/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11006433]

Previously >>10980546
Keep your expectations low.

[Anonymous No.11006460]

>>11006433
When will I get my qt labcoat gf to do physics with?

[Anonymous No.11006463]

Unanswered questions from the previous thread:
Stupid questions:
>>10981215
>>10981677
>>10982621
>>10983181
>>10985923
>>10987274
>>10989270
>>10989280
>>10991587
>>10992661
>>10993115
>>10993525
>>11002032
>>11003485
>>11004449

Math questions:
>>10981796
>>10982606
>>10986936 (also stupid)
>>10989661
>>10984785 (substantially stupider than the other one)
>>10991538 (I told him he was lied to, but in retrospective I didn't actually summarise general topology)
>>10992163
>>10999123
>>10999269
>>11002150
>>11004080
>>11004933
Final trifecta: >>11006437 >>11006439 >>11006448

/g/:
>>10990506
>>11001170
>>11005002

Physics:
>>10992642
>>10996486
>>11000052 (closer to electrical engineering, really)

Biology/Medicine:
>>10992635
>>10996808
>>11001559

Best question in the thread:
>>10995611

>>11006460
When you win a nobel.

[Anonymous No.11006475]

>>11006463
By the by, if a question has a bunch of replies, people usually think it's been answered, even if those replies were shitposts, corrections and the like.
For example, the second physics question has two lads agreeing with him, and no proper recommendations.

So essentially, try not to reply to questions if you aren't going to answer.

[Anonymous No.11006500]

I’m studying communication systems right now and I have a question on bandwidth.
So the more bandwidth, the better, right? So what does this mean in terms of communication systems? So like for the internet, does this mean you “capture” more frequencies and this means more connections = faster speeds?

[Anonymous No.11006789]

Am I retarded?

[Anonymous No.11006955]

>>11006433
>>11006463
>>11006475
Good work organizing these. It makes /sqt/ a better place.
>>10991538
https://en.wikipedia.org/wiki/Topological_data_analysis
https://en.wikipedia.org/wiki/Persistent_homology
These concepts can see application in economics, or anything related to Big Data, really.
>>10986936
Hahn-Banach.
https://en.wikipedia.org/wiki/Hahn%E2%80%93Banach_theorem
It's not exactly taking a limit, but a trick of partition of unity by taking advantage of uniform boundedness.
There is also Tietze extension
https://en.wikipedia.org/wiki/Tietze_extension_theorem,
which is an application of Hahn-Banach by using the Minkowski gauge [math]\rho_A[/math] to bound [math]f[/math].
>>10984785
This might not be as stupid as you first thought. Floer cohomology is computing something similar to this, though not with [math]any[/math] ODE, but one generated by a Morse function [math]f:X\rightarrow \mathbb{R}[/math]. To be specific, the stable, unstable and irreducible critical points of [math]f[/math] form Floer cycles [math]\hat{C}(X),\breve{C}(X), \overline{C}(X)[/math] as graded (by the index) Abelian [math]\mathbb{Z}[/math]-modules, respectively. With the boundary [math]\partial a = \sum_b |M(a,b)| b[/math], where [math]M(a,b)[/math] is the space of trajectories generated by [math]f[/math] connecting the critical points [math]a[/math] and [math]b[/math], we can define the Floer cohomology groups [math]H = C/\operatorname{im}\partial[/math]. For "nice" [math]X[/math] (e.g. finite CW), these Floer cohomology groups are actually isomorphic to singular [math]H(X), H(X,\partial X)[/math] and [math]H(\partial X)[/math] by universal coefficient theorem.

[Anonymous No.11006961]

∀ x > 0, ∃ y > 0 such that y < x.

∃ y > 0 such that ∀ x > 0, y < x.

Are these statements different somehow, I don't understand why they were noted twice? Also, they're both true right?

[Anonymous No.11006962]

>>11006433
is it true that sustained magnetic fields of 45 T can be created with this tiny magnet?

https://www.youtube.com/watch?v=RNJ5jV-egs8

[Anonymous No.11006974]

>>>10992642
Very unlikely the disturbance you create will be of a single frequency. AMplitude will also be hard to measure because of dispersion. The velocity should be easy to measure though. Depending on how accurate you want it, you could just eyeball it and use a stopwatch or devise a more sophisticated device that measures interference (for example a driven oscillator creates waves with particular frequencies, and interference data gives you the wavelength. multiply them you get the speed).

>>>10996486
Halliday and Resnick is good. For a book only on modern physics, I recommend Tipler.

[Anonymous No.11006981]

>>11006961
The first one of those says that, for any fixed x, there's some y such that y < x.
The other one says that for all x larger than zero, there is a single y such that 0 < y < x.
The first one is true, the second isn't.

[Anonymous No.11006982]

>>11006961
>Are these statements different somehow
yes they are very different

>Also, they're both true right?
no, the first one is true and the second one is false
can you give me a number that's bigger than 0, such that all numers bigger than 0 are larger than it? no you can't

[Anonymous No.11006983]

>>11006961
Order of quantifiers matter.
Think of isAMotherOf(x,y) predicate.
Also, if those are positive integers, then those statements are false. Just pick x to be 1.

[Anonymous No.11006990]

>>11006981
>>11006982
1 week in and i regret picking a maths degree

[Anonymous No.11006999]

Why can't warmers shut up and lead by example?

[Anonymous No.11007963]

Are any of these polymer structures viable?

I don't have any idea what acrolein polymers look like, but the amino-, methyl ketone, and ethynyl- derivatives seem like they'd produce some really cool conductive ribbon-like compounds.

[Anonymous No.11008055]

What did he mean by this? I know you can use the composition of maps to get cup products, but those are for cohomology and not homology. How do you lift a homology class to a chain map in the first place?

[Anonymous No.11008096]

>>11008055
All I can think of is that you choose homology classes represented by cycles [math]z \in Z_p, z' \in Z_q[/math], and then check that [math]z \otimes z'[/math] is a cycle, too. Then you have that [math][ z\otimes z' ] \in H^\Omega _{p+q}[/math]. Restricting to the diagonal subgroup [math] \Delta_G := \{ (g, g) \in G\times G \} \cong G[/math], you could also replace those [math]P_* \otimes P_*[/math] -resolutions with [math]\text{res} _{ G \times G, \Delta_G}(P_* \otimes P_*)[/math], but I don't quite get the pieces fit together.

[Anonymous No.11008111]

>>11008096
The problem with that restriction approach would be the direction, though. For homology, I would have [math]\text{cores}_{ \Delta_G, G\times G} \colon H^\Omega _* (\Delta_G, k) \to H^\Omega _* ( G\times G, k)[/math], but I would be after an arrow [math]H^\Omega _* (G \times G, k) \to H^\Omega _* (\Delta_G, k) \cong H^\Omega _* (G, k)[/math]. I just feel so dumb for not figuring this out.

[Anonymous No.11008115]

>>11006999
what do you mean?

[Anonymous No.11008119]

Why can't you square root a negative number? What's really happening under the radical?

[Anonymous No.11008123]

>>11008119
Yeah you can... √(-4) = 2i

[Anonymous No.11008129]

>>11008119
You can, but it won't be a real number. You know when complex numbers have the form a+bi, that i is the square root of -1, and it is called the imaginary unit. What the radical does to x is that it gives you such y that that y^2 = x. If x=0, then you only get y=0, for x>0 there are two possible values for y, and if x<0, then there are also two but they come with that i attached to them and are thus imaginary instead of real.

[Anonymous No.11008146]

Why do so many people find incest detestable?

[Anonymous No.11008152]

>>11008119
A square root is a number that when multiplied by itself, gets the number it is a square root of. So the square root of 9 would be 3 because 3*3=9
To get a negative number through multiplication, at least one of the factors must be negative, meaning you can’t multiply a single number by itself to get a negative. So they invented imaginary numbers.

[Anonymous No.11008227]

>>11008111
Fixing a homology class and choosing a representative cycle [math]y \in Z_q[/math], I would then get a homomorphism [math]P_p \to P_p \otimes P_q, x \mapsto x \otimes y[/math], and hence a chain map [math]P_* \to \text{res}_{G \times G, \Delta_G} (P_* \otimes P_*)[/math] of degree [math]q[/math]. This would certainly be a lifting of [math]y[/math] to a chain map.

I could then take [math][x] \in H^\Omega _p(G, k), [y] \in H^\Omega _q(G, k)[/math], and use this chain map defined by [math][y][/math] to get [math][x] \otimes [y] \mapsto [x \otimes y] \in H^\Omega _{p+q}( \Delta_G, k) \cong H^\Omega _{p+q}(G, k)[/math]. I think I got it, but I would still appreciate it if someone would confirm the soundness of my reasoning.

[Anonymous No.11008345]

trying to prove that the countable complement topology on an infinite set X is a topology

one property of a topology T on X is that any union of a sub-collection of T is open, but does that include UNCOUNTABLY infinite unions?
i feel like that would invalidate the proof, since it holds because the COUNTABLE union of countable sets is countable

[Anonymous No.11008474]

What does a negative 1 exponent mean?
e.g. to find the angle of a 2D vector, the formula is tan^-1 * (a/b)
What does tan^-1 mean?

[Anonymous No.11008554]

>>11008474
Also what would the angle (direction) of the vector be if one of the components or both are 0?
e.g. given v = {0, 4}, finding theta would include 4/0.

[Anonymous No.11008560]

>>11008345
>does that hold for uncountably infinite unions
Yeah, open sets are closed under arbitrary unions.
You might also want to review which sets are open in that topology.
>>11008474
For functions, tan(x)^-1=1/tan(x), and tan^-1(x) is the inverse function. That is, tan^-1(y)=x if and only if tan(x)=y.
>>11008554
>what would the angle be if one of the components is zero
Some multiple of 90 degrees.

[Anonymous No.11008698]

>>11008345
Show that the collection of the subsets with countable complements gives you a basis for a topology, or equivalently that the intersection of two such sets contains a set with a countable complement. Assuming you have such results to use.

[Anonymous No.11008737]

>>11006433
Which form of the energy equation do I use for the following question?;

"The proton is a particle with a positive charge equal in magnitude to that of the electron and with a mass 1,840 times that of the electron. Calculate the energy, in electron volts, of a proton with a wavelength of 0.01A."

Do I use the charge of the electron at all or is that a red herring? I really want to use F = eE and change force into mg.

[Anonymous No.11008891]

What are some classic chemistry books that don't look like pic related on the inside? I'm reading Linus Pauling's General Chemistry currently and find it engaging. I'm probably going to snag a copy of Coulson's Valence and maybe Pauling's other book, The Nature of the Chemical Bond, but the latter two are, to my understanding, more casual and less formal or challenging.

Is there anything I should be keeping in mind while self learning chemistry? Obviously I don't have lab access, I might audit a lab course next year though. Any good lectures/videos you'd recommend?

[Anonymous No.11008961]

>>11008560
>You might also want to review which sets are open in that topology.
I feel like this also depends on the properties of X.
If X is countably infinite, then all of its subsets are countable, and the complement of any subset of X is countable.
But if X is uncountably infinite, then can we construct a subset of X whose complement is countably infinite? and is such a subset countable or uncountable?

It seems like for the countable complement topology to be a topology, we need to restrict X to a countably infinite set, and restrict the axiom of closure under arbitrary unions to closure under countably many unions. But maybe I'm wrong I need to write that down.

>>11008698
haven't done basis for a topology yet but thanks

[Anonymous No.11008978]

>>11008961
Ah, I see what the problem is.
You're thinking way too much, just use Morgan.

[Anonymous No.11009024]

>>11008961
>haven't done basis for a topology yet but thanks
It follows immediately from that. You just take any two sets with countable complements and note that the complement of their intersection is a union of two countable sets, and hence countable. Now you have that the intersection contains a set with a countable complement (itself) which is equivalent to the collection of such sets to form a basis for a topology.

[Anonymous No.11009077]

I’m going to a career fair in a few days and I’d like to make a cover letter for a few companies.
Should I staple that to my resume, or hand both separately?

[Anonymous No.11009097]

>>11009077
Use duct tape.

[Anonymous No.11009219]

How is this stack for starting at undergrad level?

I'm not sure what would come after (Munkres' Topology?) - I imagine you could also add in Enderton for Set Theory and Logic.

>Tao - Analysis I & II
>Hoffman & Kunze - Linear Algebra
>Feller - Probability I & II
>Knuth - Concrete Maths

[Anonymous No.11009233]

WTF am I doing wrong here? I've modelled this problem twice over and I cannot get the whole thing factored.

Q: Three consecutive numbers have a produce of -210, what are these three numbers.

So I figured first I would model it like this to eliminate the "X^2" term, making it easier to find a zero.

x(x+1)(x-1)=-210
(x^3)-x+210=0

turns out (-6) is a zero. so I synthetically divide and get these factors.

(x+6)((x^2)-6x+35))=0

This can't be factored anymore, WTF!

Next up, I do it the brainlet way
x(x+1)(x+2)=-210
(x^3)+(3x^2)+2x+210=0

this time we get (x+7)((x^2)-4+30)
Once, again not factorable.

So then I thought, well obviously the numbers are -5,-6 and -7. I'll just expand those factors.

But (x+7)(x+6)(x+5) creates this monstrosity
x^3+18x^2+107x+210

[Anonymous No.11009254]

Anyone know why this can be the case?

[Anonymous No.11009275]

>>11008737
>I really want to use F = eE and change force into mg.
Don't. Energy and charge are decoupled local degrees of freedom. The former comes from the [math]\mathbb{R}[/math] time-translational invariance, while the latter from the [math]U(1)[/math] gauge invariance (conservation of probability). The latter, compact connected Lie symmetry, implies that the Hilbert space of particle states [math]\mathcal{H}[/math] form an irreducible [math]U(1)[/math]-representation labeled by [math]\mathbb{Z}[/math], and as the Hilbert spaces vary [math]t\mapsto \mathcal{H}_t[/math] continuously with time, this discrete label cannot change. This is an example of Coleman-Mandula theorem, which states that the internal symmetry group [math]G = \mathbb{P}\times K[/math] of a relativistic local field theory is a direct product of the Poincare group [math]\mathbb{P}[/math] and a compact gauge group [math]K[/math]. In our case [math]\mathbb{P} \cong \mathbb{R}[/math] and [math]K \cong U(1)[/math] for a (0+1)D theory describing a charged particle (with no internal degrees of freedom) moving in time.

[Anonymous No.11009280]

recommended a good book for undergrad electromagnetism bros
have an assignment tomorrow, in need of desperate help

[Anonymous No.11009292]

>>11009280
I know absolutely nothing about it, but everyone I've seen here recommended Griffith.

[Anonymous No.11009301]

>>11009280
Griffiths

[Anonymous No.11009303]

>>11009292
Griffith did nothing wrong.

[Anonymous No.11009307]

>>11009280
J_____

[Anonymous No.11009316]

>>11009219
anyone?

[Anonymous No.11009436]

>>11009219
Tao's analysis is way too easy. I used it for self study after finishing Jame's Stewart's calculus and it was good for that level of maturity and exposure.

Hoffman and Kunze wasn't comfy to me, I only read the first couple chapters but vastly preferred the content found in Axler's Linear Aglebra Done Right and Valenza's Linear Algebra: An Introduction to Abstract Mathematics.

I tried Concrete Maths but that was impractically difficult for me at the time. The book is probably best used as a second look into those topics, not an introduction, unless you're very mathematically mature.

No idea about Feller. As for afterwards, abstract algebra, topology and diff geo would be good candidates. But book list are stupid. Grab some for the topics your reading and come back when you're done. Reading all the books you just listed concurrently would be idiotic.

[Anonymous No.11009478]

>>11006433
If I pat your hat...will you die?

[Anonymous No.11009578]

>>11009233
Anyone?

[Anonymous No.11009597]

>>11009578
just do it in your head, 5*6*7 is 210
so x is -6

[Anonymous No.11009603]

>>11009597
You're not allowed. I already did it in my head, that was the last part of the post. But the unit is about factoring polynomials, so I am supposed to find the numbers through factorization only.

[Anonymous No.11009607]

>>11009578
sorry, seems you knew that already. you just need to stop there after you find the 0, you can only solve for x, it's one variable, the other two numbers were already defined as +/- 1 in terms of x

[Anonymous No.11009645]

>>11009607
But even if I get one factor, how do I know which one it is? In the first case the factor you get is the second factor. In the second case you get the first factor. Even having both those factors how do I know the factors aren't -6, -7 and -8? Of course its easy enough to test but clearly I am meant to derive all the factors more rigorously than just guessing what the numbers are. Like I said, it was entirely obvious that it was -5, -6 and -7 in the first place because "-210" is factorable by all of them. So if I wanted to, I could just circumvent the entire calculation altogether but I doubt I'd get marks on a test for it.

[Anonymous No.11009682]

>>11009645
if you have the equation x*(x-1)*(x+1)=-210
the ONLY factor is -6
if the equation were
x*(x+1)*(x+2)
the only factor would be -5

just a side note, there is other factors but they're complex numbers and likely isn't what your teacher wants

[Anonymous No.11009715]

>>11009682
forgot pic

[Anonymous No.11009725]

>>11009682
So the question is a dud? I'm just glad that I'm not as confused as I thought I was.

[Anonymous No.11009731]

>>11009682
Fuck.. fucked that up x*(x+1)*(x+2) would be -7
x*(x-1)*(x-2) = -210 would factor to -5
fugging negatives fugging shift up

[Anonymous No.11009737]

>>11009478
it would be very painful

[Anonymous No.11009739]

>>11009578
>>11009233

x * (x+1) * (x-1) = -210
x * (x+1) * (x-1) + 210 = 0
x^3 - x + 210 = 0

guessing a zero: -6
(x^3 - x + 210) / (x + 6) = x^2 - 6x + 35

using PQ-formula (or whatever way you use to get zeroes of quadratics):
x_1|2 = + 3 +- sqrt(9 - 35)

! There are literally no other real solutions beside -6 for the original equation.
When it comes to cubic equations where you cant factor any more, you are forced to guess and divide the original equation and check for more solutions.
You cannot factor any more than what you already have and I'm not sure why you still want to factor.

[Anonymous No.11009766]

>>11009739
>and I'm not sure why you still want to factor

because once again there are three possible sets of numbers if I only have one factor and if I'm going to just guess which ones are the other factors, why not guess the whole thing? I think the question is just a dud and the teacher didn't realize you can't find all the zeroes with factorization of a basic model of the problem.

[Anonymous No.11009773]

>>11009766
the other two numbers would be complex numbers
the way you built the equation defines the other two numbers and you will only get one Real out of it

if you had the equation (x+1)*(x+2)*(x+3)=-210
you would get the factor -8
from that -8, you would know the 3 consecutive numbers were -7,-6,-5

[Anonymous No.11009926]

Can you still use Fubini's theorem for a function with only finite points in which it is discontinuous?

[Anonymous No.11009947]

>>11009436
>Tao = way too easy
What would be a more appropriate text? Tao is meant to be for senior level afaik.
Comparing the text to some other university courses around 2nd year to honours level, it seems to meet all the requirements. Also I thought Stewart was a first year calculus text, not analysis.

>Hoffman and Kunze not comfy
I'm not too worried about comfiness, more about rigor and a good base for moving to higher level / graduate stuff.

>Concrete
I wasn't planning to start with this text until after Tao and Hoffman as prerequisites.

>abstract algebra, topology, diff geo
cheers

[Anonymous No.11010143]

>>11009947
>Also I thought Stewart was a first year calculus text, not analysis
It is, that should tell you how easy Tao's Analysis is. I was able to grok it as a brainlet straight outta the calc series. Spivak's Calculus is a better analysis text, desu. The canonical recommendation for analysis is Rudin. Personally, I would just check the wiki: https://4chan-science.fandom.com/wiki/Mathematics

>comfiness
Well, that has more to do with how we define and apply the word. I find rigor and appropriate challenge very comfy, and I didn't find H&K as rigorous or challenging as the other text I mentioned. But I didn't get very far in it for those reasons.

>I wasn't planning to start with this text until after Tao and Hoffman as prerequisites.
don't get too caught up in planning, a good analysis book alone can take upwards of a year of study - and by then, you will know much more about what you should reading next. good luck m8

[Anonymous No.11010158]

>>11009926
pls respond. I was going to say yes because you can still subdivide the integrals into continuous zones and then just apply Fubini over them.

[Anonymous No.11010172]

>>11010158
Isn't a function with finitely many discontinuities measurable?

[Anonymous No.11010175]

>>11009926
If it's discontinuous at a finite number of points, it's a fortiori Riemann integrable, and a fortiori Lebesgue integrable, and thus Fubini applies.
>>11010158
You can also do that.

[Anonymous No.11010185]

>>11009478
This is a science and maths board, please don't engage in roleplaying.
>>11009307
>t. Witten

[Anonymous No.11010287]

>>11010172
>>11010175
Alright, thanks frens!

[Anonymous No.11010596]

>>11009766
> there are three possible sets of numbers
x*(x-1)*(x+1)=-210 only has one real root; see pic related. The other two roots are complex: 3±i√26.

Looking at the graph, you can see that x*(x-1)*(x+1)=k only has 3 real roots for a very narrow range of k. Specifically, for |k|<2/√27 ~=0.385.

[Anonymous No.11010739]

>>11010143
>>11009947
don't listen to this troll, Spivak and Stewart are memes

Tao is perfectly fine as are the other books

[Anonymous No.11011110]

>>11009926
You can do even better than finite. You can apply it for a function that it's set of discontinuity has lebesgue measure 0. That means your function could be discontinuous in all the rational numbers and you can still apply Fubini.

[Anonymous No.11011119]

Why are cooling towers shaped like hyperbolas?

[Anonymous No.11011121]

>>11011110
You could go uncountable too. Let f have the cantor ternary set of discontinuity.

[Anonymous No.11011158]

>>11009233
x * (x+1) * (x+2) = -210
(x^2 + x) * (x+2) = -210
x^3 +3x^2 + 2x = -210
x^3 + 3x^2 + 2x + 210 = 0
a way to factor a cubic polynomial is to find the factors of 210, since the free terms have to multiply together to get it
the factors are
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105
from there you can test numbers and divide them out from the equation to get a quadratic and use the quadratic formula to solve that. however, you can just see 5, 6, and 7 are all sequential numbers, so the answer is
(x+5)(x+6)(x+7) = 0
dunno if that's the method your teacher would want, but that's the best way i see that still shows some work

[Anonymous No.11011165]

>>11010739
Stewart I concur. Spivak is definitely not even a little bit of a meme.

[Anonymous No.11011204]

>>11011119

[Anonymous No.11011340]

>>11009275
I get it now, thank-you so much!

[Anonymous No.11011346]

>>11011110
>>11011121
>tfw just a chemist doing multivariable calculus
Thanks for the help, though!

[Anonymous No.11011889]

is this true?
[math] vct \left{ 1,1+X,1+X^2 \right} = vct \left{ 1,X,X^2 \right} =vct \left{ 1+X,1+X^2 \right} =\mathbb{R}[X]_{\leq 2} [/math]

[Anonymous No.11011893]

>>11011889
[math]vct \left{ 1,1+X,1+X^2 \right} = vct \left{ 1,X,X^2 \right} =vct \left{ 1+X,1+X^2 \right} =\mathbb{R}[X]_{\leq 2}[/math]

[Anonymous No.11011942]

>>11011889
Are you asking if the vector space generated by the polynomials [math](1, 1+x, 1+x^2)[/math] is equal to the vector space generated by [math](1, x, x^2)[/math]?
Yes, it is.

[Anonymous No.11011947]

>>11011942
Ah, I forgot to mention, but the criterium you'll usually want to use is that the two sets span the same subspace if and only if every element of one spanning set can be written as a linear combination of elements of the other.

[Anonymous No.11012002]

I have a linear function where y is increasing in x. How come the following relation is true? Is it something to do with the positive covariance between the variables?

[Anonymous No.11012039]

>>11012002
Is [math] \overline{x}[/math] notation for the average of x?

[Anonymous No.11012066]

Is this notation acceptable if I want to highlight that f is a function of x? I'm not a mathematician, but I'm making a report that I need to define some operations on a scalar field.

[math]f(\mathbf{x}): \mathbb{R}^{n}\rightarrow \mathbb{R}[/math]

I usually only see [math]f : \mathbb{R}^{n}\rightarrow \mathbb{R}[/math]

[Anonymous No.11012076]

>>11012066
People will understand you at least. Why not just write f(x)=*expression*?

[Anonymous No.11012082]

>>11012039
yes

[Anonymous No.11012089]

>>11012076
Because I'm defining an operation in which I'm more interested in the argument of the function than in the function itself, which could be any. That's why I want x to be explicit in the definition so I can use it later.

[Anonymous No.11012094]

>>11012066
That makes it seem like you have a function [math]f\colon X\times \mathbb{R}^n \to \mathbb{R}[/math], and when you fix some [math]x \in X[/math], you get [math]f(x) \colon \mathbb{R}^n \to \mathbb{R}[/math].

[Anonymous No.11012095]

>>10990116
>when does the citric acid get neutralized?
I don't know. That's why I'm asking.

Do you have brain damage? Do you not understand the point of a 'stupid questions' thread?

[Anonymous No.11012113]

What the heck is this [math]X_{(n)}[/math] distribution?

[Anonymous No.11012115]

>>11012089
If you have no explicit description to give, then "let [math]f:A \rightarrow B[/math] be a (whatever) map" is all you need to say. If you're trying to give some qualitative description, you can follow it with "that sends a vector x to ..."

[Anonymous No.11012308]

>>11012082
Prove it for n=2 and apply C R E A T I V E I N D U C T I O N.

[Anonymous No.11012336]

Two questions:
How would you quantify Voltage, Current, and Resistance? For example "measuring ___ using a multimeter
Also, would being able to use an oscilliscope be considered a skill to add to a resume?
"Display signals in a system using an oscillscope"

[Anonymous No.11012348]

X ⊆ {1,2,3,4,...}

What does this actually mean when X={x is a positive integer | x ≤ 917}. I assume the answer is that X is not a subset of that group since it stops at 917.

[Anonymous No.11012380]

Actually, nevermind. I think it is.

[Anonymous No.11012403]

>>11012348
>X={x is a positive integer | x < 918}
>why is X contained in the set of positive integers?

[Anonymous No.11012422]

>>11012403
Haha I was misinterpreting it, thinking that it meant that X was all positive integers.

Still got the question wrong though.

[Anonymous No.11012517]

>>11012066
people will probably understand, but it's a shitty notation, don't do that.

[Anonymous No.11012526]

>>11012517
I settled for [math]f : X\subseteq \mathbb{R}^n \rightarrow \mathbb{R}[/math].

[Anonymous No.11012566]

>>11012526
That doesn't mean what you think it does.

[Anonymous No.11012571]

>>11012566
f is a function from X, which is a subset of R^n to R?

Enlighten me before I embarrass myself.

[Anonymous No.11012631]

>>11012571
>>11012526
That's correct, if that's what you're trying to say.
Was x from before just an arbitary element of X?

[Anonymous No.11012633]

>>11012631
Yes. I decided to define x later and say it's an element of X.

[Anonymous No.11012836]

I'm working on an exciting project and my brain is very big, so I'm getting ideas/thinking about solving problems related to the project constantly. How do I stop that so I can get some sleep?

[Anonymous No.11012849]

[math]
[\forall m \in N ,\forall n \in N [(m < n \land P(m)) \rightarrow P(n)]] \rightarrow \forall x \in N,P(x)
[\math]
Why can't we write induction as shown above instead of the induction shown below?
[math]
[\forall m \in N ,\forall n \in N [(m < n \rightarrow P(m)) \rightarrow P(n)]] \rightarrow \forall x \in N,P(x)
[\math]

[Anonymous No.11012852]

[math]
[\forall m \in N ,\forall n \in N [(m < n \land P(m)) \rightarrow P(n)]] \rightarrow \forall x \in N,P(x)
[/math]
Why can't we write induction as shown above instead of the induction shown below?
[math]
[\forall m \in N ,\forall n \in N [(m < n \rightarrow P(m)) \rightarrow P(n)]] \rightarrow \forall x \in N,P(x)
[/math]

[Anonymous No.11012866]

>>11012836
lobotomy

[Anonymous No.11012877]

>>11012866
Tips on that? Is anyone even doing it anymore?

[Anonymous No.11012888]

>>11012877
It's more fun to do it yourself and figure it out as you go along.

[Anonymous No.11012890]

>>11012866
>>11012877
>>11012888
HAHA TRIPLE DUBS HAHA

[Anonymous No.11012916]

>>11006433
doe's a set of all fractions include all decimals?

[Anonymous No.11012923]

>>11012890
You mean double dubs and single tiples

[Anonymous No.11012935]

>>11012923
Dubs are a subset of triples

[Anonymous No.11012949]

>>11012916
If you mean all non-integers then no, by definition they wouldn't include any of the irrationals.

[Anonymous No.11012957]

>>11012916
Finite decimals, sure.

[Anonymous No.11012964]

>>11012949
>>11012957
Thanks a ton

[Anonymous No.11013353]

How to go from 2 to 3?

[Anonymous No.11013447]

My father is trying to build some kind of machine these days I dunno how it works but there is this component of his he made, is just a steel coil, imagine a straight stick with a coil at the end like a metal cone.

And I noticed that if you hold it with something non metallic as an handle and put it in between 2 of the same objects, it moves by itself, it remains still otherwise but moves when put between 2 of the same object regardless of their materials.

Why is that?

[Anonymous No.11013485]

>>11013353
Integration by parts, where the functions are x * (x*e^(-ax^2))

[Anonymous No.11013498]

>>11013485
Ahh, I was trying to do IBP using x^2 and e^(-ax^2).
Thanks anon!

[Anonymous No.11014093]

If [math]X[/math] is a topological space and [math]Y\subseteq X[/math], what inclusions exist for the following class of functions?
[math]C^0(X,X),\,C^0(X,Y),\,C^0(Y,X),\,C^0(Y,Y)[/math]

[Anonymous No.11014172]

>>11014093
[math]C(X, Y) \subset C(X, X)[/math] and [math]C(Y, Y) \subset C(Y, X)[/math] are the only inclusions.
There's also the restrictions and Tietze extension, if X is normal and Y is closed.

[Anonymous No.11014186]

Undergrad physics student here. Once I get out in the real world, I will only have one question. Are calculators allowed in a laboratory setting?

[Anonymous No.11014283]

>>11014172
Thanks. I was specifically thinking about [math]X[/math] being the extended reals [math][-\infty,+\infty][/math] and [math]Y:=\mathbb{R}[/math]. I was trying to find inclusions when I realized this could be framed in a more general way. I found the second inclusion, but not the first one. I'll do some more investigating on my own.

[Anonymous No.11014321]

>>11014186
I don't see why that would be an issue. You're in lab to do lab work, not to do computations in your head or by hand.

[Anonymous No.11014374]

>>11014283
The inclusion really is just [math]A \subset B[/math] implies [math]C(X, A) \subset C(X, B)[/math].
It's different for the extended reals because a function from them restricts to a unique function in the real line (because continuity).
That is, a function on the extended real line is uniquely defined by all of its real values, so you can get an inclusion from that too.

[Anonymous No.11014550]

>>11014374
Ah OK, that was the other inclusion I was getting. So is this the best we can do?
[math]C([-\infty,+\infty],\mathbb{R})\subset C(\mathbb{R},\mathbb{R})\subset C(\mathbb{R},[-\infty,+\infty])[/math] and [math]C([-\infty,+\infty],\mathbb{R})\subset C(\mathbb{[-\infty,+\infty],[-\infty,+\infty]})[/math], which would be the trivial one you mentioned.

[Anonymous No.11014671]

>>11014550
Yes.
sin(x) is defined on the entire real line and doesn't admit extension to the extended real line since it has no limit at infinity, so that inclusion is a no go.
If we extend it's image, we show that the other inclusion is also a no go, and thus we have proven we've exhausted the possible inclusions.

[Anonymous No.11014707]

>>11014671
Thanks so much desu
The example with [math]\sin(x)[/math] was something I also tried.

[Anonymous No.11015410]

Anyone tried any free CAD software? It's come time

[Anonymous No.11015426]

Anyone tried any free CAD software? It's come time that I start using it again and I don't want thirty separate modules of a fuckhuge software package shitting up a system I've deliberately kept neat.

[Anonymous No.11015617]

I am about to work a lot but taking the first step is kinda hard

[Anonymous No.11015869]

Should I wear a jacket to a career fair? It would be over a dress shirt, but it’s a nice polo jacket. Reason is because it’s going to be <70 degrees and possibly rain. I don’t want to bring an umbrella in and I’m already leaving my backpack in my car.

[Anonymous No.11015878]

What's a good book to get into Multilinear Algebra? I have a pretty decent background in regular Linear Algebra, I'll just need to brush up on some concepts I haven't used in a while. But I haven't really learned much about Multilinear other than some very basic stuff about bilinear forms, and I wanna learn about Tensors and stuff so I think I need to learn the previous concepts first.

[Anonymous No.11016037]

How do yall read textbooks through when self studying/semi self studying? I have never really read books but i am starting grad school next year and one of the qualifying exams during the program requires you to self study material for future classes to test ability to study independently. I know what book i want to read but how do i go about it? Should i take notes while reading or just do some example problems at the end of each section or just read and test myself later?
Or is this something i should just test out myself and see which approach works best for me? I was planning to mostly read at night before bed unless i have other free time during the school day

[Anonymous No.11016068]

>>11016037
Haven't most instructors in your experience simply taught the book or given an alternate take? Books are written by instructors, mostly. If you felt you needed notes in lecture, take notes. If you only needed a reference to pull from while doing problems, then do that.

[Anonymous No.11016334]

I am trying to write a short story whose plot develops around WW2. Supposing a misdirected V2 rocket exploded near a manor house like pic related, would it destroy it, or could it survive?

[Anonymous No.11016506]

What If I accidentally ate a dead worm ?
Google is so fucking stupid I fucking wrote DEAD and shit doesn't show results.

[Anonymous No.11016515]

>>11016334
Depends how close 'near' is anon

[Anonymous No.11016550]

>>11016515
>>11016515
Well, what radius did those have? I know the nazis killed plenty of Londoners with them but I'm not sure how big the overall destruction was. Let's say it lands right in front of the manor.
The thing is, I want the house to be visibly damaged but not completely destroyed. What kind of WW2 bomb, rocket etc. would do that and where would it have to land? I know I could just say a bombardment took place or something, but I want the scene to be scientifically accurate.

[Anonymous No.11016583]

>>11016550
Yeah, someone is definitely going to cross-reference the shear strength of century old masonry with the intensity of a V2 blast wave at whatever distance you settle on. Understand that you need to actually understand science if you want to even know what questions to ask or what expectations to have, let alone write something scientifically accurate.

Probably the closest thing you'll find is reference tables for modern explosives and modern masonry. Find the yield of a V2 and make a rough guess.

[Anonymous No.11016597]

>>11016583
>you need to actually understand science if you want to even know what questions to ask or what expectations to have, let alone write something scientifically accurate.
Fair enough. Do you reckon the average reader or editor would think twice about me saying that it was struck by a rocket or just bombarded?

[Anonymous No.11016599]

>>11016597
Not even someone who had some idea of where to start to verify it would care. Look up some accounts from people who experienced bombings if you really care about including where the bomb landed.

[Anonymous No.11016605]

>>11016599
Truth be told, I'm just looking for an excuse as to why it is damaged that I can fit into the prose.

[Anonymous No.11016662]

>>11006433
Is it possible to have a pressure equilibrium while also having a difference in temperature?
Pressure is proportional to temperature so I would assume not.

[Anonymous No.11017295]

When 2 phosphate groups aren't connected to each other, they're named "bisphosphate", as in "ribulose 1,5-bisphosphate", but when they are, they're called "diphosphate", as in "adenosine diphosphate", so why isn't an inorganic compound such as Ca3(PO4)2 called "calcium bisphosphate"?
>>11016662
According to p * V = n * R * T
if n = const.
p1 = p2
T1 = 2 * T2
V1 is not necessarily equal to V2 so
V2 = 2 * V1
ergo
p1 = p2
T1 =/= T2
I could be wrong though

[Anonymous No.11017314]

I'm starting to see proof by induction, and so far I've had some examples, some I understand, some I don't. And then when it comes to inequalities I get lost. My professor did bernoulli's inequality, but I don't get why the nx^2 disappears, what's that got to do with being positive? and how does the last line prove the inequality?

[Anonymous No.11017339]

>>11016662
> Is it possible to have a pressure equilibrium while also having a difference in temperature?
Yes. Pressure will equalise much faster than temperature.

> Pressure is proportional to temperature
(P*V)/(n*T)=R
If temperature increases, either pressure will increase or volume will increase or some combination of the two. If you have a closed container of gas and you heat some of the gas, the overall pressure will rise with the average temperature, and the proportion of the volume occupied by the hot gas will increase while that occupied by the cold gas will decrease.

[Anonymous No.11017341]

>>11014186
Sure, but during my time in an experimental lab I only used a calculator (i.e. my phone) for 2 things: adding together a bunch of optical path lengths (cuz I ain't adding 10+ numbers by hand), and multiplying the result by 2.54.
Anything else I needed to calculate was nontrivial enough to warrant numerical code (typically post processing calculations).

[Anonymous No.11017379]

>>11017314
>why nx^2 disappears
Since [math]nx^2 \geq 0[/math], [math](1+x)^n(1+x)=(1+x)^{n+1} \geq 1 + (n+1)x + nx^2 \geq 1 + (n+1)x[/math].
>how does the last line prove the inquality
Because the last line is the inequality.

[Anonymous No.11017412]

>>11017379
Wait, I think I get it now, is transitivity a common technique in proofs? Maybe that was what I wasn't noticing. Thanks
>Because the last line is the inequality.
kek, I don't know how I didn't notice that

[Anonymous No.11017417]

>>11017412
>is transitivity a common technique in proofs
Yeah. Stringing up a bunch of inequalities in a row to reach a final one is pretty common.

[Anonymous No.11017558]

Can somebody explain the rational for pic related?

[Anonymous No.11017998]

Is there any Riemannian Geometry textbook that isn't either filled with tensor physishittery(i.e. Petersen) or with the worst definitions possible(Chavel)?

[Anonymous No.11018003]

>>11017998
Nakahara.

[Anonymous No.11018016]

>>11018003
>Geometry, Topology and Physics
I completely expect to be disappointed, but I'll take a look.

[Anonymous No.11018024]

>>11018016
I did take a look, and it essentially only covers stuff I already know about, plus physics.
Anything else?

[Anonymous No.11018031]

>>11012113
Order statistics, ie the nth largest value in the sample

[Anonymous No.11018042]

Is delayed reward a meme? It doesn't feel nearly as satisfying as an immediate reward, so why does research say that delayed reward is better? It could also be that immediate reward is so much more powerful nowadays that research is behind. There's for example no real reason to plan something a year or more ahead since immediate rewards are a far better reward than something you don't ever experience and once you do, isn't even that exciting since it required the loss of many immediate rewards.

[Anonymous No.11018076]

are quantum and/or nano optics a meme or are there some jobs for it?

[Anonymous No.11018262]

Is ay/by (where y is a unit vector) just a/b (a scalar)? Or is it still a vector?

[Anonymous No.11018273]

>>11018262
No, it's nonsense.

[Anonymous No.11018323]

I don't have chegg so I can't see the answer, but this is the problem I'm working on: https://www.chegg.com/homework-help/questions-and-answers/2-four-plate-capacitor-capacitor-made-four-parallel-plates-equal-area-evenly-spaced-small--q40364192
Did I do it correctly (pic related)?

[Anonymous No.11018392]

>>11015869

[Anonymous No.11018443]

How do I show that [math]\sum_{k=1}^\infty[ \frac{x}{2+k^3x}/math] is continous at x = 0? I can consider any individual term in some small interval [math][0,\epsilon][/math] who will then all satisfy uniform convergence, but I have no way to express the n'th partial sum, and thus no way to check for uniform convergence there.

[Anonymous No.11018448]

How do I show that [math]\sum_{k=1}^\infty[ \frac{x}{2+k^3x}[/math] is continuous at x = 0? I can consider any individual term in some small interval [math][0,\epsilon][/math] who will then all satisfy uniform convergence, but I have no way to express the n'th partial sum, and thus no way to check for uniform convergence there.

[Anonymous No.11018453]

How do I show that [math]\sum_{k=1}^\infty \frac{x}{2+k^3x}[/math] is continuous at x = 0? I can consider any individual term in some small interval [math][0,\epsilon][/math] who will then all satisfy uniform convergence, but I have no way to express the n'th partial sum, and thus no way to check for uniform convergence there.

[Anonymous No.11018475]

>>11018262
You don't divide by vectors in general, instead you use inverses. So the proper way to write it is like this
[eqn]\frac{ay}{by} = \frac{a}{b}yy^{-1} = \frac{a}{b}[/eqn]
Notice that if you replace vector y with a scalar, then these equivalences are the same as the arithmetic we're used to. The first expression is however nonsense, never write a vector in the denominator like that.

[Anonymous No.11018484]

>>11018475
Also I forgot to mention this only works in vector spaces that have invertible elements. Matrices are vectors in that sense for example. It doesn't work with row or column vectors at all.

[Anonymous No.11018507]

>>11018453
[math]\displaystyle{\Sigma_{k=1}^{\infty}}\frac{x}{2+k^2x} \leq \displaystyle{\Sigma_{k=1}^{\infty}}\frac{x}{k^2x}=\displaystyle{\Sigma_{k=1}^{\infty}}\frac{1}{k^2}= \frac{\pi^2}{6}[/math]

[Anonymous No.11018514]

>>11018507
Actually, I'm not sure what I was thinking when I posted this, but I'm sure it was important.

[Anonymous No.11018543]

>>11018453
Nevermind, figured it out.

[Anonymous No.11019835]

Bump.

[Anonymous No.11019866]

>>11018543
Show us how ye did it then.
>>11018024
Sakai

[Anonymous No.11019951]

>>11018031
Oh ok. Thanks. I guess you would have seen this if you came to stats via probability instead of via experimental design.

[Anonymous No.11019985]

>>11018042
In econ, finance and similar subjects, 'delayed reward' is another way of saying 'time value of money' or 'positive interest rate', so you'll have an easier time understanding a delayed reward if it's monetary (or at least a tangible asset) rather than psychological feelings.

(Indeed, what little I've read on the psychological side of utility theory suggests that our happiness levels don't trend upwards or downwards as we age, they largely stay constant. Don't know how reliable this is, but it seems reasonable.)

[Anonymous No.11019993]

>>11019866
>Sakai
Naisu, but I've decided to just work my way through the Encyclopaedia's autism.

[Anonymous No.11020025]

>>11018484
You could define an algebra on a vector space so that you can multiply vectors together. If your algebra has a multiplicative identity, then you can talk about dividing vectors. That's one way to construct the complex numbers by defining a multiplication on [math]\mathbb{R}^2[/math].

[Anonymous No.11020121]

How do I find B when AB=BC where A and C are known invertible matrices and B is non zero?

[Anonymous No.11020148]

because bisphosphate is a functional group as opposed to diphosphate, which is just two phosphate anions. It just has to do with the way they're connected

[Anonymous No.11020152]

>>11020121
That's the Sylvester equation with C=0 (up to a sign change) and can be solved by vectorization, look up the Wiki page.

[Anonymous No.11020170]

>>11020148
>>11017295

[Anonymous No.11020221]

Retarded question here

according to symbolab, the x of x^2-3=0 is x=√3 and -√3

but only √3 makes the expression equal to 0:
√3^2-3=0 and -√3^2-3=-6

what am i missing?
https://www.symbolab.com/solver/function-domain-calculator/x%5E%7B2%7D-3%3D0

[Anonymous No.11020226]

>>11020221
tell me what is (-√3)^2

[Anonymous No.11020254]

>>11020226
ohhhh, 3

i intuitively didn't put the brackets, and √3^2-3 equals 0 so it made sense

thanks anon

[Anonymous No.11020505]

What does /sci/ think of the the Open Logic Project? If I study Forallx: Calgary & then the Open Logic textbook where would that leave me in terms of academic level?

[Anonymous No.11020618]

>>11020505
bump

[Anonymous No.11021837]

which is more "prestigious", working in a national/government lab (sandia, los alamos, jpl, etc), researching at a top company (apple, microsoft, intel, etc), or research at a lab like MITLL, JHUAPL, GTRI, etc? or are they all about even? I believe the company ones pay more but is it mostly due to location?
also which one works on the coolest/futuristic shit like aliens?

[Anonymous No.11022187]

>>11006433
They photographed a black hole that is millions of kilometers away but they still can't find planet 9. How?
don't throw that shit about planet 9 not reflecting any light from the sun... well a black hole is a BLACK HOLE! it doesn't let light escape from it so you can't even see it.
How can you explain this?

[Anonymous No.11022212]

>>11020618
The Vatican.

[Anonymous No.11022229]

>>11022187
>it doesn't let light escape from it so you can't even see it.
but it can bend light that doesn't actually cross it's event horizon. much like a lens, in fact it's called gravitational lensing

[Anonymous No.11022238]

>>11022229
you need a medium to make a lens, space is empty so why are you talking nonsense?

[Anonymous No.11022242]

>>11022238
no u

[Anonymous No.11022260]

>>11022242
another prove that scientist tare lazy, they can photograph stars thousands of kilometers away but they can't find planet nine. Lame.

[Anonymous No.11022261]

Which is larger, the number of true statements or the number of false statements?
Does the answer change if it's provably true vs provably false statements?

[Anonymous No.11022264]

>>11022261
Yes

[Anonymous No.11022269]

>>11022261
that's easy. they obviously have the same cardinality.
proof by conjunction

[Anonymous No.11022316]

>>11022269
What's the cardenality?

[Anonymous No.11022409]

>>11022261
Define larger. The collection of all true statements is not a set and as proven many many times in the past(Russell had a big problem with it, many followed) it can't be. It's a proper class. Rigorously extending the notion of cardinality to proper classes is unimaginably harder than you think. You'd think the answer should be equal if you can define it rigorously enough and that wouldn't be in ZFC. You could probably formulate a consistent theory where the answer is anything you want it to be. You could define class as being a large discrete category or the subset of a Grothendieck universe, both of which have some ground already laid down on the concepts of cardinalities I think. That's as far as I'm gonna go with logic nonsense though. Good luck.

[Anonymous No.11022483]

What is tan^-1?
I thought tan was a function and didn't have a value itself. Why are there formulas like tan^-1 (b/a)? Or is b/a the input to the function?

[Anonymous No.11022492]

>>11022483
It's a retarded way to denote "the inverse function". Write arctan instead. Arcus tangens makes much more sense than tan^-1

[Anonymous No.11022513]

Examples of R such that R is not a unique factorization domain but R[x] is?

[Anonymous No.11022563]

>>11006433
I'm currently testing some motors on a car with a motor controller (Tritium WaveSculptor22). I've entered the radius/diameter of the wheel correctly, but it appears I'm having issues getting an accurate value of velocity.

The motor controller supplies us with a motor velocity it calculates through the RPM->KPH equation, but it seems to be off by a factor of two. Why would this be? We have also manually calculated what velocity we should be getting at a given RPM and we get the same answer as the motor controller, so we aren't sure where the factor of two is coming from.

[Anonymous No.11022590]

>>11022563
>but it seems to be off by a factor of two. Why would this be?
That sounds like a "diameter instead of radius" mistake...

[Anonymous No.11022629]

any takers
>>11022622

[Anonymous No.11022741]

If [math]G[/math] is a finite group, [math]BG[/math] its classifying space and [math]BG^{\Lambda}_p[/math] the Bousfield-Kan completion of the classifying space with respect to a prime [math]p[/math], then why is it the case that [math]\pi_1(BG^{\Lambda}_p) \cong G/O^p(G)[/math]?

[Anonymous No.11023149]

>>11022492
This right here.
I had a HW assignment one time that asked about pre-images of subsets of the reals under the trig functions. Too many plebs got messed up thinking that preimage of {0} under sin was just arcsin(0).

[Anonymous No.11023206]

I need to calculate T1,T2, and m

I've got three unknowns but only two equations. What am I missing?

[Anonymous No.11023222]

>>11023206
Show your free body diagram

[Anonymous No.11023232]

>>11023222
So this is the only way I could think of solving it, but I still don't fully understand tension, and when to add it or subtract it

[Anonymous No.11023238]

So like lets say Aa
A is an allele for brown eyes
a is an allele for blue eyes
Those two make up the gene of brown eyes?

[Anonymous No.11023243]

>>11023222
This is what I did, but I just guessed because I don't fully understand what T2 is doing, or how to work more complicated problems with tension, for that matter.

[Anonymous No.11023327]

>>11022212
What is that supposed to mean?

[Anonymous No.11023355]

>>11023206
One equation for forces in x, one equation for forces in y, and one equation for relation between T2 and m.

[Anonymous No.11023383]

>>11008146
I'll give you the guesses

[Anonymous No.11023418]

>>11022741
Maybe the fact that [math]BG \cong K(G,1)[/math] would help?

[Anonymous No.11023440]

If I have a Span (lets call it S) full of trigonometric functions (sinh x, cosh x etc.) and I'm asked to show that basis (B) is a basis for S, how do I go about showing that. Its worth mentioning that the basis is identical to the span in form, its essentially the same vector.
Linear Independence? Some other trick since they're identical?
(I'm really bad at linear algebra)

[Anonymous No.11023571]

>>11023440
>sinh x
>cosh x
>trigonometric functions
You show that any element of S can be written as a linear combination and apply ye old tricks for linear independence (namely, you set up the usual equation, assume it zeroes and derive a contradiction).

[Anonymous No.11023614]

>>11023571
>>trigonometric functions
Sorry, I'm a retard and ESL, dont bully
Would it be enough if I could show that the span was made up of linearly independent functions? If I show that, then by extension B must be a basis of S, no?

[Anonymous No.11023663]

Can you split[math] f(x)=x^2 [/math] into two curves like you can ± [math]\sqrt x[/math]?

[Anonymous No.11023733]

>>11022590
Well, I thought so too at first, but the motor controller takes in diameter, my calculations takes in a radius, and we both get the same answer. Additionally, I hand-derived the formula, so I'm pretty confused why this factor exists.

The 2*pi*r factor comes from transferring one revolution to linear distance (which is just the circumference: 2*pi*r), so I'm not sure shy we would use the diameter in this case.

We're driving two motors, if that helps at all.

[Anonymous No.11023901]

Anyone know how to customize the Latex bibliography/reference list using BibLatex? I simply want to move somethings around. I want something like(for a book):
Sebesta, Robert W. 2016. \textit{Concepts of Programming Languages}. 11:e uppl. London: Pearson.
But get:
Sebesta, Robert W. \textit{Concepts of Programming Languages}. 11:e uppl. London: Pearson. 2016
For websites I want:
[Writer]. [Title(italics)]. [Year].
URL: [url]
(Read [Date])
With line breaks where they are, but get:
[Writer]. [Title(italics)]. [Year]. URL: [url] (Read [Date])

Any way to easily do this?

[Anonymous No.11024000]

>>11006433
How does the t get dropped here from v0t to t?

[Anonymous No.11024020]

>>11024000
because you got trips, I'll give you a hint, it says right there y(t) = 0

[Anonymous No.11024047]

>>11023901
nvm found it.
It seems I was just retarded, actually checked this https://tex.stackexchange.com/questions/12806/guidelines-for-customizing-biblatex-stylesspecific tread earlier but managed to miss it completely.
Throwing "\DeclareBibliographyDriver" and it's things in the preamble did exactly what I wanted.

[Anonymous No.11024072]

Do you think college professors look down on other their kid’s K-12 teachers during Parent-Teacher conferences?
Imagine going to your 1st graders class for those mandatory meetings. Do you think those teachers get intimidated?

[Anonymous No.11024074]

>>11022513
This can't happen. R embeds as a subring of R[x], so you would need a prime element of R to stop being prime in R[x]. This implies it factors as a product of two positive degree polynomials. But products of positive degree polynomials are still positive degree since R has no zero divisors.

[Anonymous No.11024122]

Who is or was the dumbest non defective person ever?

[Anonymous No.11024190]

>>11023614
>the span was made up of linearly independent functions
If you're working over finite dimensional vector spaces you can calculate it's dimension, and if your set spans the entire vector space you know it's linearly independent if it's cardinality is the same as the vector space's.
But that's extremely convoluted in most cases, just derive the contradiction.

[Anonymous No.11024314]

>>11024122
you

[Anonymous No.11024589]

What's it called when you force your face to turn red?

[Anonymous No.11024611]

>>11024589
It's called being a massive fagtron.
I bet you do that when your mom refuse you something.

[Anonymous No.11024706]

Is anyone here that's in math/physics just fucking tired of it all
Like you lay in bed exhausted thinking "Jesus man, I know a lot of fucking shit"

[Anonymous No.11024771]

Can integral itself viewed as function?

[Anonymous No.11024778]

>>11024706
No.
>>11024771
It's a linear functional on measure spaces. Suppose [math](X,\mu)[/math] is a measure space, then [math]f\mapsto \int_\Omega d\mu(x) f(x)[/math] is a linear functional.
On the other hand given a rank-[math]k[/math] vector bundle [math]V\rightarrow X[/math], the fibre integration [math]\pi_*:\alpha \mapsto \int_{V_x}(d\operatorname{vol}_k \alpha)(x)[/math] defines a linear map [math]\Omega^\bullet(X) \rightarrow \Omega^{\bullet -k}(V)[/math] on forms that descends to a map [math]\pi_*[/math] on cohomology that fits into the Gysin exact sequence.

[Anonymous No.11024790]

>>11024611
I was just wondering what you were doing was called

[Anonymous No.11025085]

How to overcome the feeling of knowing the communities I frequent will one die die out

like this page

[Anonymous No.11025131]

>>11023418
If I knew how that would help, I wouldn't have asked it in the first place.

[Anonymous No.11025151]

>>11009307
>Jackson for Undergrad

Noice

[Anonymous No.11025178]

A binary relation R is left-quasireflexive if, forall x and y, xRy implies xRx.
Can this property be expressed in relation algebra, like how reflexivity is expressed as [math]Id \subseteq R[/math]?

[Anonymous No.11025184]

>>11025178
Less than one minute after posting this, and I've stumbled on [math]Id \cap (R^{-1} \circ R) \subseteq R[/math].
I think this works...

[Anonymous No.11025185]

>>11025178
No

[Anonymous No.11025198]

Retarded mongoloid here.
Since Newtons are kg*m/s^2, how will a force of 100N be written in that form?
100kg*m/^2?

[Anonymous No.11025205]

>>11025198
Yes. F = ma

[Anonymous No.11025233]

>>11025205
But why is there no value for meters?

[Anonymous No.11025244]

>>11025233
Im not entirely sure what you mean
F (Force) = N
m (Mass) = kg
a (Acceleration) = m/s^2
Meters are part of the acceleration. Acceleration is meters per second squared
If you wanna know why thats the case, give it some thought and really think about what m/s^2 means

[Anonymous No.11025256]

The formula below looks like the formula for the distance between two points, except the X2 and X1 values are added together, whereas in the distance between two points formula they should be added together. What is going on?

[Anonymous No.11025263]

>>11025256
they should be substracted in the distance between two points formula** I mean

[Anonymous No.11025266]

im positive this has something to do with the intermediate value theorem but i cant put the pieces together

[Anonymous No.11025267]

>>11025184
What do you mean by the composition symbol? Also A circle B = { (x,y) : there's a z such that (x,z) in A and (z,y) in B} ? Also I assume R^-1 is {(b,a): (a,b) in R}?

[Anonymous No.11025269]

>>11025266
Hint. Pick let a= min(f(x_i)) and b=min(f(x_i)). Then the average of the right, call it C satisfies a<=C<=b. Do the rest for yourself. It's easy.

[Anonymous No.11025285]

>>11025269
of course, thanks fren

[Anonymous No.11025310]

>>11025267
Basically yes, except that A circ B is the other way around since I'm using the function convention, where g circ f = g(f(x)).
Personally I think this is utterly retarded notation and always use your style, except written A;B. Fair warning though, if you use this in public, prepare to be accused of programming sympathies.

As for 'relation algebra', you can look that up on wiki. I've read that every first-order expression with up to 3 free variables can be expressed in relation algebra, or something like that.

[Anonymous No.11025386]

I'm a subhuman and don't understand this.
Please help.
I've labelled the stuff that is causing confusion.

1) What is the diagram saying, what is the Up (+ve) and right (+ve mean)
2) Why does Sigma Fvert = 0?
3) Why are we trying to resolve vertical forces by using the cosine, shouldn't that be for resolving horizontal forces?
4) and 5) Basically 2) and 3) restated in a different context.

[Anonymous No.11025412]

>>11025386
>1) What is the diagram saying, what is the Up (+ve) and right (+ve mean)
It tells you the direction on the graph in which the values get bigger. Essentially tells you how to assign coordinates to the diagram.
>2) Why does Sigma Fvert = 0?
Because the point B is not moving. When an object is stable, the net force is zero.
>3) Why are we trying to resolve vertical forces by using the cosine, shouldn't that be for resolving horizontal forces?
Draw the right right triangles and you'll see why.
Both the horizontal component and the vertical component are zero.

[Anonymous No.11025443]

>>11025412
>It tells you the direction on the graph in which the values get bigger. Essentially tells you how to assign coordinates to the diagram.
But what does the "ve" stand for for? And if instead it was "-ve" pointing up, it would mean the values where getting smaller in that direction?
>Because the point B is not moving. When an object is stable, the net force is zero.
So Sigma is used to denote whether something is moving? If it it equalred 5, it would mean the object was moving?
>Draw the right right triangles and you'll see why.
>Both the horizontal component and the vertical component are zero.
Will try that out now

[Anonymous No.11025448]

>>11025443
+ve = positive
-ve = negative
plus and minus
>So Sigma is used to denote whether something is moving? If it it equalred 5, it would mean the object was moving?
Sigma means sum. Sigma F is the sum of the forces acting on B. If the sum of the forces is nonzero, that means the object is accellerating.

[Anonymous No.11025460]

Why does this thread exist?
I thought /sci/ is full of elitists that don't help plebs.

[Anonymous No.11025521]

>>11025460
It's called a containment thread.

[Anonymous No.11025570]

>>11025460
I post dumb shit here to satisfy my ignorance
And then I post ridiculous shit everywhere else

[Anonymous No.11025770]

>>11025521
But people in here are answering questions and being nice

[Anonymous No.11025868]

>>11025770
If we didn't answer people would make entire threads to catch attention.
It also helps pass the time.

[Anonymous No.11025881]

Why do people struggle with math and why is it taught at such a slower rate in America than other countries?

[Anonymous No.11025917]

>>11025412
>Draw the right right triangles and you'll see why.
>Both the horizontal component and the vertical component are zero.
Okay, I can't fucking do it, not sure what I'm doing wrong. I worked out the hypotenuse for both triangles and it's not the one given in the answer.

[Anonymous No.11025933]

>>11024314
You don't even know me.

[Anonymous No.11026022]

What the fuck is this shit? Could someone explain it to me?

[Anonymous No.11026032]

>>11026022
Rules of the logs: the difference of two log is the same as the log of the quotient of their arguments.

[Anonymous No.11026036]

>>11026032
Yeah but how the fuck do you turn that shit into log(5)5^2 and in what world does log(5)25 = 5?

[Anonymous No.11026044]

>>11026036
25/7 is the reciprocal of 7/25 since subtracting logs divides the dividend by the divisor which is a fraction, then you just multiply by the reciprocal, which after all the multiplication inside the parentheses is a nice number of 3125. That just so also happens to be 5^5 which is also coincidentally going to be a log base 5, so due to the law of logarithms, those are taken out and you’re left with 5.

[Anonymous No.11026046]

>>11026044
Nevermind, I'm retarded and I misread the exercise kek

[Anonymous No.11026048]

>>11026036
>log(5)5^2
Where do you get that from?

[Anonymous No.11026050]

>>11026036
> Yeah but how the fuck do you turn that shit into log(5)5^2
Read it again. It's 5^5, not 5^2. 25=5^2, 25^2=(5^2)^2=5^4, 35=5×7 => 7×35×25^2/7^2 = 7×(7×5)×(5^4)/7^2 = 7^2×5^5/7^2 = 5^5.

[Anonymous No.11026051]

>>11026048
Probably dyslexia, see >>11026046

[Anonymous No.11026127]

How do I show that this is a linear transformation?
I don't need an exact answer I think, its just that I've never seen an exercise like this before so I'm a bit thrown off.

[Anonymous No.11026130]

>>11026127
Oh, forgot to add.
T : A -> R^3
A is in R^5 if I'm not completely wrong

[Anonymous No.11026216]

>>11026127
>>11026130
Nevermind, pretty sure I've figured it out.

[Anonymous No.11026271]

Today my professor said that a free-falling eraser could be considered an inertial frame, but I'm having trouble wrapping my head around that due to the fact that the object itself is accelerating. What am I misinterpreting here? To be fair, he did specifically say that if we were falling with the eraser, then the eraser would be an inertial frame, and I originally took that to mean that it is inertial from the eraser's point of view, but now I think he actually means it would be inertial if we were to, say, skydive on top of the eraser.

[Anonymous No.11026322]

The eraser feels a though it isn't accelerating

[Anonymous No.11026353]

>>11026271
That's relativity for you.

[Anonymous No.11026358]

>>11026271
It just means that we're setting the erasers coordinates as constant and preserve its direction.

You could have my foot as as an inertial reference frame as I'm running but it would be literal hell to do any calculations.

[Anonymous No.11026474]

Is a PhD in nuclear engineering worth considering? I have 2.5 years left on my undergrad in physics, but I've already had a professor try to sell me on working under him after that's done.

[Anonymous No.11026733]

i only learned physics with example problems dealing with point masses. how do forces work with non-point masses i.e everything you'd find irl? like a chair. if i grab a leg of a chair the thing might tilt over, because i applied the force on the leg. this naturally makes sense but i don't know how to expalin it physics-wise.

how does gravity act on that chair? theres no point where gravitational force is being applied, it's applied to the entire thing. how is that possible? my feeble mind visualizes forces as little arrows, and arrows can only hit one precise spot. this is never an issue for practice problems and material dealing only with point masses or something close enough like tennis balls or whatever the fuck

[Anonymous No.11026742]

I have to start thinking about doing a senior project for my math undergrad. Since half of my math department are probabilists, what are some cool things in probability that I understand/research?

[Anonymous No.11026754]

>>11026271
>What am I misinterpreting here?
It's the Universe that's moving/accelerating

[Anonymous No.11026755]

>>11026733
It's a subject called continuum mechanics.
>>11026742
Algebraic statistics.

[Anonymous No.11026807]

How do I mathematically prove I'm not gay down to a science?

[Anonymous No.11026826]

>>11026807
have sex

[Anonymous No.11026860]

>>11026755
No. Continuum mechanics deals with - as the name suggests - how to describe continuum ie. liquid. When you wonder how gravity acts on a rigid body like a chair, you basically need to work with it's center of gravity, which then behaves as a point mass, but you need to take into account also the fact that the rigid body can rotate around it's center of mass in various fashions, this complicates things, but not as much as it might sound.

Basically start with something simple, like a triangle. If you want to know what happens when you throw it into the air, you consider the triangle as being composed of three point masses being held together by ideally rigid binds, that's where the rigid body name comes from. From then, you calculate the center of mass and then you apply forces to the center of mass and consider it a point mass, but that's only if you're not concerned about how it might roll around in space, then you need to also calculate it's moment of inertia and then through Euler's equation you can finaly compute the the angular momenta of the various rotational degrees of freedom, so called Euler angles. As you can guess, it gets complicated for any rigid body. Calculating the motion of a flywheel being affected by gravity was the pinnacle of mathematical physics for quite some time in the 18th century for example.

https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics)

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

[Anonymous No.11026862]

>>11026860
Meant for >>11026733

[Anonymous No.11026914]

>>11026322
>>11026353
>>11026358
>>11026754
Right, so I understand that from the frame of the "falling" eraser, it's not moving at all. I even understand that according to GR, gravity is not even really a force (although this is only SR so I don't think this is what my professor's getting at). But my question now is, wouldn't the falling eraser frame violate the litmus test of inertial frames? Suppose that we have an isolated Earth-eraser-ball-cannon system. The eraser is falling, and the ball is launched out of the cannon at a velocity of [math] v_{0} [/math], parallel to the path of the eraser. If we set the eraser as the frame, the ball's speed would decrease at a rate of 9.8 m/s^2, pass the eraser, then the ball's speed would increase at a rate of 9.8 m/s^2 away from the eraser. The ball would eventually stop moving, and then the ball would finally be moving at a constant speed. This would all be done by some "mysterious" force in the perspective of the eraser which is obviously not true. I get that this is established science, and that the falling object is definitely an inertial frame of reference, but where/how does my visualization fuck up?

[Anonymous No.11026922]

>>11026914
Whoops, I just realized that at the "apex" of the ball's path (from an observer's frame) the ball would still have a velocity in the eraser's frame, but there's still all the other things I mentioned to be accounted for.

[Anonymous No.11026946]

>>11026826
That's only a little less reasonable than string theory's need for a particle accelerator the size of a Galaxy

[Anonymous No.11026987]

Is it mathematically correct to do algebra shit with differentials like
[math]A = \frac{df}{da} /*da[/math]
[math]A da = df[/math]
If so, how?

[Anonymous No.11027000]

>>11026987
Yes, given you have the correct interpretation. Given a smooth real manifold [math]M[/math], [math]dx^\mu[/math] forms the coordinate representation of a basis of the cotangent space [math]T_x^*M[/math] which comes equipped with a non-degenerate pairing [math]\langle \cdot,\cdot\rangle: T_xM\times T_x^*M \rightarrow \mathbb{R}[/math] given by [math]\langle \partial_\nu,dx^\mu \rangle = \delta_{\mu\nu}[/math].

[Anonymous No.11027002]

>>11026987
https://en.wikipedia.org/wiki/Differential_of_a_function

[Anonymous No.11027024]

>>11006433
What do the # and & signs mean in wolfram alpha?

[Anonymous No.11027054]

Is it feasible to finish my degree in Computer Systems, work a few years, and return to school for a PhD in Mathematics? I think I might really fall in love with upper-level math but it's not an immediate objective, I would pursue it purely out of personal fascination.

[Anonymous No.11027074]

>>11027024
that your linux distro's fonts suck donkey dick

[Anonymous No.11027178]

Can fucking ANYONE explain how these capacitors were grouped and simplified to find the charges and voltages across each capacitor as well as the equivalent capacitance? It WAS homework but I got every fucking part wrong. I tried so many different things and even when I try to work backwards from the right answers I can't get it.
fucking PLEASE, this shit is killing me and my professor is a retarded fuck who couldnt help me

[Anonymous No.11027508]

Let f:R->R, f(x) = 2x^2 - 8x + m
Determine m for which the coordinates of the vertex of the parabola are equal

xv = yv => -b/2a = ∆/4a
∆= b^2 - 4ac = 64 - 4*2*m = 64 - 8m

-b/2a = 64-8m/4a
8/4 = 64-8m / 8
2 = 64-8m / 8
=> 64-8m = 16
=> 8m = 48, m = 6

But the textbook says the answer should be m = 10. What am I doing wrong?

[Anonymous No.11027628]

What kind of physical abnormalities or injuries can result in pic related's skull shape?

[Anonymous No.11027694]

>>11027628
This is making me feel weird because that's exactly how my hair looks after I wear my headphones for an extended period of time.

[Anonymous No.11027717]

>>11027178
> Can fucking ANYONE explain how these capacitors were grouped and simplified
C3 and C4 in series = 4.9/2 = 2.45uF.
C2 and C3/C4 in parallel = 2.45+4.9 = 7.35uF
C1, C2/C3/C4, C5 in series = 1/(1/9+1/7.35+1/9) = 2.79uF

Having found C, Q=CV. Capacitors in series have the total charge on each capacitor, capacitors in parallel divide the charge in proportion to capacitance.
So Q = 240*2.79 = 670uC = Q1=Q5=Q234.
Q2 = 670*4.9/(4.9+2.45) = 670*(2/3) = 447uC
Q3=Q4 = 670*2.45/(4.9+2.45) = 670*(1/3) = 223uC.

[Anonymous No.11027738]

>>11027508
> Determine m for which the coordinates of the vertex of the parabola are equal
2x^2 - 8x + m
= 2(x-2)^2 + m-8
=> the vertex is at x=2, y=f(2)=m-8
f(2)=2 => m-8=2 => m=10

[Anonymous No.11027773]

>>11027628
Breh, just about any moving object capable of carrying a handful of Joules can do that.

>>11027508
You're solving it as if the situation you want is y=0, which isn't the case here, it's y=2. See >>11027738

[Anonymous No.11028005]

What the fuck is wrong with social constructionists? I actually talked to one today and they thought I was buying into something conspiratorial because I buy men's shampoo instead of women's

So sci, is there something scientifically advantageous about my decision or am I a sucker? I think a man should smell like a man so he can get the fucking goose once and a while. Aren't I statistically limited to the minority of s.c.'s that wouldn't care what my hair smelled like? This is just basic civil conduct as far as I'm concerned

[Anonymous No.11028025]

>>11028005
If you buy a men's shampoo because for men is written on it and despite liking the smell of a particular women's shampoo better, you are a gigantic faggot.
Men's shampoos smell generally better though.

[Anonymous No.11028040]

>>11028025
Well yeah obviously I wouldn't buy one I think smells like shit, Jesus man

[Anonymous No.11028146]

>>11027738
>>11027773
I did the math with yv = ∆/4a like a retard instead of -∆/4a like the formula for y of the vertex says

∆ = 64-8m, -∆ = -64+8m so
-b / 2a = (-64+8m) / 8
2 = (-64+8m) / 8 = -8 + m
2 = -8 + m = -8 + 10 => m = 10

[Anonymous No.11028369]

what is a tensor product of modules?

[Anonymous No.11028378]

>>11028369
do you know what tensor product of vector spaces is ?

[Anonymous No.11028382]

>>11028378
not really

[Anonymous No.11028409]

>>11028382
Let's start with tensor product of two vector spaces of dimension 3 ([math] \mathbb{R}^3 [/math] if you want).
Given a basis of each vector space,a_i and b_i, with i=1,2,3, you can construct a basis of the tensor product of those two vector spaces by writing the pair (a_i,b_j). This gives you a basis of 9 elements. Is it clear?

[Anonymous No.11028417]

>>11028409
yes

[Anonymous No.11028427]

>>11028417
Then, it is more or less the same for modules. The only thing is that you need to tensor product a right module with a left module in order to have a well defined multiplication by an element of the ring.

[Anonymous No.11028453]

>>11028427
so the module "spanned" by the symbols of tensor product of elements of the original modules is the tensor product of these modules? but how exactly are the addition and multiplication by ring elements defined on this new module? or are they just required to satisfy bilinearity conditions and are purely formal constructions?

[Anonymous No.11028455]

>>11028369
Left adjoint of the hom functor that completes the currying isomorphism

[Anonymous No.11028462]

>shitty state uni
should i just give up hopes of graduate study?

[Anonymous No.11028466]

>>11028453
>but how exactly are the addition and multiplication by ring elements defined on this new module?
(a,b)+(a,c)=(a,b+c)
(a,c)+(b,c)=(a+b,c)
(a*r,b)=(a,r*b) (This last one is the reason we have to combine a right module with a left module)

[Anonymous No.11028474]

>>11028453
>but how exactly are the addition and multiplication by ring elements defined on this new module
For addition you have x⊗z+y⊗z = (x+y)⊗z, otherwise you cannot add them, for multiplication by r you have rx⊗y = x⊗yr.

Tensor product of vector spaces U and V is spanned by all elements u⊗v, but the rules for addition and multiplication explained above are imposed. With vector spaces these rules are the only relations that are satisfied, this is because all vector spaces are free modules. With general (not necessarily free) modules it's more complicated, for example Z/p ⊗ Z/q is zero whenever p and q are coprime.

[Anonymous No.11028491]

>>11028427
>>11028455
>>11028466
>>11028474
thanks

[Anonymous No.11028523]

>>11028491
no problem anon, we're here to help and encourage

[Anonymous No.11028696]

>>11028523
c:

[Anonymous No.11029036]

>>11028462
what's wrong with state unis? If you mean like one of the big public ones I think they're perfectly fine, maybe go to grad school elsewhere though

[Anonymous No.11029878]

>>11028005
PROTIP appeal to human nature is, 99% of the time, the ultimate appeal to authority in disguise. Even something as menial as your judgment of which shampoo smells better can be, and is, shaped by social forces (that's the whole point of marketing, after all), regardless of whether it has any genetic basis.

[Anonymous No.11030334]

>>11022741
The author didn't mention the groups were [math]p[/math]-perfect. For such groups [math]G[/math], one has [math]\pi_*(BG \hat{_p}) \cong \pi_* (BG) \hat{_p} \cong G\hat{_p} \cong G/O^p(G) [/math]. Thanks for the help.

[Anonymous No.11030336]

>>11030334
*=1, oops.

[Anonymous No.11030360]

Today I had a test and one of the questions was
>Let [math] f : \mathbb{R} ^{n} \to \mathbb{R}^{m} [/math] be a linear transformation. Prove [math] f [/math] is differentiable at [math] a \in \mathbb{R}^{n} [/math] and find [math] \mathcal{D}f(a) [/math]. Hint: How are linear transformations from [math] \mathbb{R}^{n} [/math] to [math] \mathbb{R}^{m} [/math]?
The proof was quite trivial but I really don't understand how does the hint help at all so it makes me feel like I forgot something.