/sqt/ - Stupid Questions Thread, Stealing Last OP Edition

If the universe is 13B y/o why is 90B ly in diameter?

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I'll start. Suppose I want to show that p(x) = x^4+1 is irreducible over Q. I have already done this by showing it can't have any roots, and that a factorization into two 2-degree factors can't happen either. However, could I also do this by just saying that if a is a root of p, then equivalently a-1 is a root of q(x) = (x+1)^4+1? This one I can check using Eisenstein's criterion (which could potentially be faster). I don't see why this would be wrong, but I'm tired as frikkin heck, so maybe I should just kms.

How much calculus do I need to know to start learning from an introductory physics book like friedman?

>>8878911
Can anyone find a pair of positive integers a and b such that:

gcd(a,b) > 1
gcd(a+1,b) > 1
gcd(a,b+1) > 1
gcd(a+1,b+1) > 1

It is part of a problem. I have to characterize a family of integers that are a generalized version of what I am describing here but I have failed at even encountering an example.

My intuition is that such numbers must have many many prime factors, if this helps anyone.

>>8878940
You should be at a point where you
1) Understand parametric equations
2) If I gave you any any function, you should be able to find its derivative
3) If I gave you any function, you should be able to find its anti derivative or, if it is a particularly tricky one, at least be able to know what to research to solve it

>>8878964
14 and 20

protip just write some code
for x<1000, y<1000
if gcd(a,b)>1 and ...
print x,y

>>8878987
My man. I have some hope now.

Best way to study derivations? I have a Physics 3 final this week and we are expected to know about 10 derivations (only one will be on test) as well as some other problems. For the last test I just wrote the 5 down and read them over and it seemed to work well enough as we got the easiest one (Bohr radius/velocity/energy)

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how do i do (ii)?
i did part (i) with the ratio test for power series and got |a|<3 but im not sure what to do for the next part. i know that the radius of convergence is less than or equal to the one in (i) but thats it

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It's been a while since I've had to use multivariable calculus and I'm having trouble setting up this double integral (in 1. (a)).

I know 0 < X < 10 - Y < 10 defines the region (domain) of interest, and that if we ignore X we have 0 < 10 - Y < 10. Since 10 - Y < 10 we have that Y > 0, and 0 < 10 - Y implies Y < 10.
Would the region of integration then be (x,y) in R^2 such that x is in (0, 10 - y), y in (0, 10)? and then I would use these as my limits of integration, integrating with respect to y first?

>>8879044
Oh, and would it be easier (and correct) to evaluate a) P( X > Y) as

P( X > Y) = 1 - P(X < Y)?

>>8879031
No, absolute convergence implies convergence (while the reverse is not true). That means the radius of convergence of (ii) might be bigger than the one of (i). I think the answer to both is r=3 though

(Absolute convergence implies convergence since |an| >= an for all an, and if the bigger series converges, so does the smaller one)

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Shouldn't u be in K? And shouldn't the point be to show that u is algebraic over F, not in the fucking field extension????!?!?! belrtvwykiu egrstw

what's /sci/'s opinion on 3blue1brown? based or normie-tier?

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>>8879127
People who make posts like yours are generally gigalow IQ wheelchair-stuck mouthbreathers who struggle with not drowning in their own spit. You won't be doing any topology without people like 3blue1brown making "normie-tier" videos. Keep watching, my dude.

Is there a formula for testing whether or not a number is an integer?

Heard the latest Waking Up podcast with Sam
Harris and Charles Murray recently and it got
me interested in the book The Bell Curve.

Is there a decent updated version of this book
which adds interesting new discovery/research
to complement the book itself in an introduction
chapter or something?

Why did a man of Stephen Jay Gould's caliber get triggered by this book anyway?

>>8879126
>Shouldn't u be in K?
probably

>And shouldn't the point be to show that u is algebraic over F, not in the fucking field extension????!?!?!
probably

>>8879138
> Is there a formula for testing whether or not a number is an integer?
if floor(x)=x, if sin(x*pi)=0... etc.

>>8879143
Gould was a fraud and his book The Mismeasure if Man is literally libel against the dead. Morton's experiments were even reconducted and shown to have no bias. It isn't surprising that Gould, who has clearly demonstrated he places his ideologies over scientific investigation, would be triggered by such research - most especially because the authors make themselves clear on how their findings should affect our public policies. If it were up to Gould, research into such questions would be forbidden, which is a shame: public policy notwithstanding, physical anthropology and modern human evolution are both very interesting.

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How do you become a normie?

EE sophomore, what should i be learning for finding internships?

Do the floor and ceiling functions have any interesting formulas?

>>8879405
Are you going into sophomore year or junior year? It really depends on what courses you can take. With power courses you can easily find open internship positions. I did electromagnetic/RF courses junior year that helped me get a nice internship with relocation package and everything. Just think of companies that you are interested in and see what they do/need and take classes related to that if you can. Also list any class or outside projects that may be relevant on your resume or cover letter.

So I come from a computer science background and need to learn the math required to understand some advanced physics like Schrodinger's Equation (PDEs) and Quantum Chromodynamics (Group Theory). From what I can gather, knowing the mathematics is probably the most important step in understanding these topics, and that's mainly where I'm lacking.
My mathematical understanding stops at Calc II, Bayesian Statistics, and Discrete Mathematics. Are there any self-study guides out there for working my way up to the math needed to delve into these physics topics?
I usually can gain a decent understanding of a topic if presented with proofs and an intuitive explanation in a textbook and some challenging problems to work through, although video courses wouldn't be bad either. I've looked on MIT's opencourseware, but i'm not sure what the best progression of topics should be from my current understanding.

>>8878935
Because space can and does expand much faster than the speed of light.

On https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
in "An example for the matrix version" are the lines "We want to use the equation... in the form". Why? Why we want? And later, in "An example for the equation version" I also saw two version with and without using T and C.

If b is in aH (the coset), is it then fair to say bH is contained in aH?

>>8879647
no

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>>8879648
Aren't they equal, though? b in aH means b = ah_1, so bH = { ah_1*h | h in H }, but h_1 * h, where h goes through all of H is just all of H again, hence bH = { ah | h in H}.

IF YOU SAY I AM WRONG I WILL FUCK YOU UP

>>8879647
>If b is in aH (the coset), is it then fair to say bH is contained in aH?
why would b ∈ aH imply bH ∈ aH, that makes no sense

Suppose that I have two numbers a and b such that their gcd is not 1.

Suppose then I compute
gcd(a,b+1)
gcd(a,b+2)
gcd(a,b+3)
...

Is there some kind of bound on how long I'd have to keep going to find an integer of the form b+c such that gcd(a,b+c) = 1 ?

>>8878968
in other words, put the shit into wolfram alpha bc thats what my calc 3 professor told us to do lmao

>>8879650
>>8879650
>>8879650
>>8879650
FUCKING
RESPOND

>>8879648
>>8879659

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>>8879014
i would say that having the intuition to come upon the solution yourself is 1000x more useful than reading over the derivations and trying to memorize them. recently i've been reading this book called " How To Solve It " by George Polya and he has a list of steps for approaching any problem through heuristic reasoning. mainly though coming up with the solution yourself is immensely more satisfying than regurgitating information. good luck anon

>>8878911
Why do symmetric matrices always have real eigen values?

>>8879031
>>8879044
>>8879054
Please someone help. I got P(X>Y)= 1/2 for the first, which makes sense since f(x, y) is constant, must integrate to 1 over the whole region, and we are concerned with half of it. But I'm stuck on part (b).

I know the marginal distribution of Y is

[math] \int^{\infty}_{-\infty}f(x,y)dx [/math]

but i'm not sure what the limits of integration should be. Will they be x = 0 to x = 10 - y?

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Give me a quick rundown on these topics /sci/

What is the weirdest usage of the modular function in an equation?

>>8879998
which modular function...?

>>8880009
oops, meant the modulo operation.

Basically, wondering if there are any equations that have it mixed in with a ton of other operations. Wondering because the equations I have seen are all really simple.

>>8880037
https://en.wikipedia.org/wiki/Ramanujan%27s_congruences
https://en.wikipedia.org/wiki/Kronecker%27s_congruence
https://en.wikipedia.org/wiki/Kummer%27s_congruence

How hard is it to get into grad school for EE at UIUC, UMich, Berkeley, and other top tier schools that aren't Stanford/MIT/Caltech level but are still great? I have a 3.85 gpa and plan to keep it there. Have research through SMART program labs.

I don't really have a question.

I just wanted to share that I'm going to horribly fail my linear algebra test tomorrow so I don't feel as bad with myself.
When all we do on class is calculate determinants and solve simple eq systems and then the test throws a curveball with shit I can't even fucking read and even less prove, that's where I throw the towel.
If you wonder how I know that, we were given unsolved old tests to practice, and they all share the same characteristic of being marginally more complex than anything we've seen in class.

>tfw you're a brainlet
>no face cause too ashamed

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>>8878911

Greetings /sci/,

was watching video on dimensions and when they explained imaginary numbers they explained it like you see in the first two graphs in the left of the picture.

the way they presented it made me wonder. If you follow the reasoning that [math]\sqrt-1[/math] is just a quarter turn, then what do you call eighth turns, sixteenth turns, and so on until you reach 1 again? what would the algebra look for systems with smaller and smaller turns? what would the algebra look like if you had "continuous" turning? what would a "continuous" imaginary number look like?

not homework or highschoo just a curious NEET.

>>8880127
>what do you call eighth turns, sixteenth turns, and so on until you reach 1 again?
https://en.wikipedia.org/wiki/Root_of_unity

>>8878936
makes sense

>>8879647
Yes it's fair.

Indeed, choose any bh in bH. By hypothesis we have b=ah', for h' in H. Then bh=(ah')h=a(h'h) which is an element of aH.

>>8879648
>>8879650
>>8879659
Kek

>>8880064
Why is this ok?

>>8879586
Replying to myself, but I found a good resource if anyone else is interested
https://hbpms.blogspot.com/

anybody knows a good list or a book with an OK variation of exercises about Vectors in Phyiscs (high school)? I'm getting somewhat stomped by this subject but now I'm motivated to dominate it!

ty in advance

>>8878371
>>8878501
>how do I show that
[eqn]\frac{k^{2}}{k^{3}-1} \geq \frac{1}{k} [/eqn]

but what if k is negative?

>>8880420
Hartog Mechanics maybe?
I rarely check the exercise section, but it's my favorite first book for mechanics.

Walk me through this.

Let's say I predict 8 out of 10 events correctly. Each event has a 50% chance of occurring.

I can get the standard deviation with sqrt(5 * (1 - 0.5)) = 1.581, which means I was ~2 standard deviations off.

How do I get a p-value from there?

>>8880930
k^3 >= k^3 - 1

>>8880930
Multiply both sides with [math]k\cdot(k^3-1)[/math] (this works unless k=0 or k=1, in which case one of the sides of the equation is undefined, otherwise k^4-k is guaranteed to be positive, and therefore the inequality still holds)

Then you get [math]k^3 \ge k^3 - 1 \equiv 0 \ge -1[/math]

>>8878968
I thought not every function has an anti derivate

>>8881233
all continuous functions do

>>8880930
>>8881225
Oh, and that is assuming k is an integer. If k is real, for any k between 0 and 1, the formula does not hold (the multiplication does not work since k^4-k is negative then)

>>8881254
What's the antiderivative of f(x) = abs(x)

>>8881258
x*sqrt(x^2)/2

>>8881258
http://www.wolframalpha.com/input/?i=Integrate%5BAbs%5Bx%5D%5D

Does sound wave have a weight?

>>8881301
Yes

>>8879398
You don't

>>8881312
Elaborate. Please.

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How can you write that awkward stage of definite integration when you found the average integral but haven't plugged and subtracted yet?

You'd have some long formula for y(x), but now you want to signify somehow that that's what the original expression equals to so you can keep the equality chain.

>>8879044
I doubt you need to integrate. Just looking at the problem, note the pdf is constant. P(X>Y) is just area of the domain where X>Y times 1/50. You probably just need to calculate the area of a triangle.

>>8881436
>How can you write that awkward stage of definite integration when you found the average integral but haven't plugged and subtracted yet?
>You'd have some long formula for y(x), but now you want to signify somehow that that's what the original expression equals to so you can keep the equality chain.
Do you mean [math]z(x)|^b_a[/math]?

>>8879126
f(u)= 0, f poly of degree n. Divide by u^n.

>>8881461
So is it gonna be
> x^2 + 5 - x^3 |^b_a

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> Find a median of an ordered sample of the first 9 whole numbers from the range of values of the function
WTF DOES THIS MEAN FFS?!

>>8881482
A median or the median?

>Writing a thesis on stochastic simulation and markov chain monte-carlo
>Every application seems to have a similar deterministic implementation that is often better optimized

Is Monte-Carlo a meme?

>>8881491
I don't fucking know it's not in fucking ENGLISH.

How THE FUCK do I integrate sqrt(-x^2 + 2)? Substitution clearly doesn't fucking work since it's just f(g(x)) without g'(x) factor.

Does anyone think richard feynman looks like the guy that reviews junk food on youtube in suit?

>>8881528
>How THE FUCK do I integrate sqrt(-x^2 + 2)? Substitution clearly doesn't fucking work since it's just f(g(x)) without g'(x) factor.
Substitution CLEARLY WORKS, the problem is that you want a direct answer after substituting. Try
x=Sqrt[2]*Sin[y]
and work until you get something.

>>8881528
Try trig subs

>>8881546
>x=Sqrt[2]*Sin[y]
WTF does sin have to do with it? Where does this come from ffs?

>>8881565
Expand PLEASE.

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WTF IS UP WITH THIS WHOLE ROOT&MINUS SIGN BULLSHIT?! IT'S ALWAYS SOME FUCKERY WITH THESE TWO FFS.

>>8881482
>compute f(0), f(1), ... f(8) (I assume the first 9 whole numbers are 0..8, could also be -4, -3, ... 4)
>take median
>done

>>8881604
Well THAT'S WHAT I FUCKING DID - at least started to, and I get -3 3 5 15, so clearly it's not gonna be 0, which is the answer.

>>8881568
>>>8881546 (You)
> >x=Sqrt[2]*Sin[y]
> WTF does sin have to do with it? Where does this come from ffs?
Trig substitutions are very common. The idea is that, when you have to integrate a function of the square root of ax^2+b it is easier to use the properties of the trig functions.
Sqrt[ax^2+b]=Sqrt[b] Sqrt[(a/b)x^2+b]
substituting x=sqrt[b/a]Sin (y) this becomes
Sqrt[b] Cos(y)
and
dx=sqrt[b/a] Cos(y) dy

Therefore
Sqrt[ax^2+b]dx= (b/sqrt[a]) Cos(y)^2 dy

>>8881582
It's clearly the third answer though

Just try squaring both of them:
[math]-2b\sqrt b = \sqrt{-4b^3}[/math]
Then if you square both sides
[math] 4b^2 * b = -4b^3[/math]

>>8881604
> I assume the first 9 whole numbers are 0..8
That's the thing too, I have no fucking idea what do they mean by this.

>>8881582
\sqrt{-4b^3} = 2ib \sqrt{b}, which is the answer to A

>>8881582
>>8881614
Although the question does not make sense, since the first answer is also valid

>>8881620
That's what I meant. But for some reason the answer it the third ffs

>>8881629
You could write it as [math]\sqrt{-4b^3} = \sqrt4\cdot\sqrt{-b^3} = 2 \cdot \sqrt{-b^3} = -2b\cdot\sqrt{-b}[/math]

>>8881582
>>8881614
>>8881620
>>8881629
>>8881628

I cannot believe how RETARDED people itt are. IT'S UNDER THE ROOT FFS which means b IS NEGATIVE, which means THE ROOT OF b IS NEGATIVE. So the green answer is the only valid one.

Fucking idiots.

>>8881582
>WTF IS UP WITH THIS WHOLE ROOT&MINUS SIGN BULLSHIT?! IT'S ALWAYS SOME FUCKERY WITH THESE TWO FFS.
1. The - inside the square root stays in the square root. If you take it outside you get an "i", you dumbass. That's why your "obvious solution" is wrong.
2. Because the square root they are giving you is supposedly real this means that b<0, therefore sqrt[b^2]=-b instead of b.

There you have it, you only have to think about it for ONE SINGLE MINUTE, instead of sharing your dumbness (like the last 10 times you posted here).

>>8881580
sqrt(2 - x^2) = sqrt(2)sqrt(1 - (x/2)^2)

Turn x/2 into z

so you have

sqrt(2)sqrt(1 - z^2)

Now do the substitution z = sint.

>>8881650
But where the fuck does sin come from? It has nothing to do with powers and shit that we have up to that point.

Differential Equations 1 final Thursday

I freeze up when given an equation to solve.... no idea where to start I know there isnt enough time to try every method (seperation of vars, variation of parameters, etc)

>>8881647
>>8881649
The root of 4 can be -2 and 2, so A is still a valid answer

>>8881649
Nice try except I solved it faster than you did >>8881647

You see because I'm not as slow as you, I post problems here AS I SOLVE THEM MYSELF, so it's parallel processing, which makes it faster. I don't normally ask question unless it seems literally impossible, but I have a crucially important test in less than 3 weeks, so no time to really enjoy the process.

I'm a brainlet, should I cut my losses and go for CS?

Is there some kind of lower bound on how early the first prime gap of size n can occur?

For example. Lets say if I wanted to know in what number the first prime gap of size 500 starts? But I don't know need to know the exact number, just a lower bound.

Like for example: It is trivial to show that there cannot be a prime gap of size n below the integer 2n. But how up can I go? What bounds have been found?

>>8881660
We introduced the sin. This is called a trigonometric substitution.

Remember: sin^2x + cos^2x = 1.

They work like this.

If you see sqrt(1 - x^2), substitute x = sint. Why? Because then,

sqrt(1 - x^2) = sqrt(1 -sin^2t) = sqrt(cos^2t) = cost

If you see sqrt(1 + x^2), substitute x = tant. Why? Because then sqrt(1 + x^2) = sqrt(1 + tan^2t) = sqrt(sec^2t) = sec^t. (you can derive this from the pythagorean identity and just dividing both sides by cos).

This is a pretty standard trick that is usually given an entire unit in calc books like Stewart.

>>8881660
>But where the fuck does sin come from? It has nothing to do with powers and shit that we have up to that point.
The sin comes from its usefullness. Because it's a way to eliminate the square root using the Fundamental Theorem of Trigonometry.
Of course you can use any of the other trig functions and they will do the same job.

Would there be energy without gravity? Does fusion impart energy onto particles in addition to releasing it?

>>8881582
sqrt(-4b^3) = sqrt(4)sqrt(-b^3) = 2sqrt(-b*b^2) = 2(-b)sqrt(-b) (since the -b is under the square root, it means b is actually negative and a square root cannot give you a positive number) = -2bsqrt(-b).

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>>8878911

Was walking and noticed that the image of objects near the horizon line seemed to "fall into" or curve into the horizon line. The effect was more obvious when walking on hills and moving my head up and down by jumping or squatting. I've noticed this effect before but never took the time to actually write it down and try to draw it, and was wondering if there is a name for the effect and or if there is a formula that describes the distortion of the image of the object.

Not a homework question just curious NEET.

>>8881672
https://en.wikipedia.org/wiki/Prime_gap

>>8881689
I already read that wikipedia article and it doesn't talk about what I am asking.

Or did I skim past something important? Please tell.

>>8881482>>8881611

Please help.

>>8881698
If I understood your question and the wikipedia article correctly, you should be able to use the "Lower bounds" formula. Just choose a "c" and increase the "n" in the formula until you get the bound you want.

>>8881611
>>8881713
You know that 0 is the answer? How are whole numbers defined in this context (do they include negative numbers)?

General skewness in statistic is defined as:

[math] g_x = \frac{1}{n} \sum_{i=1}^{n} \frac{(x_i - \bar{x})^3}{s} [/math]

And the adjusted g for samples is defined as:

[math] g_x = \frac{n}{(n-1)(n-2)} \sum_{i=1}^{n} \frac{(x_i - \bar{x})^3}{s} [/math]

Can someone tell me why? I really don't understand why the [math] \frac{1}{n} [/math] has to be changed. Please help

>>8881718
Those bounds talk about infinitely recurring gaps.

I don't care about gaps that happen infinitely often. I care about lower bounds on how early a prime gap of size n can occur. Even if it never occurs, or if it only occurs finitely many times.

[math]\int_0^1 \sqrt{1+x^2}dx[/math] I know this one can be solved by substituting [math]x[/math] for [math]tan[/math] or by integration by parts. Are there other methods for solving this integral? Preferably something concise.

Given a line element
[math] \textup{d}s^2 = -\textup{d}t^2 + \textup{d}r^2 + (b^2+r^2)(\textup{d}\theta^2+\textup{sin}^2 \theta \textup{d} \phi^2) [/math]
How do I calculate the components of [math]T^{\hat{\alpha}\hat{\beta}}[/math], the stress-energy tensor as measured by an observer at rest?

>>8881919
[math]{T_{\mu \nu }} = \frac{{ - 2}}{{\sqrt { - g} }}\frac{\delta }{{\delta {g_{\mu \nu }}}}\left( {\sqrt { - g} {\mathcal{L}_{matter}}} \right)[/math] is the definition.


But it would probably be easier to just plug the metric into EFEs.

>>8880193
It's not. I flunked it as expected.

Shamefur dispray etc.

Is it generally harder to prove equalities, or inequalities?

>>8878911
say i have a helium balloon, 1x11.5x11.5 metres, and it's 20c hot
would this balloon achieve more lift if i heated it up?

Can anybody recommend a good book on electrorefining?

>>8882097
I meant why is prof allowed to do this?

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>>8882367
Tight schedules is my guess. They have to stick a shitton of subjects in ~4 months so I mean, I can't really blame them.

We did see some semi-similar exercises just literally yesterday. Apart from that it was simple matrices and equations.
On the flip side, I'd say the exam was more simple than the same exams on past semesters, but like fuck it was enough.

Around 90% of the notation and terminology I had zero idea what it wanted from me. For example, one goes roughly like
>Suppose this equation with X, b, A and C (can't be bothered to transcribe it here, just picture it has those matrices and some transposes in there), use matrix algebra to find the numeric value of the X matrix that corresponds to the equation
(Might be wrong on some things, I'm rewriting it from memory)
>Assume C equals <some 3x3 matrix> and B <some 1x3 matrix>, determine the resulting X matrix using the given equation
I'd post my exam but it's on tacospeak, so it might be pointless.

Call me a bitch if you want, but this completely killed my spirits. Now I just feel stupid.

>>8881301
The medium sound travels through has weight, but the wave itself is just the transfer of energy, not a mass movement, so no

if someone came up with another law of thermodynamics that was more fundamental than the Zeroth Law, would they call it the Negative First Law of Thermodynamics? Or would they rename all the laws?

>>8882519
they'd call it the -1/12th law

>>8882527
Make sense. Since it's so fundamental it contains all the laws

>>8878911
What is your personal holy grail for exceeding in college?.

I'm in computer science, and I want to beat everyone's asses in terms of tests scores, however. I'm poor and have to work part time. The other students seem to be more talented and I have to work a lot harder to keep pace,

Any study habits, or tips you guys have for a collegefag like myself.

>>8882552
study a lot, go to office hours, suck the TA's dicks

>>8882527
toppest of keks

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No idea what they're asking of. How exactly is this a pattern obtained by translating a 2x2 square with a 2,1 vector?

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>>8882616

>>8881908
Find the Taylor series for that puppy then integrate. Your welcome.

>>8882570
Can't go to office hours
>t. wagecuck

Why do derivatives use [math]dx[/math] instead of something like [math]d_x[/math]?

>>8882624
Wew, ty.

>>8881908
(sqrt(2) + log(1 + sqrt(2)))/2

Can someone solve this for me? I want to go to sleep.

A massive 100 kg object is sitting on a rough surface. You push it with 100 N , and it does not move. You push harder and harder up to 320 N , after which it starts to move at a constant velocity of 3.0 straight m divided by s over a distance of 2.0 m .

The work done by static friction on the object is...

Thanks to those who are willing if any.

>>8882925
Nevermind. I got it.

what the heck does injection surjection and bijection tell you about functions or sets? is it a connection between functions and sets?

Is the empty function constant?

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For the love of G_d I can't do this one, the Jacobian is a bitch to figure out.

I have a question about context free languages.

I know they are closed under Kleene star, but if I have
L=L1+ and L1 is a context free language. Does that mean that L must also be context free? I have a feeling it does, but how would I figure this out or prove it?

Thanks

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>>8882985
A function [math]f\colon X\to Y[/math] is constant if [math]f(x)=f(y)[/math] for all [math]x, y\in X[/math]. Choose [math]X=\emptyset[/math], and suppose [math]f[/math] is not constant. Then there must be [math]x, y\in\emptyset[/math] such that [math]f(x)\neq f(y)[/math], which is obviously not true.

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>>8883103
Yes, that is exactly my point. If it was non-constant, then the empty set would not be empty.

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What should be the reading speed for a reasonably dense, but introductory text?

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To all the algebraists - how does one go about finding the isomophism between these two groups?

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>>8883158
Note that the identity element in the second group is not 1, but [math]\frac{1}{3}[/math]. It follows that we must have a homomorphism map 1 to that, and now, a reasonable guess would be [math]f\colon\mathbb{R}^*\to\mathbb{R}^*[/math], [math]f(x)=\frac{x}{3}[/math]. This is a homomorphism: [math]f(xy)=\frac{xy}{3}=3\cdot\frac{x}{3}\cdot\frac{y}{3}=f(x)*f(y)[/math] for all [math]x, y\in\mathbb{R}^*[/math], and clearly invertible: [math]g\colon\mathbb{R}^*\to\mathbb{R}^*[/math], [math]g(x)=3x[/math], so you have an isomorphism.

>>8883183
Ahhh cheers heaps for that mate, I was trying to fiddle around with f(x)=3x but wasn't getting anywhere. Legend!

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>>8883192
You're welcome. You should always ask yourself what is the identity of the codomain/range group, and how do you map your domain group's identity so that it is sent to that element.

>>8882218
Hot-air balloons work by heating regular air, so yes, but only if helium has enough space to expand.

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Hello /sci/
How do you learn something?
For instance, when learning calc, there is a need to touch on limits. And when doing exercises on limits, there is a need to touch on certain trig functions. And this only applies to calculus.
How do you ensure that you know all material when you start on something more advanced, such as fluid dynamics?

>>8883430
Textbooks usually have a preface in which this is written.

>>8883430
you don't randomly try to learn topics. you ask someone knows what he's doing what a reasonable order is and you follow something along those lines

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How would I do this?

>>8883560
Here's my guess
Get the eigenvalues, and eigenvectors
then
[math]e^A=I+A+\frac{1}{2}A^2... \\
e^{PAP^{-1}}=e^D=I+D+\frac{1}{2}D^2+...=I+P(A+\frac{1}{2}A^2+\frac{1}{3!}A^3+...)P^{-1} \\
[/math]
P is the matrix you make with the eigenvectors,
D is the eigenvalue matrix,
D has to converge because of it's property (D^2 is just each term in D times itself), therefore e^A has to converge since [math]e^{\lambda}[/math] converges.

>>8883602
Doesn't this assume A is diagonalizable?

>>8883611
yep

>>8882650
Because intuitively the derivative of a function f is itself a function itself that returns the instantaneous rate of change of f. Remember rate of change is synonymous with slope, I.e. change in y per change in x. When working with lines in algebra we use delta-y over delta-x as the slope of the line. In calculus we are working with more general graphs / curves where each point graph has a different rate of change than the previous. Hence instead of delta-x we use dx to signify an infinitesimally small change in x.

>>8882650
Notationally, since these elements are usually in fractions, they would be hard to read if they had subscripts. Notation like [math]\partial_{x}[/math] is not uncommon with operators.

>>8878911
What do you guys think about this proof? This is something I dreamt up and quickly scribbled down on paper. I soon forgot the proof until I went back and read it.

Proof that 0.999... = 1

[eqn]S = 0.9999...[/eqn]
Add 0.1111... to both sides
[eqn]S + 0.111... = 1.11111...[/eqn]
Then subtract 0.1111... from both sides
[eqn]S = 1.00000...[/eqn]
And we know S is:
[eqn]0.999... = 1[/eqn]

No multiplication involved. Just adding and subtracting the same number.

>>8883759
>Assume 0.9999... = 1
>Then it follows that 0.9999... = 1
Ok

>>8883759
Well, sure, if you assume that 0.999...+0.111... = 1.111...
But you're either assuming it equals one or using some weird unjustified method of infinite carrying

>>8883560
Hmm. The textbook I'm reading hasn't covered eigenvectors/values, are there any other ways to do it?

>>8883764
Wrong.

>>8883765
>or using some weird unjustified method of infinite carrying

0.9999... + 0.1111... is the same as:

[eqn] \sum_{n=1}^{∞} (\frac{9}{10^n}) + \sum_{n=1}^{∞} (\frac{1}{10^n})[/eqn]
Which is equal to:
[eqn] \sum_{n=1}^{∞} (\frac{10}{10^n}) [/eqn]
Which is equal to:
[eqn]1 + .1 + .01 + 0.001 ... = 1.1111...[/eqn]

>>8883780
Meant to reply to>>8883602

>>8883764
>Assume 0.9999... = 1

Nope. He assume that S = 0.9999..., which is not the same thing as you incorrectly claimed he assumed.

>>8883765
>some weird unjustified method of infinite carrying

No, it's not unjustified. You could define a procedure for infinite carrying that's provably equivalent to the underlying proof that 0.9999... = 1. That's not a common approach, but a good mathematician could set it up to be rigorous enough.

>>8883759
it's not obvious (to a skeptic) that 0.999... + 0.111... = 1.111...

>>8883873
See: >>8883781
I'll add this to the proof.

.99999999999.../.99999999999... = 1
1/1 = 1
coincidence?

>>8883781
>>8883781
Do you think maybe there is subtlety related to pure reliance on the rules of real analysis to treat a transfinite problem? One that, perhaps, can only be analyzed with rigor using the tools of transfinite analysis?

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>>8882616
>>8882616
>>8882616
>>8882616
DOES THIS PATTERN ADMIT ANY ROTATIONS I DON'T THINK SO BUT I NEED TO CHIGGITY CHECK INNIT

>>8881721
Yes and yes. I tried -4 to 4 (the only thing that makes sense aside from 0 to 8) but that doesn't work as well.

Assuming median means average.

>>8884031
Okay, so I googled what median actually was, but IT STILL ISN'T FUCKING 0. It's 3 with -4 to 4.

What's the longest you have stayed up to study?

>>8881650
Do I change dx to dt then? What about boundaries of integration?

WHAT THE FUCK WHO DELETED MY POST FFS?! WTF?! IT SAYS IT'S ME BUT I DIDN'T DELETE IT, WTF?

SOMEONE HAS A PMS?!

>>8881673
Does dx change to dt and what about integration boundaries?

Is it for some reason impossible to isolate x from [math]a=x+\dfrac{b}{x}[/math]?

>>8878911
If I have that
[math] k^2 \equiv 1 \mod n [/math]
Is that only possible if and only if
[math] k \equiv 1 \mod n [/math]?

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ARE THEY FUCKING MORONIC OR IS IT SOME SORT OF CONVENTION WHERE "THE BIGGEST" MEANS "THE SMALLEST" WHEN TALKING ABOUT NEGATIVE NUMBERS? WTF?

>>8884065
Use the quadratic formula.

>>8884065
[math] a=x+\dfrac{b}{x} \iff ax=x^2 +b \iff x^2 - ax +b = 0 [/math]

Because it is a second degree polynomial. If you could isolate it with normal operations, you'd lose information. But you can use the quadratic formula with the last expression to "isolate" x.

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I have already shown that (24)(31) and (1234) is in the group, and that the order of the group is either 8, 12 or 24 (by Lagrange). How would I go on about showing that it's closed at a certain point without having to multiply every element with every other element in the group?

>>8884107
>you'd lose information
Are there cases where "doing it anyway" produces useful results even if they aren't technically right?

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>>8884231
It can be 6 too.

>>8884238
No, it can't, animeposter. With those 2 extra elements, and the identity, its order is at least 7. Idiot

>>8884048
>>8884088
>>8884097
Please help on any. It's very important I got a test very soon.

>>8884233
Yeah. In cases when you luck out and pick the right branch to follow.

>>8883906
What? How do you analyze this problem with transfinite analysis??

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>>8884231
Just view the problem geometrically. You have a square whose corners are numbered 1,2,3,4.

>The element (12)(34) represents a reflection along the green line.
>The element (14)(32) represents a reflection along the blue line.
>The element (24) represents a reflection along the red line.
>The element (13) represents a reflection along the yellow line.

What can you get by combining several of those reflections?

>>8884297
So it's isomorphic to D4, that's quite neat. How would I do it without looking at a square, though? Because currently, I have all the elements of D4 (as a subgroup of S4 that is isomorphic to D4). How would I reason that it actually is closed under the operation on its elements, though?

subject; Kinematics
sub; Elastic collision

If I throw a ball at a wall and the collision is 100% elastic. How much energy does the wall absorb? How much energy does the ball retain?

If I'm in a microgravity environment and throw the ball at the wall I end up moving in a direction opposite the ball. If the ball hits a wall with a 100% elastic collision and I catch it on the rebound did I just double my motion?

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>calculate the fourier transform of X(1/2(x-2)) + X(1/2(x-4)), where X is a top-hat function

what do i do with the 1/2? can't find anything on this.

>>8884425
>>8884421
Sorry, I meant to make this a new thread (in case shitposting gets in the way of people's homework). Here it is: >>8884426

Hello,
bollean algbra, can you simplify that please in showing the details:
not(x).not(y) + y.z + not(x).y.not(z)

Is high bounciness a property that is useful for anything other than destroying household table lamps?

>>8884441
>high bounciness
Of what kind of objects?

What is charge?

>>8884441

Landing rovers on Mars.

>>8884582
do you feel in charge?

>>8884078
no

3^2=1 mod 4

>>8878911
>subject; Kinematics
>sub; Elastic collision
>If I throw a ball at a wall and the collision is 100% elastic. How much energy does the wall absorb? How much energy does the ball retain?
>If I'm in a microgravity environment and throw the ball at the wall I end up moving in a direction opposite the ball. If the ball hits a wall with a 100% elastic collision and I catch it on the rebound did I just double my motion?

???

can anybody help me with soem basic chemistry stuff?

I had an exam on this stuff, but I'm pretty sure I did this wrong.

Say you have a sample of S8 in solid form and its heated up to 25 celsius and the molecule turns to gas.

Then it, the molecule decomposes from S8(g) to S2(g) at 1000 Celsius and at equilibrium, the pressure is .25 atm.

How do you solve this problem? Do you find your initial moles and then solve for their pressure at the highest temperture and make an ice table to find the individual pressures and get the K constant?

Why aren't reciprocals notated as a fraction without a numerator? It saves space and kind of makes sense since you're dividing the empty product by some number.

>>8884846
But the empty product is not a blank space
it's one
which is why we write a one there

>>8884849
The additive identity isn't a blank space either, it's 0, but we don't write negative numbers as 0-1.

>>8884857
You can write reciprocals with inverse notation too, it looks like this [math]5^{-1}[/math]

>>8884870
But if you want to apply that to several values, you need to use parentheses.

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>>8878911
Trying to plot both the contour map of a function and its gradient (The gradient as a quiver plot)
[math]f(x,y) = e^{-y}*cos(x)[/math]

I have the below code in matlab, but the quiver plot is acting weird. (Why is the quiver plot gjoing from zero to well beyond the range? and why are there a lot more arrows than there are points in the meshgrid?)

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Any algebraists here? Is this possible?

>>8884942
Nevermind, solved through the function call
quiver(X, Y, DFDX, DFDY)
(because I wasn't inputting the locations where I wanted the quiver plot)

I should read the documentation more

>>8885116
no

>>8880214
Thank you! Bookmarked

The hands on a clock form a perfectly straight line at 12 o'clock and 6 o'clock. But clearly because the minute hand makes a full circuit every hour, it the hands must make a straight line approximately once an hour. What other times does this happen?

Only really asking about hour and minute hands, but if you can figure out the second hand too go for it.

If i want to relearn calculus, should i use a calculus book like Spivak or go straight into analysis?
If the answer is analysis should i learn topology first?

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>>8885143
you won't relearn calculus by doing analysis

so yes, get an advanced calculus book (i.e. not an introductory book)

>>8885139
angular position of hour hand=360*t (t is measured in hours)

angular position of minute hand=360*60*t

solve

360t=360*60t mod 180

360*59t=0 mod 180

360*59t=n*180

t=n/118 hours, where n is an integer

>>8878911
for the chemist(s) out there

do you know where can I download MOPAC files for different molecules? I need to check a bunch on GABEDIT but can't find a database

Would it be possible to make a Black Hole cease and desist? Like get it to stop working or maybe even brake it?

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>>8885151
> advanced calculus
> not Loomis

>>8884437
I assume you know resolution and that "simplify" means prove SAT/UNSAT

[math]\bar x \bar y + yz + \bar x y \bar z[/math]
Resolution on z: [math]y\cdot \bar x y = y[/math]
[math]\bar x \bar y + \bar x y[/math]
Resolution on y: [math]\bar x\cdot \bar x = \bar x[/math]
[math]\bar x[/math]
So it's satisfiable

explain to me how to efficiently factor these expressions:
64-9x

7y^2-19y-6

x^2-12x-28
i simply cannot find a concrete explanation for the process of factoring

>>8885530
you won't have to do it manually outside of school

one way is to just "see" it if it's a particularly easy one which lets you use the difference of two squares or some other rule

but for example:
http://www.wolframalpha.com/input/?i=Factor%5B7y%5E2-19y-6%5D

there are two roots, one at y=3 and one at y=-2/7 so to factor 7y^2-19y-6
it's (y-3)(7y+2)

similarly, for example y=(x-3)^2 has a double root at x = 3 (when x is 3, y is 0)

so you can solve for the roots to derive the factored expression

>>8885544
thank god, this is the only mathmatical problem which i actively hate to solve. would i be right to assume that it's inefficiency is due to seemingly random prime distribution?

>>8885544
>there are two roots, one at y=3 and one at y=-2/7 so to factor 7y^2-19y-6
>it's (y-3)(7y+2)
I would write 7(y-3)(y-2/7) to totally factorize it, but that's only being nitpicky. .

Anyone know any good way to test for weaknesses in math? Like to see what kind of things to go back to? I'm talking about the subject overall, not just for 1 class. Like some good comprehensive test for the subject as a whole, or several comprehensive tests for each individual course. I'm worried that my classes are for brainlets and that I'm not learning as much as I should, or that my teachers missed valuable information.

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how do you get a sinc filter with the desired cutoff frequency if you have a continuous "signal", effectively making the sampling rate infinite?

>>8885710
Your question is nonsense. The entire concept of discrete signal processing requires a finite sampling rate.

>>8885722
a FIR filter is just multiplying n samples with some function of n, usually which resembles a sinc filter

if i have infinite "samples" as f(t), i can numerically integrate the function multiplied by the "filter"

with the simple box filter the "samples" are linearly weighted so that f(t_start) is multiplied by 1 and f(t_end) is multiplied by 0. this works great with the numerical integration method.

however, the box filter is generally quite bad, so i would need a "filter" that more closely resembles a sinc filter.

so, my question is how this "filter" would be determined if i desire for example a 10 Hz cutoff frequency or a 100 Hz cutoff frequency?

Is moving out when studying at a university near home a good idea?
I've been doing my bachelor's living at home, and every exam season, EVERY SINGLE ONE, someone finds a bunch of distracting things that I "have to" come along to. If I refuse, the arguing that ensues steals as much study time, if not more, as just going along.
I'm absolutely certain that this environment is impacting grades, which are currently mostly Bs.

At this point, it's becoming increasingly difficult to justify still living at home for my masters' degree, as the primary benefit is economic.

I live in a country where student grants can easily let me live alone without having to get a job.

Will moving out positively affect my grades, /sci/?

>>8885844
study at the library

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>>8884432
bump.

>>8885530
Just use p q formula to get the roots

>>8883560
Let | | be the operator norm on your space of matrices (i.e. R^{n^2}). (Note that since its a fin. dim. vector space they are all equivalent)

Then estimate the norm of e^A by using triangle inequality, the factors that it is submultiplicative and continuity of | |. On this way e^{|A|} is an estimate

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Some questions regarding multivariate calculus and limits and continuity:

Why can't you use L'Hospitals Rule when it is indeterminate form? As in 0/0, for example. Why is L'H limited to single variable expressions?

When finding a limit of two variables, sometimes you set y=x. When finding a limit of three variables, is it ok to set y=x=z?

And lastly, what's up with this y=mx nonsense?

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This is a very dumb one.
What's the meaning of these ds?
Just for you to know:
the "n" is a number of molecules and "t" is time (obviously)
S is an adimentional number.

Suppose that I need to find the a pair of numbers x and y such that:
gcd(x,y) > 1
gcd(x+1,y) > 1
gcd(x+2,y) > 1
gcd(x,y+1) > 1
gcd(x+1,y+1) > 1
gcd(x+2,y+1) > 1
gcd(x,y+2) > 1
gcd(x+1,y+2) > 1
gcd(x+2,y+2) > 1

Is there some way to find/describe these numbers? Perhaps using the chinese remainder theorem? Maybe at least get an idea of how big x and y have to be for this to be possible?

>>8886415
that's some terry tao level sht

>>8886335
https://en.wikipedia.org/wiki/Leibniz%27s_notation

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the answer is 3*4! right?

>>8886544
>the answer is 3*4! right?
Aye

>>8878911
I'm too dumb for STEM but I'm even remotely not interested in anything else. Any advice? I was going for comp sci but I'm not even smart enough for that. I'm thinking civil engineering, I hear even brainlets can pull that degree off, even though I think electricity is way cooler.

>>8886415
It's been two hours so I'm bumping for my question here.

Has anyone seen a similar problem?

>>8886415
>>8886697
You can quickly calculate the gcd with the euclidean algorithm. Take x=1308 and y=1274 then

gcd(x,y) = gcd(1274,34) = gcd(34,16) = gcd(16,2) = 2
gcd(x+1,y) = 7
gcd(x+2,y) = 2
gcd(x,y+1) = 3
gcd(x+1,y+1) = 17
gcd(x+2,y+1) = 5
gcd(x,y+2) = 4
gcd(x+1,y+2) = 11
gcd(x+2,y+2) = 2

>>8886724
Yeah, I know a couple of examples.

But I care about how big or how small those numbers have to be.
For example, another pair I found using a computer program is this: (594,3128)

Notice that 594 is much smaller than both of 1308 and 1274.

But how low can I go? Is there a way to at least estimate a strong lower bound?

Let's say there's a space ship traveling at relativistic speed towards a location 100 light years away.

How much time passes for the person on the space ship to reach the destination?
And how long does it take someone on Earth to watch him cover the distance?

When sampling from a posterior probability distribution, am I stupid for picking a uniform prior by default?

Find polynomial p(x) which maps all integers to integers. However, one of the coefficient of p(x) must be 1/7.

>>8886415
Bumping my question here, hoping for at least a hint from someone who knows more. I want even just a hint or direction I could take for establishing a good lower bound for this.

Clarification of what I mean in this problem:
I want to find at least how big a number has to be to be able to have that property.

>>8886890
p(x) = x(x+1)(x+2)(x+3)(x+4)(x+5)(x+6)/7

>>8886913
how'd you figure that out

>>8886919
Clearly 7 has to be able to divide one of the numbers in a sequence of seven numbers: x+0, x+1, ..., x+6 so it divides the product.

>>8886928
oh shit man, I though this problem was a lot harder than it was. thanks

>>8878911

There is exactly one element which has all of the following properties about its nomenclature. Name this element. Don't look it up; think about the conditions and name the element if you are able.

1. The element's symbol, or abbreviation, consists of two letters.
2. The element's symbol has the same first letter as the element's full name, as given in English.
3. The second letter of the element's symbol does not occur in the spelling of the element's full name, as given in English.
4. Distinctions between American English, British English, etc, are immaterial to the language used in 2) and 3).

>>8886941
Copper?

>>8884656
anybody?

>>8884656
>>8887057
Wha is the question?

How important is it to know statics well as a mech engr major?

If I finish this semester without properly having learned it, am I gonna pay for it later?

>>8887070
how to solve that type of problem?

How do I get connections and a job as a Chemistry major?

Please no meme answers

>>8887003

Correct. Well done!

>>8885740
> so, my question is how this "filter" would be determined if i desire for example a 10 Hz cutoff frequency or a 100 Hz cutoff frequency?

Convolving a signal with sinc(f*t) removes all frequencies greater than f.

So for a 10 Hz cut-off, you'd convolve with sinc(10*t) where t is in seconds.

>>8878911
I know next to nothing about physics but I was wondering about gravity today. What little I do remember about my one stage one physics at uni described most physical force as "pushing" forces. Gravity seems to be the opposite though, it literally pulls matter towards it. Is that special in any way?

>>8887127
What information are you given? Initial mass? Pressure of one component? K? Volume?

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Integrate (e^x - 3)^(1/2) dx.

integral-calculator.com shows some double substitution shit and I can't into math anymore

>>8887188
yea they gave me a sample size of S8, which I then used to find the moles of. I'm being asked to find the K constant for that reaction at a 1000 celsius with a pressure of .25 at equilibrium.


Just wanna know how to go on about solving it since there seems to be a change in temperature that's very drastic. if I make an ICE table, how would I go on about my initial pressure for S8? Do I solve for P at the new temperature or is it a delta T ?

is there any way i can prove i have an allergy to hops? as distinguished from a normal hangover?

>>8887406
1. Solve for P at 1273 K
2. Note that 1 mole of S8 produces 4 moles of S2, so you have to find the amounts that produce 0,25 pressure. Solve initial - 3x = 0,25
3. Replace in the expression for Kp

>>8887410
get a blood test

>>8884432
Ended up with:
[math] f¥(x) = 2exp^{2ik} X¥(2k) + 2exp^{-4ik} X¥(2k)[/math]

==>

[math]4exp^{-3ik} * \sqrt{2/pi} * ((sin(k)cos(k))/k)

Not sure, but will go with it.

>>8887647
[math]4exp^{-3ik} * \sqrt{2/pi} * ((sin(k)cos(k))/k) [/math]

>>8887445
ok right on, I'm pretty sure I did that during the exam.

Since you answered this how about this one (which im sure I answered wrong).

Say you have given concentrations of two different molecules(I forget the exact ones), but say that instead of pressure the volume is the one that is changing. Say I go from .750L to 3L and I'm to find the new concentrations once equilibrium is reached.

How do you solve it? You are given the concentration of the two reactans at one volume, but then it asks for the reactants and product once equlibrium is reached.

>>8887698
I will assume this is in aqueous solution. Adding water does not affect the equilibrium consideraly and it can be ignored.
So you can either calculate the concentrations at equilibrium and then applicate the dilution equation or the other way around.

>>8887269
http://www.wolframalpha.com/input/?i=Integrate%5BSqrt%5Be%5Ex+-+3%5D,+x%5D

I want to get far in optimization (in real domain).
Currently I have studied real analysis, convex optimization.
I'm thinking about getting to work on some differential geometry books.
Will they help?

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How the hell would I do this question? I can never seem to get a start on these kinds of questions. Any ideas or tips to get me in the right direction?

>>8887914
I have no idea what this is but you should probably use the fact that L is context-free and the definition of context-free

>>8887140
By sending your CV? Don't wait for the position that you want, just send it. Dow, basf and Bayer are pretty much everywhere, but there are probably smaller local companies near you.
For connection you can ask some professor at uni, or just get a job and start from there.

>>8886423
So we're talking of very very small amounts of molecules over a small amount of time?

>>8887762
Water wasn't added, just the container increased to 3L

>>8888113
or rather, the rate of change at a point in time, how quickly the number of molecules is increasing

https://www.youtube.com/watch?v=rjLJIVoQxz4

Can I get an engineering masters degree in EE (in europe) if I have a BS in applied math?
please respond

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Can someone please explain what is a kernel, a basis, and an image is in linear algebra?

Would really appreciate it, thanks

>>8888469
linear algebra feels like literal bullshit
either that or I haven't understood it quite good
It's just not explained elegant at all compared to calculus

>>8888469
if V is a vector space then a basis for V is a minimal set of vectors such that every vector in V can be written as a finite linear combination of vectors in the set. for example {(1,0,0), (0,1,0), (0,0,1)} is a basis for R^3 since any (x,y,z) in R^3 can be written as x(1,0,0)+y(0,1,0)+z(0,0,1)

let T: V -> W be a linear transformation between vector spaces V and W
then kernel(T)={v in V | T(v)=0}, image(T)={w in W | there exists v in V with T(v)=w}

>>8888469
The kernel of A is the solution set of the equation Ax=0.
The image of A is the set of possible values of Ax.
A basis of a vector space is an linear independent set of vectors that span the space.

>>8888476
This is so true. I have my final next week and I'm screwed. I am using Bretscher, but I don't really like how it explains.

Do you have any recommendations for textbooks or online resources for linear algebra?

>>8888492
Try some of /sci/'s resources in the wiki
I'm currently searching for any handy textbook there

>>8878911
what disease does that man have?

Okay I feel like a retard for asking this but it really grinds my gears.

I am currently having a discussion with my statistics prof about grouped data. Let's suppose you have some classes:

A 0-1499
B 1500-2499
C 2500-3499

Now the width of the class is defined as x_max - x_min. BUT that doesn't make any sense. Let's take class B as an example. Since 1500 isn't part of class A and 2499 isn't part of class C, there are 1000 values in class B. However, the width of the class is 999. How does this make sense? If there are 1000 values in a class, how can the width be anything else than 1000?

I checked countless statistics text books and even wikipedia, and the formula x_max - x_min is mentioned everywhere. Can someone just please tell me why. I really don't get it.

>>8888530
>How does this make sense?
because the width of the class doesn't measure the number of values in the class, it measures the difference between the largest and smallest value in the class

>>8888540
then statfags are retarded. this is an off-by-one error if i've ever seen one

>>8888530
Same with the range. Also defined as X_max - X_min, which also doesn't make any sense.

>>8888546
you can always define some other word to be the number of values if you want...

why do you insist on using width to describe it when it already has it's own meaning?

>>8888540
So how does this make sense? You didn't give any explanation on this. Why would you be interested in the difference, you are clearly trying to find the width, which is obviously 1000.

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>>8888549
this box clearly has width 1

why do you want it to have width 2?

>>8888557
see
>>8888559

>>8888132
But the reactants are in aqueous solution? Or are they gas?

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>>8888559

>>8888559
I guess it makes some sort of sense.. I see how it's meant to function now. Thanks.

Just to make me feel better tho, let's say you have like 5 of these classes with "width" 999. You'd go from 1-5000, yet only have a cumulative width of 5*999 = 4995. It seems to me like some information is lost there.

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>>8888581

>>8888581
What are you trying to say?

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>>8888589
>>8888592
fucking retards. if you're dealing with integers like 0-1499 etc, there are 1500 "slots", so the width would be 1500, not 1499

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>>8888595
>>8888595
>so the width would be 1500, not 1499
but we've already been through this

width is defined as maximum - minimum, so in your example width=1499-0=1499, not 1500

why are you using a different definition? just use a different word

>>8888597
it's not applicable in this case. if it's a spectrum from 0 to 1500, the width is 1500. if you have 1500 different integers at 0.5, 1.5, ... 1499.5, the width is 1500.

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>>8888602
>>8888602
>it's not applicable in this case.
but it is, it's literally just applying the definition of width.

if you want to use a different definition, pick a different word, 1499.5-0.5 is still 1499, not 1500

width has an obvious physical interpretation when looking at the data which you completely ignore for some reason

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>>8888607
kill yourself

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>>8888608
8-1=7 which you got right the first time underneath your boxes, but then put a picture of a guy holding the number 8

why?

>>8888615
the horizontal pixels in your image could be numbered from 0 to 401, but the width is clearly 402, not 401

>>8888615
>a guy holding the number 8

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>>8888619
but we're talking about a definition used in statistics to talk about data, not the pixels in an image

why are you changing the subject?

>>8888623
fuck off, if what you're saying is even true, then statfags are simply retarded

>A 0-1499
>B 1500-2499
>C 2500-3499

clearly the intention was to split the classes at 1500, 2500 and 3500, and the reason they don't do to 0-1500 etc is because the values are numbered by integers and you don't want to repeat 1500 etc

http://tistats.com/definitions/class-width/

AHAHAHAH FUCKING RETARD KILL YOURSELF

>Difference between two consecutive lower class limits
>Difference between two consecutive upper class limits

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>>8888627
>>8888627
>if what you're saying is even true
it is

> then statfags are simply retarded
why?

>>8888630
KILL YOURSELF IT'S NOT EVEN MAX - MIN it's MAX2-MAX1 or MIN2-MIN1

PATHETIC RETARD GET A LIFE FUCKING SHITTY TROLL

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>>8888632
like i said, if you want to use a different definition, use a different word

>>8888639
you're objectively wrong. you're convincing no one. you fail at life.

>>8888648
data points are points brainlet, not intervals, picking arbitrary box sizes doesn't make any sense, i could draw the same picture with boxes of width two and now the width of that class would be 4, this shouldn't depend on your drawing, only on the data values

[math] \int_a^a dx = 0 [/math]

>>8888652
http://tistats.com/definitions/class-width/
>Difference between two consecutive lower class limits
>Difference between two consecutive upper class limits

http://www.math.utah.edu/~anna/Sum12/LessonPlans/Section21.pdf
>The “class width” is the distance between the lower limits of
consecutive classes.

>>8888663

>>8888665
use the fucking catalog next time you dumb faggot
kill yourself

>>8888671
quit reposting threads before they hit the bump limit you cancerous retard and fuck off with your shitty width bait

Can someone please explain special relativity, specifically with reference/inertial frames?

I really don't get the train thought experiment

Any good resources on it?

>>8888828
the speed of light is constant. a guy on the moon will have the same speed of light as you on earth. but you're moving and have a speed relative to each other so if you add his speed to the speed of light it doesn't add up. but special relatively fixes this with time dilation so that everything looks normal to you except if you and the moon guy both have a clock and the guy comes back to earth the clocks will not be synced up.

>>8888530
Note that your classes have a width-1 gap between them, e.g. the range 1499<x<1500 doesn't fall into any class.

If you think of the variables as being reals rather than integers, the definition makes more sense (and "number of values in the class" makes no sense, given that continuous subranges of the reals are uncountably infinite).

>>8889981
http://tistats.com/definitions/class-width/
>Difference between two consecutive lower class limits
>Difference between two consecutive upper class limits

http://www.math.utah.edu/~anna/Sum12/LessonPlans/Section21.pdf
>The “class width” is the distance between the lower limits of
consecutive classes.

>>8878911
hey fags. How do you call the point in history where the power granted by science to individuals will be tremendously important? It was supposed to happen in 2030, I don't remember well.

>>8890278
the singularity?

if you have a 10 pixel wide image, you can number the pixels from 0 to 9, but the width is still 10

>>8890287
Thank you, English is not my first language, and I have a hard time remembering some words and expressions at times.

>>8885844
You can always use good ole excuses
"something came up in x, have to go" or "sorry, I have other plans for that day"

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Why would we expect the clock to run slower?

Can someone explain this please?

>>8890368
if you would add the ISS speed (from your point of view) to the speed of light, it's greater than the speed of light, but the speed of light is the max, so time would be slowed down (from your point of view) so that from the ISS point of view they can still have the correct speed of light

>>8890382
And a clock on Earth will appear faster from observor on ISS?

And clock on ISS just looks normal to person on ISS, correct?

>>8890396
>And a clock on Earth will appear faster from observor on ISS?
slower. from the earth point of view, you are stationary and ISS is moving. from the ISS point of view, they are stationary and earth is moving. if you travel from earth to the ISS, your clock will appear to have gone slower (from the ISS point of view), the same way if someone travels from the ISS to the earth, the clock will appear to have gone slower (from the earth point of view).

>And clock on ISS just looks normal to person on ISS, correct?
correct

>>8890436
>>8888663