

the proof hinges on the fact that there is some prime p such that p| 1+2prod p' (since every integer has a prime factor). however, this immediately implies that p| 1+prod p', and this is the point at which euclid derives a contradiction and finishes the proof. the other proof goes through the unnecessary step of plugging everything into the sin function without first stopping to ponder the implications of the formula p| 1+2prod p'.

[Anonymous No.8830411]

>>8830346
It's really all three put together. Once you replace pi and the sine function with their definitions in terms of exponentials, the heart of the proof seems to hinge on the fact that pi is transcendental, which I doubt can be proved in a model of finitely many primes. I guess the algebraic closure of Q in that model would be a proper subset of the usual algebraic closure, giving rise to some kind of p-adic structure? I suspect the model will remain consistent for some kind of p-adic definition of the sine function and pi, but I don't know enough number theory to comment further on that.

>>8830366
Yeah, I have no qualms with Euclid's proof. My issues are precisely with that last 'unnecessary step', which I suspect to be not only unnecessary but unsound.

[Anonymous No.8830472]

Actually I have a response to >>8830346
If you define [math]\pi^2 = 6/\prod_p(1-1/p^2)[/math] then the irrationality of [math]\pi^2[/math] directly implies the existence of infinitely many primes.

[Anonymous No.8830501]

In the sense of creating a true artificial consciousness, does this make sense? Human brains can be broken down into neurons, atoms, or whatever smallest unit that will be individually replicated by a computer, like current AI is attempting. All human decisions are either based of past experiences, or if possible, truly random. If a decision is based on past experience, a computer can come to a conclusion based on previous data. If a decision is based on randomness, a quantum computer can be used to generate that decision. Assuming there would be no limit to the processing power needed to run this, would it be possible to create an artificial consciousness equivalent to a human mind that is capable of thought, emotion, and everything a human brain is capable of?

[Anonymous No.8830509]

So im stuck on thus question about the length of an image. heres the problem,


A pencil with length 10 cm is placed along the optical axis of a convex mirror with a focal
length of 12 cm. The tip of the pencil is at a distance of 28 cm from the mirror.
What is the length of the pencil's image?

the answer is .72cm, but i just dont know how thats the answer.

[Anonymous No.8830511]

>>8830501
it would most likely be possible to create something which from an outside point of view behaves with the same capability as a human brain. but as for whether "it" will have a subjective sense of self, if you know what i mean, is currently unknown. very little is known about the nature of consciousness. does a stone have a consciousness? does a computer have a consciousness? does a sufficiently advanced computer which behaves like a human have a consciousness?

[Anonymous No.8830516]

>>8830511
and if a computer can't have a consciousness, then what makes us so special? aren't our brains just biological computers?

[Anonymous No.8830521]

>>8830501
If you'd like to look at this further, check out the Human Connectome Project.

[Anonymous No.8830524]

>>8830511
>>8830521
Awesome, thank you

[Anonymous No.8830556]

>>8830509
nevermind, i figured it out. You just get the difference between the near end of the pencil and the far end.

Good shit ya'll.

[Anonymous No.8830567]

>>8829465
technically speaking, a tautology is a kind of formula, not a kind of argument. in propositional logic (i.e., no quantifiers allowed), there is no difference between a tautology and a theorem. if you allow quantifiers, then there are theorems which are not tautologies.

https://en.wikipedia.org/wiki/Tautology_(logic)

[Anonymous No.8830659]

Is there anything I can read that talks about how the "wave" of change propagates through a colored graph when you make certain changes to it that causes it to require a different coloring?

[Anonymous No.8830752]

>>8824893
It's the product rule. If you derive both sides then you have to derive y which becomes dy. For ux, you use product rule: d/dx(f(x)g(x)) = f'(x)g(x) + g'(x)f(x) where f = u and g = x.

I probably got notation shit wrong but whatever. It just boils down to the product rule.

[Anonymous No.8830776]

x=x^1
x^a=x^1
ln(a*e^x)=ln(e^x)
ln(a*e^x)-ln(e^x)=0
ln([a*e^x]/[e^x])=0
ln(a)=0
a=exp(0)
so a=1

[Anonymous No.8830796]

>>8830776
It doesn't need to be so damn long

x^a = x
log(x^a) = log(x)
a*log(x) = log(x)
a = 1

or you can go by if a^b = c , loga(c) = b

x^a = x
logx(x) = a
1 = a

[Anonymous No.8831060]

>>8828713
>>8828743
I've already taken calc 1 and 2, linear algebra so I assumed this was calc 3

guess it's a tad easier but I don't mind 2bh

fwiw in vector calc we studied:

double integrals, change of variables to polar, cylindrical and spherical, predetermination of paths, line integrals, work integrals, conservative fields, integrals over surfaces, surface area, flux, gauss' divergence, stokes' theorum

it seemed pretty short

[Anonymous No.8831104]

what's the difference between the two cylinders shown? how would my calculations be affected by their supports?

[Anonymous No.8831106]

>>8821849
are you fucking serious

[Anonymous No.8831118]

>>8831104
wew forgot image

[Anonymous No.8831282]

[eqn]
\left\{
\begin{array}{cc}
\alpha''(t) \cdot x_{u}(u, v) = 0 \\
\alpha''(t) \cdot x_{v}(u, v) = 0 \\
u(0) = u_i, \ u'(0) = \sin(\theta) \\
v(0) = v_i, \ v'(0) = \cos(\theta)
\end{array}
\right.
[/eqn]
where [math]\alpha(t) = \langle x(u(t), v(t)) \rangle[/math]

What can I add to this system to try and get points that are equally spaced from (u_i, v_i) along the surface of x? I was thinking something like adding s(t) to the system and using the fact that I want [eqn]\int\limits_0^r \lvert \alpha'(s(t)) \rvert \text{d}t = r[/eqn] but I can't find the right way to incorporate this.

Pic related is what I've got so far, but as you can see the red points aren't equally spaced from the black one (I've confirmed this by finding the arc lengths).

[Anonymous No.8831546]

Is it impossible to take a list of edges(described in terms of points) and be able to say whether or not they form a planar graph?

[Anonymous No.8831558]

is "∀" distributive?

by this i mean, for example, is "for all x integer and y real" equivalent to "∀, x integer, y real"?

[Anonymous No.8831564]

>>8831558
nevermind, found the answer
>the universal quantifier distributes over conjunction, but not disjunction, and the existential quantifier distributes over disjunction, but not conjunction.

[Anonymous No.8831567]

During an NSA hiring process, what sort of things do they look for? I'm very pro security, and have gorged in anti NSA propaganda plenty of times, and frequented several illicit substance forums.

Do they check that sort of stuff? They must have more information on applicants than anyone other industry in the world, so I don't see why they wouldn't.

[Anonymous No.8831979]

>>8821825
Is the Hadwiger–Nelson problem the same as the 4 color theorem?

[Anonymous No.8831981]

>>8831979
no

[Anonymous No.8832010]

>>8831979
no. the hadwiger-nelson problem is like if you start with a blank slate and draw it however you like except if you pick a point, then no other point at a distance of 1 should have the same color as the point you picked

[Anonymous No.8832059]

really dumb one here,

how would I go about showing an infinite series of tuples converges?

[Anonymous No.8832264]

>>8821825
Does anybody know how to square each component of a matrix or vector on an hp50g? It would make my life a bit easier

[Anonymous No.8832316]

>>8832059
From the definition of a limit.

The main thing is that you need to choose a metric for the tuples. If they're tuples of reals, any of the common metrics (Euclidean, Manhattan, maximum) should suffice, so just choose whichever one makes the problem easiest (can't tell without knowing how the sequence is defined).

[Anonymous No.8832326]

>>8831546
No. There are a number of linear-time algorithms (linear in the number of vertices, which means linear or better in the number of edges; a graph with N edges has at most 2N vertices, typically fewer).

en.wikipedia.org/wiki/Planarity_testing

[Anonymous No.8832395]

On Part C, I'm getting a range of:

[z - x - b, b] , where b is a real number.

But then I'm stuck at trying to come up with a basis for this set. Help would be appreciated.

[Anonymous No.8832422]

>>8832395
Oh wait,

[1, 0] , [0, 1] would work, wouldn't it.

[Anonymous No.8832801]

[math]
=tex \frac{0.3^(n+1)}{(n+1)!} < 0.001
[/math]

[Anonymous No.8832814]

[math]
((0.3)^(n+1))/(n+1)! < 0.001
[/math]

[Anonymous No.8832819]

[math]
=tex \frac{0.3^{n+1}}{(n+1)!} < 0.001
[/math]

Help me solve for n please.

[Anonymous No.8832860]

>>8832819
compute the expression on the left for n=1. if it's too big, try it for n=2. keep going until you get something less than .001.

[Anonymous No.8833138]

I am currently working through Cal newport's books.
First is the 50/10 rule.
Are there any more interesting tips to get into the good work mindset?

[Anonymous No.8833492]

I don't know where else to ask
i'm trying to boost a case of the Schwarzschild metric but i have no idea what to do now. Can this be simplified further?

[Anonymous No.8833533]

>>8821849
It's a beginning of a proof, not a proof.

>>8821825
Question : why are planets orbiting in the same plane ? I tried to use the principle of "least" action, but since it's true for the action being minimal or maximal, then theoratically the planets could orbit on planes perpendicular to each other, thus minimising their interaction and maximising their action.

[Anonymous No.8833539]

>>8833533
>Question : why are planets orbiting in the same plane ?
They don't necessarily.
>I tried to use the principle of "least" action, but since it's true for the action being minimal or maximal, then theoratically the planets could orbit on planes perpendicular to each other, thus minimising their interaction and maximising their action.
The orbits are usually similar because it's the primary plane of rotation of the star (and the cloud o'crap that the star and planets were formed from). Soak a tennis ball then spin the shit out of it. You'll see clearly that shit flies off in a disc.

[Anonymous No.8833655]

>>8821825
I know this has been mostly math, but Im running an In Situ Hybridization so Ill be sleeping in the lab for the next 18 hours. Anybody with genetics related questions, feel free to leave them laying around.

[Anonymous No.8833666]

why do these two ways of solving [math]y'/(y^2-1)=x[/math] give what look like different answers?
Integral of the form f'(x)/f(x):
[eqn] \frac{1}{2}\int\frac{2y'}{y^2-1}\,\mathrm{d}x=\frac{1}{2}\ln|y^2-1|=\frac{x^2}{2}+C\,. [/eqn]
Using partial fractions:
[eqn] \frac{1}{2}\int \left(\frac{1}{y-1}-\frac{1}{y+1}\right)y'\,\mathrm{d}x=\frac{1}{2}\ln\left|\frac{y-1}{y+1}\right|=\frac{x^2}{2}+C\,. [/eqn]
If i had to guess i'd say the first one is wrong but i dont know why

[Anonymous No.8833669]

>>8833533
They arnt orbiting in the same plane precisely, but they're all subtly pulled toward one another which smooths things out and keeps you from ending up with planets orbiting on perpendicular paths.

[Anonymous No.8833695]

>>8833666
Your substitution in the first integral is invalid.

[eqn]\frac{d}{dx}\left[y^2-1 \right] = 2yy'[/eqn]

[Anonymous No.8833700]

How can nitrogen make 4 bonds in Nitrate? I thought nitrogen only wants 3 electrons.

[Anonymous No.8833730]

>>8821825
if it's any help, for me it helps that

e^0=1 and ln1=0

ie.

e^x=a and ln(a)=x

[Anonymous No.8833762]

Need some help in Natural Deduction.
Come to this but I don't see why E->F is assumed but G is a hypothesis. Why does G need to be justified but E->F can be assumed?

[Anonymous No.8833787]

>>8821825
Log(a^b)=b*Log(a)
Therefore x^a=x --> Log[x^a]=Log[x]--->a*Log[x]=Log[x]--->a=1

>>8833700
>How can nitrogen make 4 bonds in Nitrate? I thought nitrogen only wants 3 electrons.
That is true, but N^+ (not N, but N with one less electron) wants 4 electrons and can do it.

[Anonymous No.8833795]

>>8833762
>G need to be justified
>but E->F can be assumed
It's exactly the other way around.

G can be justified (hyp2)
but E->F needs to be assumed
(I'm guessing you don't have an inference rule of the form F->(E->F))

[Anonymous No.8833829]

>>8833787
Aaah thank you! I am so stupid sometimes :)

[Anonymous No.8833876]

>>8833870

[Anonymous No.8833879]

>>8829465
No, it might be an axiom or follow from one

[Anonymous No.8833934]

>>8833876
see >>8833887

[Anonymous No.8833948]

imagine if you could manufacture two hypothetical nearly identical cubes of any material, preferrably a single-element material,. and with a perfect crystalline structure of squares at right angles, like a grid.
both cubes have the same measurmentes in length and width etc.
except one cube's atoms are shifted exactly one atom's length diagonally in relation to the other cube
if the atoms in the cube were far enough apart, could they simply phase through each other, since the atoms in one don't collide with the other's?

would this be impossible with solids because to allow such movement between the atoms, they would have to be at a distance that end up breaking the bonds between them?

[Anonymous No.8833965]

https://www.youtube.com/watch?v=GOFws_hhZs8&t=58s

How can I simulate these creatures (not the evolution, just the physics)? It seems like just nodes with varying friction coefficient and muscles with varying strength + gravity, yet I can't wrap my head around it. Thanks

[Anonymous No.8833987]

Question on numerical methods for differential equations:
Could someone explain what's going on here?

I assume we have [math] g(x) \approx _a g(a) + g ' (a) (x-a) + \frac{ g''(a) } { 2! } (x-a) + ... [/math]
With [math] g(x) = y'(x) [/math] and [math] a = t_{ n+2 } [/math], but what's x here, is it h? And how do they get the right hand taylor series?
Also I read that just replacing y by a polynomial of degree p and check for which p (1) is exact would also work to find the order of consistency, but it's only exact for p=0 and p=1. Why?

[Anonymous No.8834055]

New thread

>>8834047

[Anonymous No.8834206]

>>8821849
This only shows that if a = 1 then x^a = x, this is the converse of what OP was trying to prove.

[Anonymous No.8834277]

>>8822704
nice

[Anonymous No.8835280]

I'm a drop out and don't have acces to a someone with knowledge on the field,it is a ver basic problem I think. You have one object floating in a fluid in normal conditions. And then you have the same obejct on the same fluid BUT without atmosphere. How the obejcts reacts to this change? Does it keeps floating? What are the reasons for this change? Thanks in advance

[Anonymous No.8835377]

>>8835280
the object will keep floating because it has a lower density than the fluid. the air in the atmosphere has a very low density (lower than the object) and without an atmosphere it would have a density close to zero (still lower than the object), so with or without an atmosphere the object will still float in the fluid but sink in the "air".