/sci/ - Science & Math

How the hell does one show for positive definite matrices [math]A[/math], [math]B[/math] with the geometric mean defined as [math]A\# B:=A^\frac{1}{2}(A^{-\frac{1}{2}}BA^{-\frac{1}{2}})^\frac{1}{2}A^\frac{1}{2}[/math] that [math]A\# B=B\# A[/math]???

I am able to show that the term in the middle of [math]A\# B[/math] is well-defined. However, how the fuck can one explicitly calculate this square root?

Brainlet studying chemistry from the ground up. How complex does the math in chemistry get the further you go? I imagine it's not always gonna be a matter of simple formulae and numbers with lots of decimals.

I have done a Fourier transform and I have no idea how to plot this in the frequency domain. Please help a brainlet out. This is how it looks like:
H(ω)=(3i/2)[δ(ω+ 5)−δ(ω−5)] +ω[δ(ω+ 4)−δ(ω−4)]

I assume that I would need to find the the points you get when each of the delta values becomes 0 inside the parentheses
Thus I would get these points:
H(−5) =3i/2
H(5) =−3i2
H(−4)=−4
H(4) = −4
How can I plot the function from these?

How do i prove this limit is 0. serious question. Have analisys exam next saturday

I want to learn a statistics tool. Is Minitab a good start? I read everywhere that R is hard to learn

Retard here, trying to make a game with somewhat realistic physics.

How do you calculate the resistance of something like armor? What is that called in physics?

>>10068887
>Is Minitab a good start?
Why don't you try it and find out?

So I like a girl, but she has a dark past and all. This makes me uncomfortable. I feel like my GF should be pure or at least not degenerate. But I really like this girl.

What does science have to say about degeneracy? Is it a human construct? Do male animals care if their female companions are pure?

>>10068850
>How do i prove this limit is 0.
What have you tried?

>>10068850
cancel out the exponents m8

good luck on your analsysys

>>10068708
Spectral (eigen-)decomposition
>>10068736
How much further do you want to go? Freshmen chem will probably only use calc 1 stuff at most. Physical/quantum chem will require linalg and at least ODEs (at the undergrad level). I'd imagine research chem uses graph theory and lattices all the time.

>>10069195
Yes, I know that you can take the square root of a positive definite matrix, and obviously it will be [math]A^\frac{1}{2}=PD^\frac{1}{2}P^{-1}=PD^\frac{1}{2}P^T[/math] since the eigenvalues are positive.

But how can you explicitly calculate the middle term [math](A^{-\frac{1}{2}}BA^{-\frac{1}{2}})^\frac{1}{2}[/math]??? The nice property gets blocked by two diagonal matrices on the sides.

Is the empty set a proper subset of a set?

>>10069471
Yes if the set is not the empty set. Maybe?

>>10068708
>[math]A^{\frac{1}{2}}[/math]
This is my gripe with taking square roots of matrices. I know they exist but it's obviously not unique; they depend on how you diagonalize [math]A[/math]. For instance, [math]I^{\frac{1}{2}}[/math] has solutions in [math]\mathfrak{u}(2)[/math]: all Pauli matrices square to the identity. Writing a matrix [math]B[/math] as [math]A^{\frac{1}{2}}[/math] implies uniqueness, which implies much stronger conditions on [math]A[/math].

Is it possible to decipher 11 17 9 21 in mod 26 with a key of 13? My understanding is that to be able to decipher it needs to have a multiplicative inverse and 13 doesn't have one in mod 26. Is my understanding correct?

I woke up and I woke up with pimples on my forehead. I also have this solid lump near my right ear. It doesn't move and was never there before. My right ear sometimes hurts and I get ringing in my left ear. Should I be worried?

If [math]f,g : I \to \mathbb{R}[/math] are measurable functions, then [math]\frac{f}{g}[/math] is measurable. Proof: [math]\frac{f}{g}[/math] is measurable if and only if [math]\{x\in I : \frac{f}{g} < s \} [/math], for some [math]s\in\mathbb{R}[/math]. Given, [math]f < g\cdot s[/math] there exists a rational (density), [math]q\in\mathbb{Q}[/math] such that [math]f<q<g\cdot s[/math]. So [math] \{x\in I : \frac{f}{g} < s \} = \bigcup_{q\in\mathbb{Q}}\left( \{x\in I : f < s \}\cap \{x\in I : g > \frac{q}{s} \} \right) [/math], which is a countable union of an intersection of measurable sets.

QED?

I finally understood basic Laplace Transforms, but I'm unsure of how to deal with the sin(nt+a), I dont know what to look for on the transforms tables...

can someone lead me in the right direction?

>>10069862
>f/g is measurable if and only if [a set]
what does this even mean? Did you mean to write for all x in I? Because then you're stating it's measurable if and only if the image is bounded above, which is a very, very false statement.

>>10069870
[math]sin (\alpha) = \frac{e^{i\alpha} - e^{-i\alpha}}{2i}[/math] hth

>>10069870
sum difference identity, sin of a constant is a constant and cos of a constant is a constant

>>10069884
I meant to say if and only if [math]\{x\in I : \frac{f}{g} < s \}[/math] is measurable.

>>10069892
Then you need to fix your quantifier "some s". Otherwise you can take any nonmeasurable function which is always positive and I can just take {f(x) < 0} and claim it's measurable.

>>10069898
The argument remains unchanged if I fix my quantifier then?

Determine the simplest rectangular form for complex expression :

W = (3-J)(3-2J) / (2+3J^3)

really have no idea here, everything I'm googling shows "rectangular form" related to trig.

>>10069914
It asks you to give W in the form a+bJ.
Expand with (2-3J^3) to make the denominator real, then multiply everything out.

>>10068703
>brainlet tier questions
>everybody posting over the top shit

you want some real brainlet shit
doing my hw rn,

Is the trinomial y^2 + 9y + 81 a perfect square trinomial?

how do i figure this out

>>10069159
figured it out already, distributive, comon factor and the remaining was between -1 and 1 allways.
>>10069185
kek analysis then?

>>10069920
I'm doing this on line and the book has never asked a question like this.
so if I expand the numerator I get 2J^2-9J+9
and factor out J from the denominator I get J^2(2+3J)

after this do i cancel out like exponents and divide their coefficients?

>>10069928
>how do i figure this out
You know how squared binomials look like, right? The constant term is a square, the linear factor is twice the root of that square.
Put on your thinking cap and see if 81 is the square of half of 9.

>>10069946
thanks for the help man. i have no clue what a constant term or linear factor is, but i'll just apply the last part to the other questions. ty verymuch

>>10069944
>and factor out J from the denominator I get J^2(2+3J)

Easy there, that's not what your original expression said. You're making algebra mistakes, go more deliberately.
Then do the expansion that >>10069920 mentioned.

Also, if you write down -1 instead of J^2 as soon as it appears, that will probably help you out in future.

If I have a pointwise bounded sequence of measurable functions, [math](f_{n})[/math] on an interval, say [math][0,1][/math], such that each [math]f_{n}[/math] is bounded, does this necessarily mean that the limit supremum of this sequence is bounded?

>>10069972
On a compact set? Yes.
On a compact set, being pointwise bounded is the same as uniformly bounded, hence the sequence converges in the space of measurables.

>>10069962
Honestly I have zero idea what I'm even being asked to do here. Would I multiply the numerator by the denominator to remove it?

>>10069991
You're being asked to normalize the expression for w, so that it is in the form [math]a+bj[/math] where a and b are real numbers, no j in them.

I'll type out an example:

[math] \frac{1}{2+j} = \frac{2-j}{(2+j)(2-j)} = \frac{2-j}{2^2-j^2} = \frac{2-j}{5} = \frac{2}{5} - \frac{1}{5}j[/math]

>>10069997
ohhhh. thank you. will try this out.

>>10069985
>On a compact set, being pointwise bounded is the same as uniformly bounded

i've got another tough one...
factor the trinomial completely
98n^4 - 168n^2 + 72

so the GCF is 2 i guess,
so we got 2(49n^4 - 84n^2 + 36)

now what...

>>10070006
assuming that you know how to factor quadratics, you would probably be able to factor 49m^2 - 84m + 36. Now just do that, but with n^2 instead.

if y = f(x) = sin(x), does y = 2f(2x+ π/4) = 2sin(2x + π/4) ??

>>10070008
>assuming that you know how to factor quadratics

:c

i'm a brainlet desu, i only can do these once i'm in the rhythm, then i forget the rules completely or apply the wrong ones.

i'm trying but i dont see what you mean

>>10070009
Are those supposed to be the same y? Then obviously not (set x=0).

>>10070016
im supposed to draw the graph of y = 2f(2x + π/4), f(x) being sin(x)

>>10070010
A quadratic comes up when you square something. But you're not limited to only squaring n; you can also square n^2.

So you would write it like this
49(n^2)^2 - 84(n^2) + 36
and now this is just an ordinary old quadratic; only the variable is different. It's a perfect square (you might notice this because both 49 and 36 are squares) and so it factors into (7n^2 - 6)

>>10070021
i think i understand. i'll keep looking over what you said and try a few myself until i get it

thank you very much my friend

What are some good math books that I sould be on the lookout for that aren't currently on the reccomended book list?
The profs where i'm at frequently leave their old books at places where students are free to grab them. A lot of people are also pretty much throwing out their old editions of textbooks.

>>10070018
Then yes, you substituted correctly.

>>10069997
im confused at the point where you got 5 in the denominator here

>>10070038
What is j squared?

>>10070047
yeah i have no idea it's a variable

>>10070051
This is in an EE context, yes? You've just been taught about complex numbers?

>>10070064
this is pre-calculus, I do remember the teacher giving out something like this about j being an irrational number or something but it's not in my book which is 95% of the course. j = e or something?

>>10070068
The whole thing only makes sense if J is the complex unit number, with J^2 = -1.

Normally this is called i, but engineers use j to distinguish it from the symbol for electrical current.

>>10070071
right that's probably my problem im having. thx alot. will report back if i cant solve this thing.

It's really misty or foggy tonight and I find the air quality really refreshing. It's nice and cool, makes me feel really alive.

How would you describe the air quality scientifically and why is it that I find so pleasant?

>>10070071
so i end up with 13 as the denominator and this huge thing on top: −6j^5+27j^4−27j^3+4j^2−18j+18

so now i combine all the j except 1? to leave me with W = a + bj?

>>10070135
>>10070071
i end up with W = 41/13 + 3/13J

If [math](ab)^{n}=1[/math] in a group, [math]n\geq 0[/math]. How do I show that [math](ba)^{n}=1[/math] ?

>>10070147
>How do I show that [math](ba)^{n}=1[/math] ?
What have you tried?

>>10070128
Also why is it that stars appear clearer on nights like tonight? Cold nights, often brought on by mist or fog.

What can you say about the Fourier series for e(x)(even function) and o(x)(odd function) on the domain [-Pi,Pi]?

Can I say that the Fourier series of these two functions are the same(e(x)=e*(x) and o(x)=o*(x)) I am also very sleepy.

If squishing two particles together close enough together creates a blackhole, then does that mean any particle that collides with a piece of dark matter turns into a micro blackhole? I'm guessing that something already has to be on the verge for this to occur, but just the fact that dark matter doesn't interact with the electromagnetic force should make it easier if it's involved, right? Or does it actually make it less good at contributing to (the start of) blackholes than normal matter? I know dark matter should at least be perfectly fine for feeding blackholes that have already formed.

>>10070487
Theoretically, dark matter particles are not fermions, so they can't really collide save under the most extreme compression (not being subject to Pauli Exclusion principle), as they only interact weakly and via gravity, they are extremely unlikely to get close enough to other particles to create a black hole. Photons, similarly not being fermions, can only do this under extreme, likely artificial, conditions, and ya need a lot of em. Any naturally occuring black hole made up of the mass of a pair of particles in such an ultra-rare collision would evaporate instantly. It might happen more often near event horizons of quasars and such where compression is extreme, though I suppose this is likely part of the explanation for quasars being much more energetic than otherwise seems possible.

I have the option of taking a test with either:

a. Having been awake for 21 hours
or
b. Having only had 3-4 hours of sleep, waking up 2 hours before

Which do you guys think would be better for performance? I usually feel like shit when I wake up, particularly after not enough sleep. Yes I am a retard for allowing this to happen.

I really don't understand how to find the truth table of pass-transistor circuits. Pic related for example acts as an AND gate, but I keep feeling I analyze these kinds of circuits incorrectly, and I don't really get how you can tell that Vgs is definitely higher or lower than Vth, which determines whether or not current is flowing.
In the pic Vdd = 3.3V which is a logic 1 and 0V is a logic 0, while Vth = 1V.

>>10070736
(and obviously Vdd and 0V are applied to A and B which are the inputs, while OUT is the output corresponding to either 0 or Vdd - Vth = 2.3V)

>>10070724
I do this somewhat frequently (never for tests though) and I have found that little sleep is always better than no sleep especially with around 4 hours, but 21 isn't too long. The biggest thing about sleeping less than 6 hours is waking up is a bitch, but with staying up longer than 18 hours you have periods where you crash hard and it takes all your effort not to pass out. either way it probably is going to suck but if you sleep then at least your eyes don't hurt

>>10070745
>but with staying up longer than 18 hours you have periods where you crash hard and it takes all your effort not to pass out
What? I've never had that, but I'm a pretty jittery and high strung person. Longest I've got is probably 40 hours and even then I wasn't passing out.

>>10070755
It's not like it is a sure thing, I've had times where I've been up for 36+ hours and felt perfectly fine, but there are definitely times where it creeps up on you, where you can barely keep your eyes open and every time you close them you have to force them open. It doesn't just happen when you stay up for 3+ days, it can occur just as easily if you are barely pushing 20 hours. Plenty of people pass out even though they need to stay awake, and it isn't because they gave up, they just could not physically stay awake.

Not so much a brainlet question but I feel like I'm missing something fucking obvious here and I couldn't get any helpful answers on /wsr/

How do I solve this thing? I know it has something to do with harmonic functions and their mean value property (https://en.wikipedia.org/wiki/Harmonic_function#The_mean_value_property - NOT mean value theorem) and the definition of that property looks suspiciously close to the rhs, but I have no clue if it is indeed a harmonic function nor how to show it

What's an optimal number of reviews per day for an anatomy anki deck with 1000 cards?

>>10070332
Anyone? I recognize the second sentence is wrong but I still don't know what I can say about a Fourier series for even and odd functions around [-Pi,Pi]

Let [math]M=\mathbb{R}\times \mathbb{R}[/math] and define a binary relation by [math](a,b)\cdot (x,y) = (ax,ay)[/math] (associative but not commutative). I'm trying to find out if this has unity element(s). I notice that for [math]x\neq 0[/math], [math](x,y)\cdot \left( \frac{1}{x}, \frac{y}{x} \right) [/math] is a unity, but not from the left. Likewise, [math](1,z)\cdot (x,y)[/math] is unity but not from the right. The definition of a unity element, [math]e[/math] which I'm working with is an element such that for any [math]a[/math], [math]ae = a = ea[/math]. This is supposed to be unique too. So, under this binary operation there is no unique unity however there are unity elements if you strictly consider left and right multiplication?

>>10069841
ur gonna die bro

>>10071270
(a,b) . (x,y) =/= (x,y) . (a,b) unless either (a=x and b=y) or (a=b and x=y).

Anyone have any idea of how I begin to solve this. Usually I find laplace stuff okay but the tau is throwing me off.

>>10071270
>strictly consider left and right multiplication
Suppose "e" were the left identity element, and "f" the right identity element, such that ea=a and af=a, for any a, and f=/=e. Then ef=f and ef=e, which is a contraction.

is an infinite amount of £5 notes worth less than an infinite amount of £20 notes or are they worth the same

>>10069152
what kind of dark past?

>>10071940
>contraction
lmao.
>>10071939
>let t=0
>f(0)=-1
>hmmm I wonder how many of the options fit hmmmmmmmmmm

How are these star trails possible on a spinning sphere?

>>10071950
Thanks anon. Kind of didn't expect it to be so simple.

>>10071970
Righty.
Just to check if you properly verified whether it was -cos or -cosh, you marked -cosh, right?

Show that if μ = -1 is a Floquet multiplier for a Floquet system x' = A(t)x, then there exist a nontrival periodic solution with period 2ω.

I have no clue where to even start.

>>10071941
depends what infinity you're talking about

>>10068736
Chemistry throws you in at the deep end. It doesn’t get much more complex unless you want to go into quantum or some shit.

>>10071965
Space autists stumped?

>>10071965
I'm trash at drawing, but hopefully you get the idea.

pls help

>>10072175
24, I think.

>>10072178
I was actually over thinking. There was an output for each floor (24) so I need 5 bits because 2^5 = 32.

Is the composition of two Lebesgue measurable functions still Lebesgue measurable?

>>10072169
Can't see how that'd produce the same trails.

>>10072192
>Is the composition of two Lebesgue measurable functions still Lebesgue measurable?
What have you tried?

>>10072197
Based what have you tried poster.
>>10072196
When you look at the original, it sorta looks like the stars are spinning around a line coming off the earth, right? That line is the eath's axis of rotation.

>>10072192
Nah.

I'm looking for a university to transfer to from community college with a respectable physics and/or math department that isn't Princeton/Berkley tier. I've got a few ideas, but I'd like some suggestions

>>10072204
>When you look at the original, it sorta looks like the stars are spinning around a line coming off the earth, right? That line is the eath's axis of rotation.
Not when compared to the star trails on the left.

Humans are conscious beings partially controlled by emotions which are necessary for survival.

An artificial intelligence is a conscious being with no need for these emotions, so why do people keep asking stupid questions like "can an AI feel pain?"?.

It doesn't NEED pain, and emotions are not part of consciousness like our ballsacks are not part of consciousness. An AI needs pain like it needs a scrotum.

>>10072226
>An artificial intelligence is a conscious being with no need for these emotions
Why would AI not be concerned with survival?

>>10072221
Also are there any careers, besides maybe fighter pilot, where I could use a physics/math degree and still be somewhat physically active. I don't want to have to get stuck behind a desk the entire workday.

Also, I can weld. Would that be useful for a research group at a university or wherever?

>>10072231
Surely they could use their intelligence to assess if they're damaged or in danger of damage? I imagine they wouldn't need to go "Ah FUCK I stubbed my toe on the table AGAIN"

>>10072240
>where I could use a physics/math degree and still be somewhat physically active
Yeah, you can be a post-doc getting coffee for professors from the cafeteria.

>>10072175
>>10072178
There's 24 floors to be represented by a binary number. How many digits do you need?
Oh look, it's Exercise Number 5.

Basic math question
If I have to divide or multiply in an equation, for example
3x/2 = 2x + 1
Am I suppoused to divide/multiply both the 2x and the 1 or just the 2x?

>>10072325
Both.

>>10072325
Multiply both sides by 2, subtract 2x, solve for x.

>>10072335
>Multiply both sides by 2, subtract 2x
that would be 4x

What is the intuition behind the topological characterization of function continuity?

>>10072342
>intuition behind the topological characterization of function continuity?
Stick to the formal notion, but if you really need something, the autistic "If two points are close, their image should also be close" is the best you'll find.

>>10068703
I saw a thing about a male contraceptive that works by lowering testosterone levels to the point that sperm is no longer produced, but I thought that Low-T has similar symptoms as depression. Anyone have like an infographic of how different levels of testosterone effect men?

>>10072385
google onions boys

I'm retouching partial fraction decomp before getting into partial fraction integrals. This is at the beginning of the chapter so I feel even more retarded. Part a makes sense. Part b is giving me trouble. Where does the numerator in the first step come from?

>>10072417
> Where does the numerator in the first step come from?
Remove the parentheses. Now shorten it.

>>10072421
christ. thank you.

At what point do you have to stop relying on geometric intuition in Math?

>>10072461
Real Analysis.

So I know how the formula to find the # of derangements for a simple set of n elements. But what if you add a condition that the derangements must have, say, element 1, adjacent to its original position?

e.g. {a, b, c, d}, a must be adjacent -> {b, a, d, c}, {c, a, d, b}, {d, a, b, c}
and so on for other sets

Without the condition, the derangements would be 4!*(1-1/1!+1/2!-1/3!+1/4!)=9 to find derangements for a set of 4 elements. With the condition, would the formula be 3!*(1-1/1!+1/2!)=3 because we're now finding derangements of 3 elements with 1 position being able to hold any of the 3?

>>10068703
Can someone please explain this problem to me? I am having trouble solving the problem. When I make the schematic in LTSpice it oscillates for awhile until it reaches a steady state voltage.

I am confused on how to go about mathematically solving this problem using the natural and step responses for an RC circuit.

I am using Vc(t) = Vinitial * e^(-t/2RC) for the discharging circuit and Vc(t) = Vinput - (Vinitial - Vinput)* e^(-t/RC). But when I try solving as if it is sequentially switching, the voltage just decays down to -20 V instead of hitting a steady state equilibrium.

To solve the problem I have assigned values, R = 10,000 Ohms and C = 0.00001 F. The time constants are 0.1 second (R) and 0.2 seconds (2R). This time constants is significantly larger than the half cycle which is 1 ms.

I think I am screwing up my initial condition. I have been using that Vc initial is 10 V because of KVL but I am not sure if that is correct. I am doing that because Vc(0-) = Vc(0+).

>>10072706
Actually, I just realized it depends on the position of the original element. So that formula would be correct for the start/end elements of the set, but for the others it needs to be multiplied by 2 since we have two choices for the adjacent element.

So 3 derangements if we want an element in the derangement to be adjacent to the start/end elements, and 6 derangements for the others. Is that right?

>>10071088
anyone

>>10072721
Stop trying to do response. The question is obviously asking for the approximate steady state solution. Otherwise the value of CR would matter in determining how long it takes to reach it and the (ultra) exact value it has.

So what do we know about the steady state. Because CR>>T, we know C doesn't charge up appreciably so assume that the voltage across C is constant. But current flows so the net charge gained in one half cycle must equal the charge lost in the other half cycle or the voltage would drift. Since the duty cycle is symmetric, this means the current must be the same in magnitude and flipping sign.

>from the "current must be the same and flipping sign"
Current in the positive cycle = [positive cycle voltage out - diode drop (0V?)] / 2R
Current in the negative cycle = [negative cycle voltage out - diode drop (0V?)] / R

positive cycle voltage out / 2R = - negative cycle voltage out / R
positive cycle voltage out = -2*negative cycle voltage out

>from "voltage across C is constant"
positive cycle voltage in + voltage of C = positive cycle voltage out
negative cycle voltage in + voltage of C = negative cycle voltage out
positive cycle voltage in - negative cycle voltage in = positive cycle voltage out - negative cycle voltage out
peak to peak voltage in = peak to peak voltage out

20V = positive cycle voltage out - negative cycle voltage out = -2*negative cycle voltage out - negative cycle voltage out = -3*negative cycle voltage out
negative cycle voltage out = -20/3 V = -6.667V

-2*-20/3 V = positive cycle voltage out = 40/3 V = 13.333V

not sure where to put this crit multiplier in figure B, where can I put it?

>>10073076
nvm, took the time to guess the value of y then broke that down to see where it was off.

>>10070332
>>10071139
You should have a formula for the coefficients of the Fourier series. Now use the fact that the integral of an odd function over a range symmetric about zero, such as from -pi to pi, is zero. Short story short: the even function is the sum of only even terms (cosines) and the odd function is the sum of only odd terms (sines).

what the fuck how do i do this with numerical methods

Could someone PLEASE explain to me how come the electric potential is at its highest near the charge that creates the field? Shouldn't it be at its lowest, considering that the field is stronger closer to the charge, the kinetic energy should by the highest?
For example if you have a positive charge that creates a field, and then put + charge (A) 1cm away, and + charge (B) 5 cm away, A would accelerate much faster than B would cause it would be repelled the most?

>>10073490
A what?
>Could someone PLEASE explain to me how come the electric potential is at its highest near the charge that creates the field?
Depends on the signs and sheeit. Positive repels positive and all that jazz.

>>10073490
Potential is relative. The difference in potential (energy per unit charge) between any two points is unambiguous, but the choice of the zero reference is ... well, a choice.

But there's only one choice which really works out in practice, and that's infinity, i.e. any point infinitely far from any charges has zero potential, and everything else is measured from that.

Otherwise, you'd have to explicitly choose a zero reference for every situation. You can't choose a point coincident with a charge, as that gives you infinite potential. So you'd have to choose how far away to make the zero reference. And in the situation where you have more than one charge, you'd have to choose which one.

>>10073557
I'm sorry I'm incredibly stupid but I really don't understand what you're saying. Could you please please explain to me the example I just mentioned in >>10073490 but in more simple words ? All of this is so hard...

is this a synchronous sequential circuit?

>>10073610
For C. I know what a, b, and c are.

>>10072461
hypotenuse length, [math] n \rightarrow \infty [/math]

a+b or [math] \sqrt{a^{2}+b^{2}} [/math] ?

>>10073621
sqrt(a^2+b^2).
Can't really show it in Euclidian tho.

>>10072342
Well, over metric spaces it is equivalent to the usual definition, so i'd take that as pretty intuitive. otherwise, as other anon said, open sets roughly correspond to points that are close together, so you could think of it as "in the image, if points are close together, then they were close together in the domain"

if i have two numbers, say 23 and 30, how can i tell what percent 23 is to 30, either the full percent or the remaining percent.

>>10073797
>anon is literally asking how to divide
What the fuck.

>>10068703

I'm doing some undergrad research trying to elaborate some quality indicators, just some government data stuff.

So i have some data that ranges from 0.00 to 10.00 and i'm going to divide it by values that range from 2000.00 ish to 4000.00 ish...

Thing is, i want to normalize this stuff so my indicators can range in between 0 and 1 or 0 and 10... any suggestions? Were do i even start

>>10073806
Option one: divide the indicators by some large number.
Option two: take logarithms.

>>10072721
>I am using Vc(t) = Vinitial * e^(-t/2RC) for the discharging circuit and Vc(t) = Vinput - (Vinitial - Vinput)* e^(-t/RC).

It's not charging from 0.

Let the last voltage of the capacitor in the negative cycle be Vnl
Let the last voltage of the capacitor in the positive cycle be Vpl

>negative cycle
Vc(t) = -10V + (Vpl+10V) * e^(-t/RC)
>positive cycle
Vc(t) = 10V + (Vnl-10V) * e^(-t/2RC)

[math]\Delta Q = \int_0^{1ms} \frac{-10V-(-10V+ (Vpl+10V) * e^{-t/RC})}{R} dt + \int_0^{1ms} \frac{10V -(10 + (Vnl-10V) * e^{-t/2RC})}{2R} dt = 0[/math]
[math]\int_0^{1ms} (Vpl+10V) * e^{-t/RC} +\frac{(Vnl-10V) * e^{-t/2RC}}{2} dt = 0[/math]
[math] -RC(Vpl+10V) * e^{-1ms/RC} -RC(Vnl-10V) * e^{-1ms/2RC} +RC(Vpl+Vnl) = 0[/math]
[math] -(Vpl+10V) * e^{-1ms/RC} -(Vnl-10V) * e^{-1ms/2RC} + (Vpl+Vnl) = 0[/math]
Taylor series expansion since 1/RC<<1
[math] -(Vpl+10V) *(1-1ms/RC) -(Vnl-10V) * (1-1ms/2RC) + (Vpl+Vnl) = 0[/math]
[math] (Vpl+10V)*(1ms/RC) +(Vnl-10V) * (1ms/2RC) = 0[/math]
[math] 2(Vpl+10V) +(Vnl-10V) = 0 \\ -10V = 2Vpl+Vnl [/math]

Vpl = 10V + (Vnl-10V) * e^(-1ms/2RC) ~= Vnl + (Vnl-10V)(-1ms/2RC) ~= Vnl
since Vpl~=Vnl ~= Vc, 3Vc = -10V and Vc = -10/3V = 13.333V
so Vop = 10V - Vc = 10 - -10/3V = 40/3V and Von = -10 - -10/3 = -20/3V = -6.667V

How do I go about proving that the set on picture is same as [0, inf)? I get that in order to prove that two sets A and B are equal I have to first prove that every x \in X is also an element of Y and every y \in Y is also an element in X, but I'm having a really hard time writing an actual solution down.

>>10073637
nope

>>10073888
i'm so glad i finished that shit :3

>>10074087
Correction: meant to type "...in order to prove that two sets X and Y are equal..."

>>10073888
i'm so glad i'm already done with that shit :3

>>10074087
Let the set in the picture be written as A.
Assume that, for some real x>=0, x is not an element of A. By Archimede's axiom, let m be some natural larger than x. Let s be a natural such that s>x and r>x implies r>=s. Then, x is in the interval [s-1, s], contradicting the hypotheses. Consequently, all reals bigger than 0 are elements of A.
By the by, the interval only works for starting the naturals with one, which is what decent people do, but some niggers here might insist on zero.

>>10073610
hello anybody? :(

How do I make sure I retain and comprehend material I read. I fucked up in my teenage years living on this god forsaken website reading trash and shit posts and while I can interpret meaning from rudimentary English, I fear more advanced material is flying over my head. How do i fix myself?

>>10074376
Note down every theorem and definition you read.
Reread proofs until you feel confident you can explain why it's true to someone else.
Solve end of chapter exercises.

I've been stuck at a problem for an of hour or so, can someone give me a hint on how to solve this. It's basic calculus.

A sphere with radius r is partially filled with water. The depth of the water in the centre of the sphere is k. How much water is in the bowl?

Now, to me, this seems like it should be a solid rotation of the graph y = sqrt(r^2-x^2)-r around the y-axis. A simple trigonometric consideration gives that the width of the water along the x-axis is w = sqrt(r^2 - (r-k)^2). So the interval for the integral should be 0 to w. Rotation around the y-axis should here follow the cylindrical shell formula V = 2pi integral of x(g(x) - f(x)) dx from a to b. Just putting in the values and integrating gives me the wrong value. (I do not know the answer, but I can check if I've got it right.)

Pic related, it's me.

>>10074390
>The depth of the water in the centre of the sphere is k.
Like this?

>>10074402
No, that's not how I understood it. It's the depth of the water at its deepest point, I think.

>>10074406
Right, whatever.
Imagine you have the circle. Now, if I give you a height, you can make me a function that gives me the area of the circle at that point, right? Just use pythagoras a few times and the circle area formula. Now, if I take that area function, and integrate it, I'll get the volume, right? So just do that.

>>10074424
Did you mean
>imagine you have the sphere
and
>the area at the top of the sphere
?

If not, I didn't understand. Thanks for trying, it might be that it's really late.

>>10074432
Like pic related. I set a height, and the circle inside the sphere at that height has an area.

>>10074435
Right.
Well, the height as a function of radius is y = sqrt(r^2 - x^2)-r, so the radius as a function of the height will be the inverse: x = sqrt(-y^2 + 2*r).
Now, a formula for that circle area at a given height would be pi*x^2, which gives A = pi(-y^2 + 2*r). Integrating that over k should yield the right volume, agree?
Thanks for your help

I need help with this Real Analysis problem.

Assume f is upper semi continuous (usc) and bounded on [a,b]. Show there exists continuous f_k on [a,b] such f_k is a decreasing sequence of functions that converge pointwise to f. I was given a hint. First show that there are usc step functions.

The problem is in the textbook Measure and Integral second edition by Wheeden and Zygmund. Chapter 4 problem 9b on pg 77.

Thanks

>>10074472
>I need help with this Real Analysis problem.
>Assume f is upper semi continuous (usc) and bounded on [a,b]. Show there exists continuous f_k on [a,b] such f_k is a decreasing sequence of functions that converge pointwise to f. I was given a hint. First show that there are usc step functions.
What have you tried?

>>10074473
I understand this as a construction problem. I know that every function can be described as a limit of simple functions.But to show its decreasing is escaping me.

>>10074472
Take a random point, say "a". Let [a-k, a+k] be a neighborhood around a. By the definition, for some c, f(x)<=c. d be min c. We define g_k(x)=f(x)+d. g converges pointwise, decreases, and is continuous (you should be able to solve this on your own).

>>10074510
My finger slipped, g_k(x)=d.

>>10074510
Cool thanks for the start.

How can I be certain I've never sustained a stroke?

I am wondering how to get the other reference angle for this problem.
I used the v^2sin(2theta) = 32d to get the angle 39.2 but that is not enough to pass the wall. The correct angle is 50.8, but I am unsure how to get that reference angle. Any help would be appreciated.

>>10074671
when you use the inverse sin function you are getting an angle in the range -90 < x_1 < 90, but a second x value in the period exists such that sin(x_2) = y, it should be obvious how to find this second x value given the first if you draw out the unit circle.

you could also make the argument that the two theta values are complimentary, but the first method is probably easier to demonstrate.

>>10074736
thanks anon, go the solution.

>>10073383
bump, this is hard

>>10069841

Update. The pimples went from red to blackish. Also, my right eye is red.

>>10072894
>The question is obviously asking for the approximate steady state solution.
You are right now that I think about it. There is no "hard switching" on, the circuit is hooked up to the square wave the entire time, one could assume it was there for an infinite amount of time.

>>10073888
>It's not charging from 0. Let the last voltage of the capacitor in the negative cycle be Vnl. Let the last voltage of the capacitor in the positive cycle be Vpl
Great way to think about it, thanks! I appreciate the time you took to type and solve that.

>current flows so the net charge gained in one half cycle must equal the charge lost in the other half cycle or the voltage would drift
Is this just because Q = C* V? And since the voltage is symmetric Qpos = - Qneg, so there is no net charge?

>this means the current must be the same in magnitude and flipping sign
I guess I am confused here. Is this because i = C *(dv/dt), so i = (Q/V) * (dv/dt)? Wouldn't the current be different because there are two different resistances drawing current at different values? I know in steady state the DC component of the circuit should average out to 0. That appears to be at least some what the case in >>10074114 anon's work, where the currents will be different but overall the charge is still 0. I know current is the "rate of charge flow." So it is still the same amount of charge but it is flowing at two different rates?

>>10069519
Optimized.

>>10069862
Optimized.

>>10069985
Optimized.

>>10070026
Optimized.

>>10071970
Optimized.

>>10074455

>>10074919
(Optimized.)

>>10074908
>so there is no net charge?

There's no net ~change~ in charge. Charge is voltage (times C) so if the voltage is constant then the charge is too.

>Is this because i = C *(dv/dt), so i = (Q/V) * (dv/dt)?

No, it's because the voltage isn't changing in each half cycle (approximately), so the current isn't changing either. ∆Q = ∫i(t) dt = i_positive_cycle*1ms + i_negative_cycle*1ms = 0 and so i_positive_cycle = - i_negative_cycle

>Wouldn't the current be different because there are two different resistances drawing current at different values

The voltages across the resistors are different so it cancels out. (20/3V) / 2R = - (-10/3V) / R

My professor somehow graded my exam, gave it back to me, and apparently never entered my grade into her records and is asking people for the exam papers back. I trashed a bunch of papers two days ago and the exam was among them. What do?

>>10074945
Tell her she already took your paper and you got 100%

>>10074945
>I trashed a bunch of papers two days ago
y u do this?
>What do
Hire a hobo to go trash digging.

Looking for asymptotic value.
Lets say I have an equation like 4/x^2 + 1/log(x) +7

What would be my big O? Can it be the constant since the other two values are decreasing?

>>10069139
R=U/I

if i hypothetically were to purchase a nuclear warhead from isis on the deep web, what would happen if they caught it at customs?

>>10068703
Hello, I am not sure if this applies for /sci/ but I have a problem here in pic related.

The formula is different than the one I found in my book and I do not understand if the term in the numerator is simply the expectation at time t of D_(t+k) or something else.

Moreover, is it correct to say that the answer to point 2 and 4 is that there is no effect because the announcement is made in t_2 and I am juding the value at time t?

Thank you and if you want any clarification, I am here.

>>10075104
I am retarded and I forgot the pic of course.

>>10072750
Please respond

Why do when I leave a bottle of tap water stay for a while it develops a nasty odor and if it's mineral water such odor develops after way more time or doesn't at all? Tap water should be better than bottled, but it gets stinky. Please note that it doesn't matter how old are the pipes of the building. This has happend from old and new piping.

>>10075080
Send it back its original sender

>>10075056
Any monotonic decreasing function is O(1). Big-O notation is normally used in contexts where functions are monotonic increasing (at least asymptotically).

>>10075151
>Any monotonic decreasing function is O(1).
[citation needed]

>>10074858
I've done this before

you just write up the time-independent schrödinger equation as a discrete function (i.e. what does differentiation look like for a discrete series of values?) and then formulate it like a matrix, then solve by diagonalizing using a numerical routine

It's not hard if you just go through it step by step

if 2 dudes with hulk comic book level strength lifted each other up at the same time, could they theoretically start levitating?

>>10075210
how do you formulate it as a matrix?

>>10075219
Yes, given enough initial force, they would leave the ground and enter orbit.

>>10075186
Ah, the snide nitpicker strikes again. It should have been "... any *non-negative* monotonic decreasing function". As if the distinction would actually matter in any context where big-O notation is actually used.

When people think of time, they tend to associate it with cause and effect. For example, when they think of time going backward, they imagine something like someone dropping/cracking an egg in the past-to-future flow reverting into that egg coming back together and flying back into their hand in the present-to-past flow. But is that really true? Isn't it conceivable that time itself could flow backward without events or cause and effect being changed?

Chem anons please help...
I'm studying the way salts behave in water (acidic, basic or neutral) and got stopped by this chemical: (NaOCl)
Now I know it's a basic salt but how can I come to this conclusion knowing that the way it ionizes in water is confusing?
It could be
NaOCl + H2O = (NaO+) + (Cl-)
Where NaO+ is a strong conjugant acid and Cl- is a weak conjugant base of the strong acid HCl, thus making the solution acidic (acidic salt)?
Or NaOCl + H2O = (Na+) + (OCl-)
Where Na+ is a weak conjugant acid of the strong base NaOH and OCl- is a strong conjugant base, thus making the solution more basic (basic salt)?

>>10075186
>CS majors are this retarded

>>10074087
Let U be the union in your picture

Clearly 0 is in U, and suppose any smaller number, call it -a<0, is in U. Then there exists some natural such that n-1<=-a. ie: n<=a+1 <1. Contradiction, so clearly 0 is the smallest such number. In particular, since [0,inf) contains all numbers bigger than 0, then U is a subset of it.

Now suppose x is in [0,inf). By archimedean principle, there exists an n integer such that x<=n, and by well ordering principle, we can choose n minimally with that property. It is easy to show that x is in [n-1,n], and hence in the union

>>10074871
standard brain cancer symptoms

>>10074919
>>10074916
>>10074915
>>10074914
>>10074912
>>10074910
this is so epic

Since I'm taking stats this term, can someone explain what exactly a standard deviation measures, and how it differs from variance?

if you're writing a proof, is it valid to say something like "compute both sides" if you have a lengthy string of multiplication operations to do?
i.e. say you're doing an induction and you wind up with something like this (where n and k are positive naturals)
3(n+1) = 3n+(3k/k) - assumption
3n+3 = 3n+3 - compute both sides
is that generally acceptable, or is it better to write out every little operation?
I'm wondering because I got lazy with one and just plugged the damn thing into Symbolab because I didn't want to spend an hour multiplying everything out one step at a time

>>10073621
if b and a tend to infinite and the small sauqares are allways the same size then it is the same RETARD.

>>10076125
>is it valid to say something like "compute both sides" if you have a lengthy string of multiplication operations to do
Depends on who's marking your I don't think anyone will actually complain about you skipping algebra.

>>10075893
The standard deviation of a data set is the average amount that each value differs from the mean. It is sometimes referred to as a measure of the spread of the set.
For example let's suppose you have ten dogs and they have an average weight of 50 lbs. If every dog weighted exactly 50 lbs you would have a standard deviation equal to zero. If you had several great danes and and chihuahuas the standard deviation would be quite large.
I encourage you to examine the formula for standard deviation. You will see that you are really just taking another mean; the average of the quantities x - μ to be precise.
Don't worry about variance for now. Just think of it as another, less intuitive measure of the spread of a data set, and that you of course can easily get the standard deviation from it by taking its square root. Variance is used quite a bit on theoretical probability theory so if you stick around you will become more acquainted with it.

>>10076267
>the average of the quantities x - μ to be precise.
Let me rephrase that:
The average of the quantity x - μ, where x is a value of the data set and μ is the mean

>>10076125
>if you're writing a proof, is it valid to say something like "compute both sides" if you have a lengthy string of multiplication operations to do?
For what purpose would you assume 3(n+1) = 3n+(3k/k)? If you assume something, and then derive something you know to be true - in this case 3n+3 = 3n+3 - you haven't actually proven anything.

>>10076287
that's not the point of the question, it's just a random example I came up with to demonstrate what I was asking

>>10068703
https://youtu.be/HEXWRTEbj1I

>>10076293
>that's not the point of the question
What is the point?

>>10076267
>>10076274
All those words and you didn't even get the formula right.

When I eat/fap/exercise/breathe am I supposed to feel (what I can only assume is) the dopamine release in my head is that normal?

>>10076440
>breathe
What? Othewise yeah.

>>10076443
Yeah when I inhale I can feel the same sensation, just less intense, right behind my forehead. I've never really felt any of that before until recently

Ring Theory books recommendations?

books recommendations on Numerical analysis with applications ?

>>10076392
I never stated the formula nigger

>>10076274
> The average of the quantity x - μ
Nope. It's the root-mean-square value of x-μ, i.e. the square root of the average (mean) of (x-μ)^2. The average of x-μ is zero.

>>10076453
http://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering#Numerical_Analysis_and_Methods

Can someone help me with #5.42? What would the equation be?

>>10068703
Can someone with a course hero account please send me a couple of documents to a throwaway email?

Is this real?

>>10077735
are you retarded?
you can clearly see the two pieces grow as they move

>>10077743
The pieces are cut into 1, 2, 4 and 6, and after they are moved, there is no room for #1. They do not change size.

Got a dumb, theoretical question I thought about while working on homework for an Astronomy class today that perhaps some smart anons may know an answer: Assume that Earth or an identical Earth-like object was somehow tidally locked with the Sun, would the other half of this Earth-like object that never directly faces the sun still be habitable?

My first thought was yes, but then I thought about how temperatures drop during the night time, and perhaps without the Sun ever heating that side, it wouldn't be as habitable, although now I wonder if the greenhouse effect completely invalidates this idea. Let me know what you think, anons!

If I have a surface defined by the single patch σ(u,v)=(u,v2) and a pathλ↦u=λ,v=λ am I right that the arc length from λ(0) to 4 is about 16.819 and the metric tensor for this surface is [math]\pmatrix{1 & 0\\0&4v^2}[/math]?

>>10077787
[math]Or should it be \bmatrix{1&2t\\2t4t^2}[/math]

>>10077787
Or should it be [math]\bmatrix{1&2t\\2t4t^2}[/math]

>>10077787
Or should it be [math]\pmatrix{1&2t\\2t4t^2}[/math]

>>10077787
Or should it be [math]\bmatrix{1&2t\\2t&4t^2}[/math]

>>10077787
Or should it be [math]\pmatrix{1&2t\\2t&4t^2}[/math]

>>10074940
>There's no net ~change~ in charge. Charge is voltage (times C) so if the voltage is constant then the charge is too.
>No, it's because the voltage isn't changing in each half cycle (approximately), so the current isn't changing either. ∆Q = ∫i(t) dt = i_positive_cycle*1ms + i_negative_cycle*1ms = 0 and so i_positive_cycle = - i_negative_cycle
Sorry my bad anon, so since the voltage in the capacitor is basically not changing between each half cycle there is no change in the charge in the capacitor, correct?

>Current is constant
This is because i = C *(dv/dt) where dv/dt is the changing voltage in the capacitor. Since the voltage is not changing, the current isn't changing either. Right?

So potentially energy increases an object's mass and separating two massive objects increases each of their potential energies, correct? Are there any really strange orbits that are possible specifically due to this?

anyone know why adding two nitriles increases the rate so much? CN isnt even that good of an EWG

What percentage of children who show early signs of autism go on to fully recover? Do they even keep statistics on this?

>>10077777
The night side would be cold, but wind currents will keep it much warmer than you'd expect.

It still won't be habitable because windspeeds will be insane, and a lack of sunlight will prevent photosynthesis.

If lots of animals have unexpressed viral DNA in their genome, does that mean a mutated cell could start producing viruses?

>>10077777
Checked.
It would be the only habitable part desu. People would live in the places where it's always dusk or something.

>>10077787
Pls

How do I do part a? My guess is that since f is unbounded, for any M we can find some x in [a,b] s.t. f(x) > M. So then I can define the subinterval [a,x] or [x,a] which f would be unbounded on. This seems logical to me, but my mathematical maturity is not very strong, and plus the question states some different interval which sort of confuses me.

I'm trying to keep my keyboard rail locked into position when I push it all the way back, and when it's all the way out.

Can I stick/glue some magnets onto it to make it so it holds itself at each position? I suppose I could just make it level or inclined, but I'd rather get this to work, seems better.

I've stuck some hard drive magnets on it, but they do not appear to be strong enough. I know the force weakens greatly with distance, but I figure it should still be enough?

Any ideas? didn't know if it was /sci/ or /diy/

>>10078617
I've ended up spending far too much on this rail I think, coulda just bought a good one to start.

Turns out magnets are cheap, so maybe the real question is how much better would stacking 2-3 magnets be than one hard drive magnet?

And circles or cubes...

>>10078575
If there is such at least one x as the one you mention, then since x belongs somewhere on the interval, the only three options are that [math]x = \frac{a_{0}+b_{0}}{2} \vee x < \frac{a_{0}+b_{0}}{2} \vee x > \frac{a_{0}+b_{0}}{2}[/math]. In the first case, x is in both intervals, in the other two cases it's clear that x will be on at least one.

The question is rather trivial, you can analyze the contrapositive to check it. Assume f is bounded in both intervals. Then there is an upper/lower bound for f at both of the intervals, and you can pick the max/min out of those respectively to get a "global" upper/lower bound. Thus f is bounded in the entire interval.

>>10078084
pls respond

Following up from a previous response, for part b I said to continue cut the interval in half, check if its unbounded. If it isn't then take a sub 0 or b sub 0 as a bound while keeping a sub 1 or b sub 1 as the other bound. Then I applied the nested intervals theorem. Does this suffice?

I'm trying to diy a camera using a single photodetector and some mirrors like the viking lander. So I'm trying to to figure out what signal to noise ratio is achievable in different idealized lighting conditions to figure out if what I want to do is possible at all. Which means I need some way of determining just how much power is incident on a single pixel. So is there a way to figure out much light a diffuse white reflector radiates (?) in various ambient light conditions like office, outside sunny, outside cloudy?

You don't have to give the answer, but can you tell me if the answers to both are the same?

How the fuck do I reference shit in a math paper? When im discussing things I can do it fine, but what about definitions and theorems I get from textbooks?

Definition 3 (Group). A group is a thing with things that thing [Tit48].

Definition 3 (Group [Tit48]). A group is a thing with things that thing.

Titer defined a group as [Tit48]:
Definition 3 (Group). A group is a thing with things that thing.

I think its common to just leave it out, but this is for a class paper/project, not a real paper, so id rather just reference everything I can.

>>10078781
no

>>10078929
I wrote some code to bruteforce the answer before you replied and I got the same answer for both (.5) so I don't know if I wrote the code incorrectly or if you're wrong.

>>10078941
>I don't know if I wrote the code incorrectly or if you're wrong.
I mean no, I cant tell you because I couldn't be bothered to calculate it.

>wrote some code to bruteforce the answer
you can just brute force it on paper. Might as well show you since im this invsted in this now.
(12,23,24) / (12,13,14,23,24,34) = 0.5

(12,23,13) / (12,13,14,23,24,34) = 0.5

>>10078927
What I did in my maths papers is:

Definition 3 (Group) [p. 69, Tit48]. A group is a thing with things that thing.

However, I'm sure that, as long as you're vaguely consistent, it'll be fine. Adding page numbers will make it seem more professional, even if the source is just some online notes.

I gotta do a 700-1000 word scientific literature review, how long would it take me? I assume it shouldn't take too long (30 references required)

>>10079060
>I gotta do a 700-1000 word scientific literature review, how long would it take me?
Why don't you try it and find out?

>>10079072
Well I am, but I'm seeing if anyone has a general idea so I can plan around it. Hoping to complete it in about 3 hours but I'm not sure if its realistic

>>10078927
A group is a set with a complete associative operation.

>>10078745
pls help, here is anime girl

>>10078745
>If it isn't then take a sub 0 or b sub 0 as a bound while keeping a sub 1 or b sub 1 as the other bound
What do you mean by this? Can you explain it properly?

>>10079162
I'm having a hard time putting it in mathy terms. But basically since f is unbounded on [a sub 0, b sub 0], it has to be unbounded on at least one of the intervals when you cut [a sub 0, b sub 0] in half.

So you repeatedly check to see if f is unbounded in that interval (not really sure how to do that), and if it isn't then just throw away one of the bounds and replace it with one of the original interval's bounds, and using the same logic before, f will be unbounded in that interval. Repeat this process.

>>10079108
Thanks!

I feel like I'm missing something in this proof... Any hints?

>>10079215
Forgot to screenshot the top part of the statement,
>Given V is a subspace of Rn, we define V⊥ as the set of vector orthogonal to ever element in V.

>>10079169
I'm still not sure I understand your argument, but here's what a more formal argument would look like.

Let [math] I_n [/math] be a closed interval and [math] f: I_n \rightarrow \mathbb{R} [/math] a continuous function. If [math] f [/math] is unbounded on [math] I_n [/math], it must be unbounded on at least one of [math] I_n^{(0)} [/math] (the first half of [math] I_n [/math]) or [math] I_n^{(1)} [/math] (the second half of [math] I_n [/math]). Define [math] I_{n+1} [/math] to be [math] \cases{I_n^{(0)} \text{ if f is unbounded on } I_n^{(0)} \\ I_n^{(1)} \text{ otherwise}}[/math].
As [math] f [/math] is continuous on [math] I_n [/math], so is its restriction to [math] I_{n+1} \subset I_n [/math], and by the construction of [math] I_{n+1} [/math], [math] f [/math] is unbounded on [math] I_{n+1} [/math]. Now, by induction, this defines a sequence of nested closed intervals [math] (I_k)_{k \in \mathbb{Z}_{\geq 0}} [/math]. You can apply the nested interval theorem to this sequence.

>>10079226
thanks anon, that's what I had in my mind but I just could not formalize it.

If do people expect that an AGI will never change its value function when humans do it all the time? I guess I understand the argument for why an AI wouldn't, but but was wondering more why humans do. Is it because humans never really have well defined values and act on impulse?

I am 27 and soon done with a master's degree in physics, is it too late to go into a phd?

Had to spend a couple of years working after I took the bachelor's degree because of life

Why do dust particles float around in the air? I was standing near my window and the sun was shining in such a way it was highlighting the dust in the air. I stood a long time watching the dust, some particles were moving upwards, some down, some side to side. Why? How?

HOW DOES THIS SHOW THE LAW OF COSINES

>>10079300
High surface area compared to mass means they are easily moved by air flow. Throw in some tiny but not negligible charge and you have it I guess

How do I do pic related? I did it with 1/x^8 but I don’t think that works with this.

>>10079220
Imagine it in a geometrical setting to grasp an easy intuition.

Imagine some random plane (vector space V) in the R^3 space, that contains the zero vector. What is the set of vectors that are orthogonal to every single vector of the plane? That would have to be the line generated by the normal vector of the plane, right? By definition the normal vector is perpendicular to the plane, so as long as it goes through the origin it will generate a subspace that fits your condition. Let's call it vector space V'. Notice that the dimension of the line will be just 1.

Now, consider any line of the plane V that goes through the origin (subspace U). Evidently, that will be a proper subspace of the plane. Of course, since U was an element of the plane, all of its vectors will still be orthogonal to N. However, notice that any vector of U can be considered as a normal vector to a plane. Let's build such a plane and call it U', then. Since U will be orthogonal to every element of U' by definition, then we know that V' should be in it, as long as the new plane goes through the origin. But if U' is a plane that goes through the origin, it's definitely a vector space, right? And now it has dimension 2. AND it also strictly contains V'.

The inclusion comes from the fact that any vector that was orthogonal to V immediately had to be orthogonal to any subset of V. More specifically speaking, a vector subspace of V.

>>10079356
>since U was an element of the plane, all of its vectors will still be orthogonal to N
since U was an element of the plane, all of its vectors will still be orthogonal to V'

Changed the notation halfway through so of course I fucked that up.

>>10079284
Does this geometric phenomenon have a name?

>>10079364
that IS a stupid question

>>10079364
https://en.m.wikipedia.org/wiki/Banach–Tarski_paradox
>>10079368
Brainlet.

Kindergarten level physics here.

So we got a satellite (describing a circular orbit around the Earth) whose mass is 1000Kg and whose period is 1.5 hours.

In order to get the radius of its orbit, it's pretty obvious to me that I should just use Kepler's third law, but this particular problem doesn't give you the mass of the Earth so you can calculate Kepler's constant, which leads me to believe that they want you to find the radius in some other way with the data they gave you, but I don't there is an alternative way, right?

>>10079364
It's called "trolling".

Do you think there are any particular areas of mathematics today that genius artists of the past with obvious great visual memory could truly excell in?

>>10079547
You need to know either the mass of the Earth (5.9722e24 kg) or its standard gravitational parameter (μ = G*M = 3.986e14 m^3/s^2), or some information from which those can be derived. The mass of the satellite is irrelevant.

>>10068703
Can a rational number like 4/25 be considered a perfect square or is it only reserved for integers?

>>10079663
The terms "perfect square" or "square number" refer to the square of an integer. I'm not aware of a specific term for a rational whose numerator and denominator are both perfect squares.

could you get close enough to the sun to hear it?
a stupid question, but not one I have the faintest idea how to find the answer for.

Consider a complex separable Banach space [math](V, || \cdot ||)[/math] and a countable set [math]B := \{ \varphi_i \} \subseteq V[/math].

1) Is it correct that [math]B[/math] is a basis for [math]V[/math] iff any [math]v \in V[/math] can be written as a linear combination of its elements, i.e.
[eqn]v = \sum_i a_i \varphi_i,[/eqn]
[math]a_i \in \mathbb{C}[/math], where (in the infinite dim. case) equality means convergence with respect to the norm (I assume uniform convergence? not sure about this part either).

2) If we already know that [math]B[/math] is a basis (i.e. it is given to us), can we already conclude that it is complete in [math]V[/math]? That is, is the basis of a complete space always complete itself?

I ask this because I've had physics lectures where we find the spectral decomposition of a (sufficiently nice) self-adjoint operator, but then go on to further show that the eigenbasis (countable) is complete in the whole Hilbert space. But doesn't the fact that the eigenbasis is a basis already imply that it is complete?

>>10079364
YEAH....first one is not even 25, it is way less (do the math). and the second one would be exactly 25. very retarded image. kys
>>10079424
not even related. infinitesimal IDEAS bullshit =/= real life

>>10079663
>Can a rational number like 4/25 be considered a perfect square or is it only reserved for integers?
It's an element of [math] \mathbb{Q}^2 [/math].

>>10080111
5*5=25

>>10079364
look all the area in orange is missing my retarded frined. that is the """""trick"""""

>>10080131
yeah the first one is way less than 25 and is in no way 5*5, the secon ne is though.

>>10079312
Because there are 4 ab triangles which =2ab in area taken from the squares of a b and c.

>>10068703
What is the best possible way to make use of this information? The test is tomorrow. I'm largely prepared, but this came out today.

Problem 1 corresponds to section 13.1 (Vector Functions).
Problem 2 correspond to section 13.2 (Derivatives & integrals of Vector Functions).
Problems 3 and 4 correspond to section 13.3 (Arc Length, Curvature, T-N-B).
Problem 5 corresponds to section 13.4 (Velocity & Acceleration in 3-D).
Problem 6 corresponds to section 14.1 (Multi-variable Functions).
Problem 7 corresponds to section 14.2 (Limits & Continuity).
Problems 8 and 9 correspond to section 14.3 (Partial Derivatives).
Problem 10 corresponds to section 14.4 (Tangent Planes and Differentials).

Why can't cancer be treated the same way as venomous snakebites? That is, graft cancer tissue into a horse's body then harvest the antibodies it creates.

>>10080210
Much prayer.

>>10080210
Skim through your notes on those chapters and refresh you memory on anything your hazy on.

>>10068703
sorry if its off-topic but i am having a test to determine my "psychology " for a scholarship soon and i am afraid of it. They told us that there would be trick questions and people with unstable/labile psyche won't make it. Can anyone give some advise or a link where i can train for something like that?

4+(x+2y)i=x+2i

>>10080639
it's literally just a linear system of two equations with two variables
you only need to know that two complex numbers z and w are equal iff re(z)=re(w) and im(z)=im(w)

Why do we study ratios in calculus? All of these nice theorems fall out from limiting behavior of certain ratios. Why is it natural to compute these ratios?

Do you get similar results when looking at the limiting behavior of some other combination of [math]\Delta f[/math] and [math]\Delta x[/math]? Can we generalize to spaces without nice algebraic structure?

Would there be any benefit to considering a fabric as a state of matter?

>>10080658
>two equations
>two variables
I'd understand either of those individually.

>>10068703
what is an concentration inequaity?

What's with the Google translate responses? Why when you type some sentences with spaces between letters it answers with an intelligent response?
>pic related

>>10068703
I'm trying to do curve fitting on a graph that represents signal strength in function of distance to the source so it is a descending logarithmic curve I suppose.

What curve does best describe this logarithmic descent? Is it Log10 or ln based, or something else?

>>10080901
> What curve does best describe this logarithmic descent? Is it Log10 or ln based, or something else?
There's no difference other than the slope. All logarithmic functions are identical up to a scale factor. log10(x)=ln(x)/ln(10), ln(x)=log10(x)/log10(e).

Logarithmic plots are usually base 10 (typically dB).

>>10080901
Literally just calculate which logarithm minimizes squares.
Alternatively, take a random logarithm of all the values, do a new scatter plot with these, do a linear regression on this new data, you should have something like a log x + b=y. Now pass the a so you have log x^a +b=y.

>>10069139

>>10069139

Jesus, grab a fucking book of Mechanical Engineering. Start with Material Science. It generally focuses on steel.

Understand stress-strain relation. Yield strenght is what you are looking for.

>>10080984
My mistake, don't pass the a to the x, pass to the base.

>>10078084
bls

>>10081070
>>10080944
Many Thanks!

how do i use my imagination, am i supposed to concentrate a certain way, how the fuck do people get to see images in their head and i dont. fuck this gay earth

In the (rudimentary) education on analysis that I got, I found the definition of (limits to) infinity inadequate. We make use of ε, an arbitrary number, specifically "arbitrary small". But "smallness" is defined according to the < sign. Have we really defined infinity, or did we just push it into the continuity of the reals, without further scrutiny?

bump

>>10078745

f(x) is unbounded iff [math]\forall M ~ \exists x_m \in [a_0, b_0] ~s.t.~ |f(x_m)|>M[/math]
Let [math]x_{i \in \mathbb{N}} [/math] be the sequence of points where [math]|f(x_{i})|>i[/math]. An infinite number of these points must fall in at least one sub-interval (otherwise N would be finite as the union of 2 finite sets). Therefore that interval is unbounded.

Label that interval [math][a_1, b_1][/math] (pick the first if they both are unbounded). By the same argument as above define [math][a_2, b_2][/math] as its unbounded sub-interval of [math][a_1, b_1][/math] and so on for all [math]\mathbb{N}[/math]. Since by construction [math]... \subset [a_2, b_2] \subset [a_1, b_1] \subset [a_0, b0][/math], there exists a point c in all the intervals.

>>10081732
new
>>10081732

how can i proof that
−a = (−1) · a
on a "normal" field. only the standard definitions of a field are allowed...

>>10081734
>−a = (−1) · a
0=a*0
0=a*(1+(-1))
0=a+(-1)a
therefore (-1)a is the additive inverse for a

I'm a philosotard with an MA. I'm sick of philosophy and regret my decision. I want to involve myself in actual science with the phil sci experience I have, just like the old 18th-20th century greats. Do I have a chance in hell of getting even the most basic research assistant position anywhere? I can't do any math beyond algebra, and I have basically no knowledge of any laboratory procedures, measurement techniques, or modeling techniques. Is this dream a complete fairy tale for me? Or must I absolutely go back to school for this to be in any way possible?

>>10082239
>Or must I absolutely go back to school for this to be in any way possible?

>I can't do any math beyond algebra, and I have basically no knowledge of any laboratory procedures, measurement techniques, or modeling techniques.

What do you think? Of course you need to go back to school. All (real)science fields need Calculus. You learn the laboratory procedures in undergrad science classes. What field do you want to get into? All of them require a masters.