/sqt/ - Stupid Questions Thread: Solar Flux Edition

>>8648925
collision with a sun of ice, of course

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in this video game, a man cuts through though the head of someone with a shovel

is this even possible given that the victim is standing up? I would think he would at worst just be dented, but mostly pushed

>>8648925
>>8648947
if your ice sun would move fast enough to disperse sun's plasma fusion would stop, but any fast moving massive objest would do


now question to any possible medfags:

my head starts hurting when I try to fap (kind of dull pain all around the head), is my blood pressure too high or too low?

What does it mean when I'm solving a nonlinear ODE and the constant is transcendental?

>>8648925
>Are there any conditions or mechanisms under which a large star like the sun could suddenly extinguish?
Small stars could if they burn off enough mass to no longer be able to sustain fusion but no, large stars don't just stop burning unless something happens to them like being ripped apart by a black hole

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Pic related is some calculations on a concrete mix. How is the adjusted weight of water being calculated here?

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I haven't taken multivariable calculus in a long time and forgot the chain rule when the derivative isn't applied to a function.

In pic related, can someone tell me why [math]\frac{\partial }{\partial z} = \frac{\partial x}{\partial z}\frac{\partial }{\partial x}=\frac{1}{\alpha}\frac{\partial }{\partial x} [/math]

given that z=αx.

>>8648925
What is my trig class asking for when it asks me,
"Write the angle as a sum or difference involving π. example - 5π/6 = π − π/6"

8π/9

How do I think of this?

>>8650403
Just decompose the angle into two different angles. You can do it any way you want. For example 8π/9=3π/9 + 5π/9 = π/3 + 5π/9. You can do the same for differences.

>>8650403
This is what they expect you to answer:

[math]\frac{8\pi}{9} = \pi - \frac{\pi}{9}[/math]

>>8650413
Thank you, this helped me to understand it a litte better, although it didn't accept me just splitting it in half.

>>8650515

Thanks, this was the correct answer. Why are they asking this? what does it pertain to down the road?

>>8650554
You can use sine and cosine's sum and difference formulas to simplify some things.

http://www.algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigSumDifference.xml

>>8650554
it gets you used to thinking of and handling angles in terms of radians, pi is half a circle, or 180º, pi/6 is 30º, etc.

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I'm 28 years old who just transferred to a university last semester and I can't seem to like any of the professors at the school. I am poor who had shitty teachers that gave me a bad impression of them as a child. When I see PhD holders teach, I have no respect for them. I just feel disgust when I see them. I remember when one of them tried to help me out and I just nodded then never interacted with him ever again. Is this fixable?

>>8648925
why is 2 > 1?

>>8650750
Because blue isn't peaches.

>>8650753
oh

why does the limit of cos(x) as x approaches a = cos[limit of x as x approaches a]?

>>8650769
Because 2>1

>>8650771
don't do that

>>8650771
...but WHY

>>8650769
since cosine is continuous, lim_{x to a} cos(x) =cos(a)

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Why we always write integrals as [eqn]\int_{-\infty}^{\infty} f(x) dx[/eqn]
except in quantum mechanics where everyone writes
[eqn]\int_{-\infty}^{\infty}dx f(x)[/eqn]

>>8650795
physicists are mathlets

>>8650792
Because 1 just isn't that great, okay?

>>8650795

I asked one of my professors about this (math phys guy). He basically told me to fuck off and start asking real questions.

Anyways, here's a reasonable answer:

http://math.stackexchange.com/questions/609389/why-do-some-people-place-the-differential-at-the-beginning-of-their-integral

>>8650795
because the integrands can get very long and complicated and it is nice to keep track of what you are integrating over at the front

>>8650376

What part are you iffy on? Is it how you get partial x from partial z... or the constant alpha value?

>>8650793

does it apply to every continuous function then?

>>8650984
thats the definition of continuous
https://en.wikipedia.org/wiki/Continuous_function#Definition_in_terms_of_limits_of_functions

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If I have two non-commuting operators A and B, can I write

ln(AB)=ln(A)+ln(B)

and if not, what should I write instead?

Why do UK science PhDs require you to write a project proposal when applying?

The supervisors already have the project finalised and funded, all they want is students to help undertake the research. Why would an undergraduate or even a masters graduate be making a proposal for it?

Every one I've seen is like that. Is it just an HR copy paste from the humanities admin?

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Is it likely that there's been a species more advanced than ours somewhere in the universe?

>>8651242
Has been? In the entire universe?
Probably. The universe is a big place and it's been around for a long time.
However the vast majority of it is simply so far away that it will never matter to us, and it would be extraordinary if we somehow ended up lining up just right time-wise. The amount of time that humanity has known about the wider universe is very short when compared to the amount of time that the universe has been around.

>>8651242
Yes. Almost surely, since the universe is infinite.

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Can anyone help me understand why this common emitter amplifier isn't working?

I thought replacing Re with a current source, in this case a current mirror, was supposed to improve linearity or something but now I don't get any output.

Also, how do I calculate input impedance with a current mirror instead of emitter resistor? The Zin = β*Re formula doesn't work for that.

DIY is too slow.

Prove that there exist a bijection between any 2 bases of a vector space (infinite dimensional)
pro-tip: Zorn's lemma
>hard-mode: no cantor-bernstein arguments

>>8651299
Replacing emitter resistance with a current mirror would allow you to have the same collector current but your amplifier gain changes. Think about how your small-signal model with emitter resistance is set up. (Vin = rpi+(beta+1)Re, Vout= R1//R3) However with a current mirror, to find a similar gain, you would have to set up the combination small signal models for all three BJTs in one circuit and then calculate the overall gain of the circuit and compensate the forward current gains of your current mirror for a similar theoretical result. Furthermore, you can treat your theoretical overall gain as a value say Am and then with the assumption that all capacitors give poles to the magnitude and phase response independently, you can have Am*(Pole1), Am*(Pole2), . . . , Am*(PoleN) ,etc.
P.S. you could also have the current mirror be AC coupled with inductors too.
This is all I could see from looking at your circuit without breaking out pencil and paper for actual algebra. Good luck m8

>>8650376
Chain rule.

>>8651300
skolem lowenheim iirc

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>>8651293
>>8651290
But none advanced enough to leave even a trace of their existence for us to see?

>>8651446
Interesting..
How about a proof that doesn't use logic?

Ok I'm feeling dumb:
I have a function [math]u(\bar r)[/math] with spherical symmetry (for example the coulomb potential), and I need to calculate its Fourier transform [math]\hat u(\bar r)[/math].
Now, that wouldn't be too hard normally, but on my book it says that we can use the spherical symmetry to make the following approximation:
[eqn]
\hat u(\bar r) = \hat u(0) + o(k^2) = \dfrac{1}{V} \int u(\bar r) d\bar r + o(k^2)
[/eqn]
how?

>>8651573
>its Fourier transform [math] \hat u(\bar x) [/math]
it's [math] \hat u(\bar k) [/math] obviously

>>8651540
top lel

What the fuck does it mean when they say a protein is soluble? What exactly is disassociating?

>>8650750
because 2 contains 1
two 1's, to be precise

>>8651573
u(x) = u(-x) -> xu(x) = - (-x)u(-x)
First order terms do not exist e^x = 1 + x + ..

From an olympiad style test I took today :
[math]p,q,r[/math] are prime numbers
[math]p<q<r<q+p^{4}[/math] and [math]pq^{2} = r^{2} +1[/math]
find with proof all values of [math]p,q [/math] and [math]r[/math]
Anyone know how to do this? I'm having a brainfart

I'm having trouble with this question.
Show
[eqn]
\int_V \nabla \times \mathbf{u} \, dV = \oint_S \hat{\mathbf{n}} \times \mathbf{u} \, dS.
[/eqn]
So far I've got

The divergence theorem states
[eqn]
\int_V \nabla \cdot \mathbf{a} \, dV = \oint_S \mathbf{u} \cdot \hat{\mathbf{n}} \, dS.
[/eqn]
Hence, letting [math]\mathbf{a} = \mathbf{u} \times \mathbf{c}[/math], where [math]\mathbf{c}[/math] is a constant vector, this becomes
[eqn]
\int_V \mathbf{c} \cdot( \nabla \times \mathbf{u}) \, dV = \oint_S (\mathbf{u} \times \mathbf{c}) \cdot \hat{\mathbf{n}} \, dS,
[/eqn]
using [math]\nabla \cdot (\mathbf{a} \times \mathbf{b}) = \mathbf{b} \cdot (\nabla \times \mathbf{a}) - \mathbf{a} \cdot (\nabla \times \mathbf{b})[/math]. \\
Since [math] (\mathbf{u} \times \mathbf{c}) \cdot \hat{\mathbf{n}} = \mathbf{c} \cdot (\hat{\mathbf{n}} \times \mathbf{u}) - \mathbf{u} \cdot (\hat{\mathbf{n}} \times \mathbf{c}) [/math], this becomes
[eqn]
\mathbf{c} \cdot \int_V \nabla \times \mathbf{u} \, dV = \mathrm{c} \cdot \oint_S \hat{\mathbf{n}} \times \mathbf{u} \, dS - \oint_S \mathrm{u} \cdot \hat{\mathbf{n}} \times \mathbf{c} \, dS.
[/eqn]
So basically I'm not sure where to go from here or how to get rid of the [math]\oint_S \mathrm{u} \cdot \hat{\mathbf{n}} \times \mathbf{c} \, dS[/math] term. Anyone know what I'm missing?

>>8651771
evaluate the inequality with every possible combination of three unique primes

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Is it actually possible to teach yourself the mathematics an undergraduate would learn? I really want to, but it seems like a hopeless endeavor, because I would inevitably miss some crucial things or misunderstand something while believing I understand it, etc. since I'm not getting feedback.

>>8650795
wait
since when do you always write integrals as
[math]\int_{-\infty}^{\infty} f(x) dx[/math]?
Physicists use
[math]\int_{-\infty}^{\infty}dx f(x)[/math]
all the time, not just for qm.

>>8651787
yes, it'll probably be a bit harder though.

>>8650812
Getting partial x from partial z. I thought it was improper to treat differentials as fractions.

I conducted an experiment where I measured A. cepa growth over time under different conditions. I aimed to determine to what extent caffeine concentration affected growth over time.

I have 8 data sets, one for each caffeine level (0 - 700 mg) over a period of 1 week. (7 points per data set.) What test should I use? I've considered using regression, but I'm not sure how I would be able to implement the over time aspect. I think that the test(s) should be able to give specific conclusions regarding:

>whether there is a statistically significant difference in growth patterns between the different conditions. This is perhaps the most important.
>an equation modeling growth (I feel like regression should work here, but I'm not sure how I'd do with with 3 dimensions--caffeine level, growth, and time)
>an equation modeling rate of growth (perhaps I could just take the derivative of the growth-equation, assuming that the growth equation isn't linear)

>>8651802
>I thought it was improper to treat differentials as fractions.
dude this is physics not maths, chill.

>>8651762
oh, that was pretty obvious, thanks!

>>8648925
Im in my first real analysis course and we just introduced the standard rigorous definition of a sequence and a convergent sequence. I had no difficulty proving the the limit of a sum of conv. sequences is the sums but im having difficulty with showing the same for multiplication. Anyone have a hint? I don't want someone else to do all the work for me,

>>8648947
That would only fuel the sun.

The sun is fueled by fusion and adding water (hydrogen) to it would only make it hotter and bigger. You can't extinguish nuclear fusion by throwing water at it.

Are finance majors respected or on the same level as women's studies?

If climate change is real then why are there still apes?
CHECKM8 ATHEISTS

>>8652282
its kind of a novelty trick if you havent seen it before, you want to add 0 in a clever way inside your absolute value

spoiler: http://www.planetmath.org/proofoflimitruleofproduct

>>8652473
most of (corporate) finance can be learned in a month or so of concentrated study (training programs at investmnent banks for ex.)

First time using TeX Live, is it supposed to take and hour+ to install?

>>8650554
In every class they teach more or less the same angle identities, check which ones you were taught ( sin 30 60 90 etc are the most common) and split the angles to these familiar identities to make them easier to calculate

>>8652904
thanks anon, figured it out.

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Geology:

I remember in school learning about stratification. And how it was not the same as if you were take a bucket of sand and pebbles there would be a somewhat smooth transition between sand at the bottom to pebbles on top. I though this was called a gradient, but I can not find ANYTHING when I google gradient and geology and stratification and stuff.

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I don't understand why the 4 is factored out, why not just the whole 32?

>>8653174
Because you end up with a 1/8th later in the proof

>>8653178
That doesn't really make any sense but I figured out if I divide the original constant by whatever power the -x is to I get the answer to the problem.

I'm probably gonna fail calc 2 ;_;

>>8653174
derivative of exp(-x^8) is -8x^7exp(-x^8). So thats why you leave the 8 in to make substitution easier.

>>8653179
Read up on integration by substition. Also pay attention in class. Calc 2 is not hard but you have to exert at least some amount of effort. I'm rooting for you, f a m.

Can anyone explain to me the concept of connected or not connected?
The definition given by the professor says "A region in space is said to be connected if any pts "A" and "B" in the region "D" can be joined by a curve that lies entirely in "D"".
I've tried reading that multiple times and still can't grasp the concept of "connectection"
Like, what exactly does "connected" mean? What does it entitle?

>>8650750
relation >= on N is defined as follows

a is in relation with b (a>=b) if and only if there exists c from N such that b+c=a

you can prove that this relation is reflexive, antisymetric and transitive yourself.

>let c = 1, then 2 = 1+1, therefore 2 >=1

then you can define a relation > as follows

a and b are in relation (a>b) if and only if a>=b and a =/= b


> 2 >= 1 and 2 =/= 1 (trivial) therefore 2 > 1

QED

>>8653326
när penis möter vagina

tappa vikt

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>>8653326
It means pretty much what it says. It's helpful to draw pictures when trying to understand definitions.

The left hand side in pic related has a region D that we would consider connected. Take any two points in that region and you will be able to connect them with a curve that's entirely in D.

The right side has a region D that is not connected. The two points shown can be joined by a curve, but that curve can never lie entirely in D. It must go outside of D. So the region isn't connected.

Of course, we're only drawing pictures of 2-dimensional space, but the same idea generalizes to 3-dimensional, 4-dimensional, etc. space.

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>>8653339
>Take any two points in that region and you will be able to connect them with a curve that's entirely in D.

Oh alright, that certainly clarifies it. Thanks.

I was kind of lost on what the purpose of establishing if the points are connected or not. but the figure helped me understand better.

Could we terraform the Sahara with ice asteroids? Like if we rigged them up with rockets to slow their re-entry so they didn't just melt

>>8653515
The sahara isn't hot just because its a desert you know, the ice asteroids will just end up melting once they land and the water will boil away. It's the sun that fucks up the region

>>8653515
finally, a question worthy of this thread

why humans' bellybuttons are so easy to spot while it is so hard to see other mammals' bellybuttons? I heard other animals have the mom chew off the umbilical cords and then the baby's bellybutton will just become a flat and small scar, but why is it that humans' bellybuttons aren't flat too?

Hello, why we say closed and bounded interval ?
If an interval is closes, he is necessarily bounded, no ?

>>8653635
[0, infinity) is closed

>>8653635
Bounded means that there is a finite intervall that includes that intervall.
eg. [2,3] is included in [1,4] so it is bounded.

Closed means all point are really inside the intervall.
eg. [1,2] means that all number that are greater then 1 and smaler then 2 are in the intervall, including 1 and 2.
The open intervall (1,2) means that all number that are greater then 1 and smaler then 2 are in the intervall, not including 1 and 2.

There is no speciall relation between bounded and closed.

There are intervalls which are closed and un/bounded, un/bounded and open and even intervalls which are closed and open.

>>8653530
>It's the atmospheric circulation that fucks up the region
FTFY
subtropical ridge (high pressure bands at ~25-30 N and S) causes extremely low precipitation, producing bands of deserts at those latitudes

>>8653646
But not bounded*

>>8648925
Some group theory stuff:
First problem:
I kinda have a problem comparing groups like the rubik's group to groups like integers.
Things like the Rubik's cube group, seem to be a set of transformations on a set of states, whereas the integers are an operation with two inputs.
The way I resolve this in my head, is to define the integer group, to be the set of integers as well as the set of functions [math] \{x+n\in \mathbb{Z} \to \mathbb{Z} : n \in \mathbb{Z}[spoiler][/spoiler]\} [/math]...if that makes sense.
Is this the general sense?
None of my texts seems to go too deep into it.

But what does associativity mean in this case?
That [math] f \circ g [/math] is in the set of transformations?
Does this form another group with [math] \circ [/math] being the operator?

Question 2:
Generators
Soo my text says that [math] 1 [/math] generates the integers.
Does this mean you start from a certain value and keep applying this transformation to get the entire set? Or you can start from any value? Or are these equivalent?

Moving on from that, does the positive integers generate the positive rationals group (under multiplication)?
And finally. wth are the generators for the real groups under addition and multiplication (sans zero ofc)?

Help me with this stastic question please

A power plant has eight turbines, these functionsare independently. During the winter, it's considered that the
probability to be 0.10 to a turbine a random day does not work. Calculate
the probability that a randomly selected day more than three turbines stops working

>>8653903
>whereas the integers are an operation with two inputs.
its really just one input. an integer transforms the rest of the integers like how an element of the rubik's group transforms the rubik's cube

>But what does associativity mean in this case?
means (ab)c=a(bc) for all a,b,c, in the group

>That f∘g is in the set of transformations?
no this is just the set you're considering being 'closed under the group operation'

>Does this mean you start from a certain value and keep applying this transformation to get the entire set? Or you can start from any value? Or are these equivalent?
it means for any integer n you can write it as some (specifically n) applications of the group element 1

>Moving on from that, does the positive integers generate the positive rationals group (under multiplication)?
yes since any positive rational a/b is equal to ab^-1 in the group

>And finally. wth are the generators for the real groups under addition and multiplication (sans zero ofc)?
you need infinitely many generators under addition

>>8653977
> means (ab)c=a(bc) for all a,b,c, in the group
yeah it for some multiplication operation.
What does it mean for a set of transformations, that go along with a set?

> no this is just the set you're considering being 'closed under the group operation'
I meant [math] \circ [/math] being the composition of two of these transformations.

> you need infinitely many generators under addition
On terminology:
infinitely many generators or the generator has an infinite cardinality?

Also what are the generators? how do you describe them for say, the Cauchy completion of the rationals?

Hey mathfags, can you redpill me on the Collatz Conjecture?

What does it mean? Is it some hidden pattern in numbers? Why can't we crack it?

>>8649962
not a medfag, but probably high. when you get horny it raises, so if your head starts hurting it was probably already high

but better go get it measured faggot than asking on here faggot?

Any other sites to find articles/books other than sci-hub and bookzz.org? I need an article (book?) that isn't on there, I have its doi.

>>8654068
>Why can't we crack it?
it's sort of like the riemann hypothesis, easy to state but mathematicians just dont have the technology/proof techniques to get at the answer

>>8654081
>>8654081
>it's sort of like the riemann hypothesis

Not really, RH is much harder to state. But ironically we have much better tools for it.

>tfw no field with one element

>>8654090
maybe relatively harder than the collatz function, but RH is certainly not hard to state... the zeta function is not hard to define and its just asking when that function is zero

i'd consider something like https://en.wikipedia.org/wiki/Norm_residue_isomorphism_theorem to be hard to state since you need to know a ton of high-level mathematics before having any chance of understanding it

>>8648925
Trying to pick up some basic set theory out of Kaplanski's book here and my brainlet brain is stumped.

I've tried working it from forwards and backwards but I'm not sure where to go from here. It's also very likely that I'm making a mistake with interchanging a union and an intersection somewhere because I'm kind of prone to doing that. Here's what I have so far.

Forwards:
[math]A(B+C)=A\cap[(B-C)\cup(C-B)][/math]
[math]=A\cap[(B\cap C')\cup(C\cap B')][/math]
[math]=[A\cap(B\cap C')]\cup[A\cap(C\cap B')][/math]
This reduces to [math]A(B-C)\cupA(C-B)[/math] but that's clearly not where I need to go.

Backwards:
[math]AB+AC=[(A\cap B)-(A\cap C)]\cup[(A\cap C)]\cup[(A\cap C)-(A\cap B)][/math]
[math]=[(A\cap B)\cap(A\cap C)']\cup[(A\cap C)\cap(A\cap B)'][/math]
[math]=[(A\cap B)\cap(A'\cup C')]\cup[(A\cap C)\cap(A'\cup B')][/math]
And I'm stuck there. Any help?

>>8654149
what is + here?

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>>8654155
Whoops forgot pic

>>8654155
The symmetric difference. They're just using that symbol for it. Doesn't have anything to do with addition.

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Why do we set x = t in problems like this?

>>8654149
>>8654158
Also goddamit I hate Tex.
>[math]A(B+C)=A\cap[(B-C)\cup(C-B)][/math] [math]=A\cap[(B\cap C')\cup(C\cap B')][/math]
should be
[math]A(B+C)=A\cap[(B-C)\cup(C-B)][/math]
[math]=A\cap[(B\cap C')\cup(C\cap B')][/math]
>[math]A(B-C)\cupA(C-B)[/math]
should be
[math]A(B-C)\cup A(C-B)[/math]

>>8654166
Fuck me, I'm just gonna stop trying.

>>8654158
you can mess around with the set notation but it should be sort of clear:

A(B+C)=A cap (B-C U C-B) = elements that are in A and are in exactly one of B and C


AB+AC=(A cap B)+(A cap C)=(A cap B-A cap C) U (A cap C-A cap B) = elements in exactly one of (A cap B) or (A cap C)= elements in A and in one of B and C

>>8654175
Yeah I was the guy that posted the problem, just replied to the other guy who was asking what it meant.

I'm having a really off day today lol.

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I'm gonna read David Bohm. I want to go from his 'metaphysics' towards the hard physics.

Would you help me build the appropriate reading list?

>>8651708
It's not necessarily like a salt. Alcohol is soluble in water because of the hydrogen bonding and so are proteins.

I Don't get what the remainder of a taylor polynominal is...

How does it even work? My book has the formula which I off course can put numbers into but I don't get how to get bounds for the error of a function out of it

>>8651202
they use those to steal new ideas

>>8653622
apes have visible navels, too.
my first guess is that animals with longer gestation periods have bigger navels.

Can anyone help me out whats the equation im looking for?

Theres a liquid in a closed tank with a thin pipe connected to it. The viscosity of the liquid is so great and the pipe is so thin that normally the liquid wont enter the pipe. Whats an equation that can tell me how far the liquid travels in the pipe at a given pressure?

What's the proper way to learn differential equations? Seems like most books are just a list of arbitrary techniques. Is this just how things are?

>>8651202
>>8654265
>Why do UK science PhDs require you to write a project proposal when applying?
>they use those to steal new ideas
But that still doesn't make sense. 99% to come up with new ideas in a field, especially specialisms, you need to have decades of experience to even have the potential to produce something new rather than simply retread.

Why is the tension on two objects in Atwoods machine equal to each other? Im a math student just getting in to physics, feeling very retarded

>>8654398
when they offer the position, they already have one or three candidates or so in mind. someone they know from a congress, someone who was recommended to them by a collaborator. someone who is that advanced. and that's how they sieve out the nobodies, the extra-murals. without getting into legal troubles.

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If I say two functions/graphs intersect tangentically, is that another way of saying that they have the same derivative?

>>8654347
Yes? What the fuck did you expect? Lmao

>>8648925
what are the best studying habits?

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I feel really stupid as a chem major compared to people who study physics/math/engineer and I think it's because my chem department doesn't require us to take any math classes past calc 3. What other maths should I study if I want to be on the same footing as more mathematically rigorous degrees? Is pic related just a meme? Is it a decent competency checklist for STEM people?

What can we say about the unobservable universe?

I know why it's unobservable, but I'm wondering whether the current standard model has any guesses about it. Can we surmise based on the observable universe how much matter/spacetime there is, all-in-all? Are there any weird theories about the universe potentially being infinite, even within the standard Big Bang model?

What is the standard answer for what would happen if you went "from one side of the universe to the other"? Someone once told me that if the universe has a spherical topography, you would end up where you started, or something like that. What if it has an open/closed topography? Am I totally wrong about this?

>>8654714
>What can we say about the unobservable universe?

Nothing.

>>8654163
Typically in a situation like that it's because you're trying to describe the position of something as a function of time rather than its horizontal displacement

>>8654249
>How does it even work? My book has the formula which I off course can put numbers into but I don't get how to get bounds for the error of a function out of it
https://en.wikipedia.org/wiki/Taylor's_theorem#Estimates_for_the_remainder

>>8654502
it means their derivatives have the same value where the functions intersect tangentially, but not necessarily anywhere else

>>8654695
>Is pic related just a meme?
yes

>>8651523
You think humans are going to leave a significant enough imprint on the universe that an alien race billions of years in the future and billions of galaxies away are going to know we existed?

>>8653256
it's an online class at community college so there is no class, just assignments

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I really don't have any idea what I'm doing here.

Is this sort of right at least ?

>>8655387
you second line is wrong. the implication is false.
it should be
[eqn]\implies x \in (B \cap C)[/eqn]
Same with your second line, it makes little sense.
I dont know what the third line means.
the 4th, 5th and 6th are true although they arent very usefull.

You are proving the law for sets which have 1 element.

I dont know how exactly you were told to proove it but the usuall aproach is to write down the definitions.

And then realize that:
[eqn]x \in A\cup(B \cap C)[/eqn]means x is an a or (x is in B and C)
[eqn]x \in A \vee (x \in B \wedge x\in C)[/eqn] you can easily prove tough a truthtable that this is equal too
[eqn](x \in A \vee x \in B) \wedge (x \in A \vee x\in C)[/eqn]

If you write down the definitions of both sides of your equation you will see that this what you needed for the proof.

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>>8655409
is this better ?

I've never done anything with proofs before at all.

>>8655429
No.

It has the same problem, you are assuming that the sets have all 1 element, this is not what you are supposed to proove.

As I said, I dont know how you are suppoosed to prove it but the method i described in my last post is a pretty standard way.


Write down the definitions of both sides of your equality. Without that you dont have any chance.
After that use the formular of mathematical logic I descibed above to show that the definition of the left part of the equality is indeed the definition of the right part of the equality.


(As a side note : [eqn]\{x\}\cap\{y\}=\emptyset \neq \{\emptyset \}[/eqn] )

>>8655386
Damn that's pretty retarded f a m.

In that case I'd suggest supplementing the class with some kind of free online calculus course like Khan Academy or MIT OCW. That is, if you really want to understand what you're doing.

>>8654480
Professors aren't like that. They are good people.

>>8648925
Can somebody explain to me the proof that we can approximate measurable functions with simple functions? I can understand it, but it's pretty hard to imagine.

Does a star's diameter or radius have something to do with the max wavelength of their radiation?

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How do I prove this?

>>8655666
its not true

>>8655676
I'm trying to solve y' + 2y = delta(x) but I can't find a good solution

testing latex

[math]\textrm{nigger}[/math]

>>8655706
there is a button to test it.

you fucking [math]negro[/math]

>>8655723

where, [math]\mathrm{faggot?}[/math]

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>>8655724

>>8655727
o

>>8655666
it would help if you knew how to take a fucking photo

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>>8648925

Can somebody post the debunked version please?

>>8655806
who are more annoying pseudoscientists, the evolution fearmongerers or the climate change fearmongerers?

>>8655809

You anon. You are more annoying.

>>8655806
Can someone post the tl;dr version please?

>>8655823
>evolution be tru
>no it dont
>yes it do
>no
>(o no he destroying me!)

>>8655809
well the one pretty much just lives in rural alabama and oklahoma and the other just got put in charge of the EPA, department of energy and most of the federal government so

>>8655838
kek, that was actually pretty funny

why are there literally no good quality video lectures of topology? The one with the china guy was recorded using a flip phone im sure.

>>8655868
nvm found Bill Kenney's youtube channel. Awesome bald man to the rescue.

>>8655879
link?

>>8655939
https://www.youtube.com/watch?v=SpDQvVJZhYA

>>8655947

this aint topology but he does touch into softcore topology later on.

Does Schwarz's theorem imply that [math]\int \int dx dy = \int \int dy dx[/math]?

>>8653332
> 2=/=1 (trivial)
It can be of interest if you want to go deeper, it'll bring you toward Peano's axioms and Gödel's theorems.

>>8650638
I think it's hard if you can't stand them. Focus on the technical side of the interaction, study a lot so you can keep up with what they're telling you.

Take it as a training to work with people you don't like, which is bound to happen.

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to the mathguys here

is there any way to solve any of these without applying l'hopital's rule?

>>8656029
**on the first lim it should be x->0

>>8650638

I am in the same boat as you. Like >>8655973 said, just try to focus on the material. If your mind is engaged in the material, you won't have time to think about the professor.

Also, instead of considering them as a superior or a professor, just try to think of them as human.

You know that time when you eventually realized your parents were not Gods and were winging it? That's the same with professors. They are human beings just trying to get through the day just like everyone else.

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Is there a way to determine how close two atoms have to be before they are attracted enough to each other that they begin to move closer?

Take a hydrogen bond - How close (in angstroms) would the hydrogen atom have to be to an oxygen atom before it began moving closer to it via attraction? I understand that they are technically always going to be attracted to each other regardless of distance, but I am wondering if there is a way to calculate a the distance in which it's noticeable.

The picture is purely to draw attention to my question.

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Can someone explain to me what is happening in this? It's supposed to be an exposition of the Zeroth Law of thermodynamics but I don't understand wtf is being said. What actually are these functions, why are we factoring out the C from the arguments, and why do we need to do this in order to show f_ab = 0? Isn't that just an obvious implication of the first two statements?

Given the electrostatic potential
[math]V=ar^2(Cos^2\theta-b)[/math]
Is it true that
[math]\vec{E}=-\nabla V[/math]
Or am I getting confused?

>>8656070

It's not just a matter of distance, it's will be when the attractive potential energy is bigger than the thermal energy.

You can calculate the attractive potential by considering the molecules as simple dipoles.

https://en.wikipedia.org/wiki/Lennard-Jones_potential

>>8656074
yeah that's correct

>>8656074
>>8656097

Although are you sure that's the correct potential? It looks like it grows without bound as r increases; that's unphysical.

>>8656085
Thanks buddy :)

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When Sun (a near perfect sphere) radiates photons everywhere, do the photons get more and more separated when they get further away?

Like the photons are quantized right? So the angle separating two photons must be larger than zero?

I understand photon is wave, so it doesn't have definite boundaries, but I'm talking about really fucking far away from the Sun

is norm (real analysis) just a generalized absolute value??

>>8656349
Pretty much iirc

>>8656102
That's just what the question is

why the FUCK is the accumulation point of N is empty


real analysis btw

>>8656349
>is X Y
>>8656350
>yes

These human scum.

>>8656372
wat?

>>8656370
what is N?

>>8656029
Yes. I'll post my work below.

For the third one, let [math]e^{-t} = x, \lim_{x\rightarrow 0} x\ln{x} = \lim_{t\rightarrow \infty} -te^{-t} = 0 [/math]

The second one is a little more difficult to prove without using l'hopitals rule. Basically multiply the numerator and denominator by x/x, and solve two separate limits, (lnx/x) and (x^3 / x^3-2x+5), the first one is 0 because 1<=ln(x)<=sqrt(x), divide all by x and the rest is trivial. The second one is 1, and the reason should again be trivial.

The first one is pretty fucking difficult. I ended up googling just the equation to see what would come up and a youtube video on a very different problem came up, so I ignored it. Later on throughout my work I got closer to that actual problem, so before I do anything, I must prove that [math]\displaystyle \frac { \sqrt{(x+1)}-1} {x} < \frac {\frac {1} {\sqrt{(x+1)}} -1} {x}[/math] for x<0, and is > for x>0. Proving the latter is a case of proving [math]x\sqrt{(x+1)}(\sqrt{(x+1)}-1)^2>0[/math] which is trivially x>0. Proving the former is also trivial, and uses the previous answer as a contradiction. Now we can get to your actual problem. Your problem is equivalent to [math] \frac{(\sqrt{1-x}+1)(\sqrt{x+1}-1)}{x} [/math] The first term near zero is 2, so let's keep that in mind and solve that second term divided by x. We've just proven that (sqrt(x+1)-1)/x = (-1+1/(sqrt(x+1)))/x at x=0 above, so using the video I cheated with: https://www.youtube.com/watch?v=9DkEgTdzfhk you'll get -1/2 as your answer, multiply that with the other term 2, and get -1 as your answer.

Yes I know I cheated, but I'll use the fact that I don't have any pen and paper available as my excuse. Thanks for giving me something to do for 2 hours, though.

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>>8648925
Can someone help me solve some basic chemistry problems with molarity? I can't seem to find out how to do it step by step anywhere online.

Question 1:Can you dissolve .35 moles of Potassium Permanganate (KMnO4) into 500 mL of water? Why?/Why not?

Using M = mol/L, I found the molarity of Potassium Permanganate to be 0.480 M, but i'm unsure of how to get any further.

Thanks in advance. Regards,

>>8656387
you're a godsend

>>8656386

the set of all natural number bro

like for any n in N, why is the acummulation point of n empty.

>>8656405
because the interval (n-1/2, n+1/2) contains no other points of N

>>8656404
th-thanks. I wasn't sure how formal to make the proof because you never really specified what your problem is. If this were for school, the last two problems were pretty easy and I got in like 5 minutes, but the first problem is rather unreasonable to ask. If you were just trying to test whether or not l'hopitals rule is "dispensable" or that any solution you can gain through l'hopital you can also gain without it, the answer to that is no.
Also if you're in a somewhat rigorous calc course or something, you may want to prove that -te^-t -> 0 : t-> infty on your own.

>>8656427
we have yet to read about l'hopital's rule, so we're solving limits with the usual stuff, standard limits etc

I just wanted to see if it was one of those trick exercises (some ar marked with * in my book) that will be "unveiled" as you keep reading the book

I got stuck on the third one, and the way you put it it's pretty obvious

as for the other two, I will ask the teacher and see how he solves them

thanks anon

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>>8655774
Here

>>8656415

ah right, the requirement is for all r > 0.

thanks dude.

Ftfy

Can you guys recommend me a good cryptography book?

>>8655842
Bright side: things might get so bad that we'll live long enough to say I told you so instead of having to leave that for the next generation.

If I have a function f:R⊂Rn→R Defined over a rectangle such that f(x)=0∀x∈int(R) then how do I show that the the function is integrable and that the integral is 0? I can only use the definition of integral and the cauchy criterion for integrability (plus obviously other basic properties). I tried partitining the rectangle as P={a1,a1+ϵ,b1−ϵ,b1}×...×{an,an+ϵ,bn−ϵ,bn} with ai,bi being the points defining the rectangle. However, I'm not visualizing which sections of the subrectangles are touching the frontier of the rectangle and whic are in the interior.

Need help with physics homework.

A block is at rest on an inclined plane whose elevation can be varied. The coefficient of static friction is s = 0.36, and the coefficient of kinetic friction is k = 0.15. The angle of elevation is increased slowly from the horizontal. At what value of does the block begin to slide (in degrees)? What is the acceleration of the block?

>>8656826
Find theta such that acceleration is greater than zero using mu=.36. Then, calculate Fnet with that same theta, and divide by the blocks mass.

>>8656919
>Then, calculate Fnet with that same theta, and divide by the blocks mass.
*and replace .36 with .15 for this part.

>>8656240
I'm interested in an answer to this too.

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can science explain Tarrare?

https://en.wikipedia.org/wiki/Tarrare

> He travelled France in the company of a band of thieves and prostitutes, before becoming the warm-up act to a travelling charlatan; he would swallow corks, stones, live animals and a whole basketful of apples.

>he agreed to submit to any procedure that would cure his appetite, and was treated with laudanum, tobacco pills, wine vinegar and soft-boiled eggs. The procedures failed, and doctors could not keep him on a controlled diet; he would sneak out of the hospital to scavenge for offal in gutters, rubbish heaps and outside butchers' shops, and attempted to drink the blood of other patients in the hospital and to eat the corpses in the hospital morgue. After being suspected of eating a toddler he was ejected from the hospital.

>>8657041
Wiki says hyperthyroidism

I think he had some severe food allergy/intolerance.

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Number 1 was easy but 2 is turning out to be a ridiculously long number with over 20 digits. Am I doin it wrong or is my prof just sadistic?

>>8657101
http://www.wolframalpha.com/input/?i=45,056+in+binary
16 digits

When 1.5 moles of NaOH are added to one liter of a 1 molar solution of

H 3 PO 4 (pK a1 = 2.0, pK a2 = 6.8 and pK a3 = 12.0) the solution will be:

>>8657101
No that should be between 15-16 digits so your professor is just a dick.

>>8652297
If only there was some way to prove it.

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>>8650638
I'm afraid there is only one cure.

>>8657113
trivial and left as an exercise to the readr

>>8656399
How did you find 0.480M? Or in general the molarity of a solution that you don't know if it's possible.

Anyway, what is asked here is if you can dissolve 0.35 moles of KMnO4 in water (duh), so you just have to check the solubility of KMnO4 in water.

0.35 mol * 158g/mol = 55.3 g
Solubility of KMnO4 in water: 64 g/l
You have 110.6 g/l (55.3 g / 0.5 l) and thus no, you can't dissolve 0.35 moles of KMnO4 in water. (not completely at least).

You can also do some other way around, calculate the maximum molarity and your molarity, but the number are always the same, and so is the answer.

Anyone care to point a good text about young tableaux and how to connect them with represantions?

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can someone help me with the mechanism for either or both of these? I don't know where to start...

>>8657422
I'm pretty sure that the first product lack of a OH group, and the second one has a Me too much.

If something is not clear, let me know.

Also remember that reactions/mechanism always start from electrons, either in a bond or a negative charge. Once the first arrow is drawn, everything else usually comes naturally.

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>>8657422
>>8657443
Crap, forgot image

>>8656240
>>8656953
Yes.

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

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>>8657422
>>8657444
On a second thought, the second one might be this, while the first one COULD be that, only if you add H+ and then the grignard again. Which I doubt it's the case, so I would go for the missing OH.

>>8649621
Very unlikely with a shovel.
More likely to push him over or deflect the shovel

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why is motion permitted/what stops the universe from being in a stationary state?

>>8657041
Probably hyperthyroidism plus some strange palsy that left his stomach without stretch receptors

Do bosons have quantized energy levels?

>>8648925
You know that silly "Germanium Nickel Uranium Sulphur" thing people get on t-shirts for their nerd friends, right?

I presume you could make a compound out of those four elements and get, what, a grey/brown rock. But as I'm not a chemist and I'm also a retard, would the uranium make that rock a cancer risk?

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Analysis newfag here
I can prove the first part but i dont know how to picture what this is saying or how to interpret the theoretical part

Could an EPFCG be used to power an electrically powered weapon like a rail gun or directed energy weapon?

its modular arithmetic valid/useful for rationals or reals?

e.g. 3+4 = 2.5mod4.5 or 3pi/4 + 3pi/4 = pi/2modpi

test

Ever since Trig I feel like math has just gotten easier every class. Trigonometry was the hardest math class I had to take. Calc 1-4 have been so easy that I barely even need to read the text or attend lectures.

Does this have more to do with improved study habits, or does the math just get easier as you fill out your mathematical tool belt?

>>8658100
wait nvm I'm only in calc 3

arithmetic is still hard

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Say I have a certain Petri Net, and want to find its covering tree.
Is there a way to choose whether I should use a BFS- or DFS-type search algorithm, based on the number of places and transitions, or some other factor?

Can someone prove this with induction, 'cause my math teacher coundn't do it:
3^n > n^3 where n > 3

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Hi /sci/, I'm currently studying mechanics of materials and I suspect the book we're using (Hibbeler) has inconsistencies, but I wanted someone with more experience to confirm.

Pic related is a problem I was working on. Notice that Hibbeler determines the required diameters of the steel pins from allowable stress, rather than failure stress.

This is consistent with the preceding chapter, but it seems backwards to me. Isn't the point of the safety factor to design something _above_ its working load?

>>8658120
have you tried using l'hopital's rule?

>>8658130
but it states that i have to solve it with induction.

>>8658120
since f(n)=((n+1)/n)^3 is a decreasing function for n>3, and since f(4)<2, we have ((n+1)/n)^3 < 2 < 3 which implies (n+1)^3 < 3n^3

so
3^(n+1) = 3 (3^n) > 3 n^3 > (n+1)^3 where the first inequality is the inductive step

>>8658116


i just did an assignment on petri nets yesterday. this shit has no resources online.

anyway, i think the choice relies heavily on the type of computation that you want to do. iirc BFS is good for social networking like facebook for example while DFS is good for path-finding

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why the need to distinguish finite and infinite for intersection and union of open subsets in R^d respectively?

also, will learning Haskell benefit me in any way other than move me further down the autism spectrum?

>>8658130
consider the infinite intersection of every interval (-1/n, 1/n) for n>0

this intersection is just {0}, which is not open

>>8658183
[eqn] \bigcap_{n \in \mathbb{N}} \left(-1-\frac{1}{n}, 1+\frac{1}{n}\right)=[-1,1] [/eqn]

>>8658197

i can't read that shit dude wtf

I need to learning accounting in a month. Any websites/youtube channel where I can learn it with problems?

>>8657982
Yes you can do modular arithmetic with non-integers. E.g. 0 = 5 (mod 2.5). The only time it's ever been useful for me was for programming.

>>8658213
>accounting
a1, a2, a3, a4, ..., an, a(n+1), ...

>>8658207
Okay. (-1 - 1/n , 1 + 1/n) is a family of sets. More clearly, a family of intervals.

The big intersection thingy means that you want to intersect all the members of this family.

So first replace n=1 to get the interval
(-1 - 1, 1 + 1) = (-2,2)

Then replace n=2 to get the interval (-1 - 0.5, 1 + 0.5)

and then intersect those two intervals.

Then replace n = 3, get the new interval and intersect

Then do this all the way to infinity. This, if you know how to compute this infinite intersections, yields the set [-1,1] which is closed.

So an infinite intersection of open sets can yield a closed set.

>>8658226

no, i meant my browser can't read the latex that you wrote, but that was actually caused by me not permitting the extension to read link or whatever.

thanks for the writeup tho, appreciate it.

>>8658226

im not sure if we have had spent time specifically on infinite intersections but if we define each interval to be a < x < b for some (a, b), wouldn't taking the limit of of a,b still make the interval lim (a) < x < lim (b).

so in this case, at the 'end' of the intersection i will have -1 < x < 1 which is open.

>>8658248
Well, that is what the usual intuition would dictate but that is why we do not rely on intuition, we rely on the definitions left to us. And in this case that intersection is defined by:

[math] \bigcap_{n \in \mathbb{N}} \left(-1-\frac{1}{n}, 1+\frac{1}{n}\right)= \{ x / \forall i, x \in \left(-1-\frac{1}{i}, 1+\frac{1}{i}\right) [/math]

So here, the elements of the intersection have to be numbers such that no matter what index you pick, they will be in that set.

Well, lets think about 1. Is there any set in the family that will exclude it? Nope.

Sets will be like (1.000000000000000001,-1.0000000000000001)

Which obviously include 1. In fact, no matter which i you pick, the resulting interval will always have to include 1, as the limits of the interval will be slightly bigger than 1.

So 1 must be in the final set. The same goes for -1.

>>8658155
thanks!

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I recently read "In Praise of Small Numbers" and they had a little paradox with regards to Set Theory:

Imagine you have a Set, S, that contains all possible sets (and thus has infinitely many sets). If you take the power set of S, P(S), then you get even more sets, and thus you have a contradiction.

What's the explanation behind this (and given such an easily discoverable contradiction, how does Set Theory hold up?) ? Are we in the matrix?

I need some stats help.

A given event occurs 10% of the time if a condition is met.

If the condition is met, the effects are cumulative. If the condition is met twice, I have a 10% chance on one token and 10% chance on another token.

For a single success, would it just be 0.1 * x where x = number of times the condition is met?

What about a single success over the period of two attempts? Like, I need to roll a 10 on a d10, and I can roll x number of dice y times. How could I form an equation around this?

>>8658429
In ZFC Set Theory, that "set" is not even a set. That is how you resolve that contradiction. Basically, the author played like you like a fool.

>>8658517

So, I've been trying to work this out, and am particularly daunted at attempting to discover the odds of a single success with 5 dice being rolled as I do not feel like making tables to determine the exact number, here.

But, a guide told me the odds of failure are better to use.

x = dice rolled

1 - 0.9 ^ (x) = odds of at least one success.

senpai what do you use to write math papers?

>>8648925

What mathematical object should I 3d print

I'm probably gonna do an oloid but if I'd like something more interesting

>>8650810
Yeah pretty much this. In Physics I'd say every time you integrate in any context, a Phycisist is reading mentally "we sum over...". As some anon said, maybe it sounds stupid for integrating in one variable, but when you're in higher dimensional spaces you wanna be sure from the beginning of on what space you're making the sum. It becomes specially common when using Path Integrals.

>>8658747

...k-klein bottles

>>8658747
Something with a weird product of inertia like rattle back

3D print tops
https://www.youtube.com/watch?v=qquek0c5bt4

>>8658739
[math]\LaTeX[/math]

>>8658764

do people honestly write their thesis on notepad? Sure they use Latex, but what software do they use to assist them. Or are all of them autistic??

>>8658747
Your mom.

>>8658770
>notepad

If you don't use vim you're a fucking retard.

>>8656102
Well that's not true if you think the boundary condition is for example a conductor at constant potential.

>>8658764

[math]
\color{red}{g}\color{orange}{a}\color{yellow}{y}\color{green}{t}\color{indigo}{e}\color{purple}{x}

[/math]

>>8658770
Most people I know use Kile.

>>8658775

why do people here like to degenerate backward, i bet u retards commend each other for using smoke signals to send messages.

>>8651293
I see this fucking meme physics spouted all the time.

This is only true if the universe is completely random, which it isn't.

The sequence 0.12121212....... is infinite but it isn't random so you will never get all possible finite strings of digits.

Also it's an open question as to whether or not the universe is even infinite at all.

Dunno how to use Latex yet cuz I'm a faggot

"Find the order of the subgroup of the symmetric group S6 generated by the complex {(1234), (14)(32), (56)}"

So, I could go to town with some computations, but it could get out of hand really fast. There must be some sort of theorem that cuts the work out for me? Unless my prof is just a dick, which I am starting to believe is a possibility.

>>8648925
If the equation for a linear line is y = mx + c and c is the y-intercept then what is the equation for a line that runs parallel to the y axis and has no y-intercept?

Logically, it's just "x = whatever x is" but how to prove?

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>>8648925
There are Binary operators such as "+", "-" etc..

Are there any ternary or higher operators which can not be represented as a composition of binary operators?

>>8658901
I'm interested in this, too. I don't know anything about this so I'm thinking out loud:

A binary operator can be represented as a mapping from SxS -> S, correct? So I imagine an nth-order operator would be a map from S^n -> S. But whether or not the nth-order operator is simply a composition of binary operators, I'm not sure.

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>>8658896
PLz respond, no bully

>>8658791
Top kek

>>8658823
>This is only true if the universe is completely random, which it isn't.
I don't mean to sound like a popsci faggot, but does quantum physics allow for some amount of randomness?

>>8659007
Closest thing I could think of
https://en.wikipedia.org/wiki/Stochastic_process

I dunno if Stochastic processes are integrated into QM

>>8651787
It's not hard. There are online courses from MIT and whatnot. Grab yourself a textbook and do the problems related to the episode you watched. Check your answers. If your answers are wrong, then go back and see what you did incorrectly. I'd recommend picking a highly popular textbook so that the answers are common over a simple google search.

A large portion of undergraduate students, at least in America, don't even get past Calc I. It's a fucking tragedy quite frankly.

>>8658901
If you're allowed to cheat by allowing the operator to take values in R instead of Z, then I'll bet you can make the following work: choose a sufficiently "nasty" second-order ODE y''=f(y, y') (here [math] y\in R^3[/math] and [math] f: R^6\to R^3[/math] is some smooth function) and then define your ternary operator F by F(x,y,z)=Y(1), where Y(t) is the unique solution to the equation y''(t)=f(y(t), y'(t)) satisfying the initial conditions Y(0)=(0,0,0), Y'(0)=(x,y,z). I'm not exactly sure how you could prove that this is not a composition of binary functions, although i would be very surprised if this weren't true for "most" functions f.

You might also be interested in this:
https://en.wikipedia.org/wiki/Massey_product

>>8659278
edit: realized you could also use a first order equation y'=f(y) with boundary condition y(0)=(x,y,z) instead

>>8658901
>>8658912
I think you can show they are all composed this way by induction.

A binary operation is clearly composed of binary operations. Suppose an n-ary operation is too.

Then an (n+1)-ary operation is really a function f: S^(n+1) -> S (for some set S), which is also S^n x S -> S. But I can define a surjective function g: S^n -> S, and this can be decomposed into binary operations by the inductive hypothesis.

By applying only binary operations you change your function S^n x S -> S into S x S -> S, which is just a final binary operation.

Probably somebody can nitpick some subtleties here (especially where S is finite, since there cannot be a bijection and you will have multiple tuples that need to go to the same value) but it feels like it mostly works.

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How did he isolate Cosine Theta?

>>8659309
Remember in high school how you used to solve equations like ax+b = c? You bring the addition all over to one side and then divide by the constant.

It's the same thing here, except you're solving for [math]\cos(\theta)[/math] instead of x

>>8659317

It's been years since I've taken algebra 2, and longer since I've taken algebra 1. That's the problem.

>>8659320

Also, while it's easy enough to memorize what you just said, I don't understand the reasoning. Why? Also, why were the signs of the addition inverted?

>>8659320
>>8659324

Nevermind, I see what he did. I was thinking that he moved cos 0 to the right for whatever reason.

>>8659301
cute argument. as you note, it hinges on the fact that there is a bijection between S^n and S, which makes me think that the "arity" of a function is not such a useful concept (since any n-ary function is also m-ary, for any n and m), unless you're willing to add additional restrictions.

>>8648925
I have a question about stars.

In the biggest stars, what is being fused at the core? Is it metals?

>>8659007
Infinite particles, infinite nonzero probabilitys of infinite particles quantum tunneling into my fucking head.

Either :
Universe is finite in space.
Universe is infinite in space, but finite in matter/energy.
QM is wrong.


By random I mean as in everything is randomly distributed when the universe was created.

>>8648925
how i read this
d:X*X→R

>>8648925
I'm trying to show that Smooth Compatibility is an equivalence relation, it seemed trivial when I started but now I'm not so sure:
Let [math] \mathcal {A} , ~\mathcal {B} ~ \mathcal {C} [/math] be smooth atlases.
>[math] \mathcal {A} \sim \mathcal {A} [/math]
Follows immediately from the definition of an Atlas.
>[math] \mathcal {A} \sim \mathcal {B} \implies \mathcal {B} \sim \mathcal {A} [/math]
Let [math] ( U, \phi ) ~ \text { and } ~ (V, \psi ) [/math] be charts in [math] \mathcal {A} ~ \text {and} ~ \mathcal {B} [/math] respectively, since [math] \mathcal {A} \sim \mathcal {B} [/math] then [math] \phi \circ \psi ^{ -1 } : \phi ( U \cap V ) \to \psi ( U \cap V ) [/math] is a diffeomorphism, which means it has a continuous smooth inverse, ie [math] \psi \circ \phi ^{-1} : \psi ( U \cap V) \to \phi ( U \cap V ) [/math] Thus [math] \mathcal { B } \sim \mathcal { A } [/math]

So far so good (I think), but when I come to prove transitivity I run into a stumbling block, at first I thought:

Suppose [math] \mathcal {A} \sim \mathcal {B} ~ \text {and} ~ \mathcal {B} \sim \mathcal {C} [/math] then: [eqn] \phi \circ \psi ^{ -1 } : \phi ( U \cap V ) \to \psi ( U \cap V ) \\ \text {and} \\ \psi \circ \delta ^{ -1 } : \psi ( U \cap V ) \to \delta ( U \cap V ) [/eqn] From which it would immediately follow that [math] \left ( \phi \circ \psi ^{ -1 } \right ) \circ \left ( \psi \circ \delta ^{-1} \right ) = \phi \circ \delta ^{ -1 } : \phi ( U \cap V ) \to \delta ( U \cap V ) [/math] And so [math] \mathcal {A} \sim \mathcal {C} [/math]

BUT, that only works on [math] U \cap V \cap W [/math] So I'm at a bit of a loss as to what to do next. Anyone have any tips?

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>>8659866

why can't my latex extension read your stuff?

meanwhile

>night spent and still can't understand anon's argument that some intersection of infinitely many open sets is a closed set

>>8659873
>Latex
I don't know.
>Anon's argument
He showed that the infinite intersection would result in an intersection between (-1,1) and {-1,1}, which is the interval [-1,1], a closed set.

>>8659866
>>8659873
You guys remind me of when I was doing mathematics in college for my bachelor's degree and felt like I would amount to something.

>>8659926

im in SE, doing math for fun.

>>8659873
>>night spent and still can't understand anon's argument that some intersection of infinitely many open sets is a closed set

I simply defined an infinite intersection and then I showed you that the infinite sequences of sets looks like
(2,-2)
(1.5,-1.5)
(1.25,-1.25)
(1.1,-1.1) (for simplicity)
(1.01,-1.01)
(1.001,-1.001)
...
(1.00..001,-1.00...01)

And those always include 1, as the left boundary is always a bit bigger than 1.

Then the definition of an infinite intersections means:

Any number that is in all the members of the family, is also in the infinite intersection.

So the fact that 1 is in all the members of the family implies that it is also in the infinite intersection.

The same goes for -1. So you get [1,-1]

>>8659973

but we take the LIMIT anon! since we are working with the WHOLE NATURAL NUMBER, we have to consider some value a where a -> infinity

which makes lim (n -> inf) 1/n = 0

i might be a brainlet desu

>>8659983
>we take the LIMIT

You can only take the limit once you know how limits work for sets.

>which makes lim (n -> inf) 1/n = 0

Indeed, but there you are taking the limit of a function. Very different from a set.

Look, go back to my definition and prove these things:

1) Every number between 1 and -1 (not including 1 and -1) must be in the intersection
2) Every number bigger than 1 or smaller than -1 is not in the intersection
3) 1 must be in the intersection
4) -1 must be in the intersection

All those statements are true and easily provable. But don't use limits, just a normal argument about sets.

>>8658128
I don't know what to say to you except "no". If you design something above its working load you may allow for the structure to carry more load than it can. The safety factor is to ensure every external load don't cause more stress than the structure can handle.

What does "characterize" mean in the context of statistics?

How should I justify taking the time average of a power? I'm doing a damped harmonic motion problem and I have dE/dt proportional to 1/a * e^-(2t/a)
with a >> T where T is the time period of oscillation. So the energy doesn't vary much over a period. Is it enough just to say this? Or should I find the variance? What condition should I look for?

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If a function is defined as an equation with one output for every input, how can it have complex solutions, which always occur in pairs?

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I was too autistic to confirm it with my prof but here goes

If G is a group, and H is a subgroup of G, then I_H (I for identity) is necessarily equal to I_G. Identity is an element where I_H * I_H = I_H since H is a subgroup of G, then I_h is contained in G. Let a be that value in G, then a * a = a. Therefore a is an identity, and since identity of a group is unique, then a = I_H.

probably bullshit mathematically but i just can't articulate the 'idea'

any bros here do the proper proof?

is it possible that a prof hates people entering their class without registring for one?

i swear he looked at me couple of times.

>>8660022
What are you trying to do?

>>8660040
f(a+bi)=0 and f(c+di)=0 doesn't violate 'one output for every input', it would violate 'one input for every output' i.e. injectivity

>>8660046
you seem very confused, what are you even trying to ask? that the identity of a group is the identity in its subgroups?

Thanks m8

>>8660067
Thanks m8

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Trying to prepare for a laboration but we got stuck on this exercise. We assume the answer for a) is that it's 4-fold symmetry but that's about it. help pls

>>8660046
The idea is right, but the proof isn't. Let [math] G [/math] be a group and [math] H [/math] a subgroup of [math] G [/math], put [math]e_H, e_G[/math] as the respective identities. Since [math]H[/math] is a subgroup then it inherits the same law of composition, then we have: [math] e_H \circ e_H = e_H \circ e_G[/math], the result follows by multiplying on the left by [math]e_{H} ^{-1}[/math].

>>8660068
yes

>>8660075
don't that assume that the group has a 'multiplication' operation?

>>8660105

FUCK, a group b definition have the dot operation

>>8660105
No. I'm just using "multiplication" as a word for "take the inverse by applying the composition law on the left".

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its been sometime since the last time i did calculus, i think the derivative of F(x) exist at x=3 for the first function because the limit exist.. but not for the second one so the interval is correct for the derivative right?

>>8661142
it should say F'(x)=0 for x<3

>>8654062
bumpity

>>8661174
>What does it mean for a set of transformations, that go along with a set?
associativity means the same thing no matter what group you're working in, it's just a rule that tells you that you don't need to write brackets

>infinitely many generators or the generator has an infinite cardinality?
infinitely many generators. (a generator doesn't have a cardinality, it's just a single element of the underlying set)

>Also what are the generators?
no easy way to write them down, see
http://math.stackexchange.com/questions/354413/what-are-the-generators-of-mathbbr

Hey guys,
Browsing through my old Calculus textbook and a question has me stumped:
If set A includes all positive integers, and set B includes all negatives integers, what is A-B?
The book says the answer is the set A, whilst I think the answer is 2n (n belongs to natural numbers).

>>8661258
A-B is the set of differences {a-b, a in A, b in B}?
then
A-B=A+A=2A like you say

>>8661258
A-B is the set of all elements in A that are not also in B. None of the negative integers are also positive integers, so in this case, A-B is the set of positive integers.

>>8661273

I have honestly never seen the minus sign in set theory used this way before.

>>8661258
i assume 0 is included as a positive and negative integer

consider some values of a and b and evaluate a-b

this should lead to your textbook's answer A-B=A, not 2A

>>8662054
kek, good troll

>>8662092
if 0 isnt included in either, then the answer should be A+2 = {a+2 | a in A}

>>8661375
https://en.wikipedia.org/wiki/Arithmetic_combinatorics#Example

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