/sci/ - Science & Math

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>>10322269
>starting at the base and not the vertex

Miyu, I'm disappointed in you.

>>10322308
S-sowwy !!~

Is it dangerous/undesirable/not-optimal to take caffeine pills without eating
I feel like I'd eventually fuck myself up if I keep running in 1st gear with no fuel

I'm going to make a thread every time I have a question however small it is
deal with it

You know how dogs are colorblind? Are there cases where they can see color like how some humans can't see color?

hello smart friends, I'm working through Serge Lang's Memeing Mathematics right now and I was stuck at pic related.
I know I'm supposed to use the common denominator but I cannot find the proper one that allows me to reduce it to the answer. Thank

>>10322930
Ez mode: Pascal's Triangle \done

pleb mode: pleb mode: [math]{m \choose n} + {m \choose n-1} = \frac{m!}{n!(m-n)!} + \frac{m!}{(n-1)!(m-n+1)!} = \frac{m!(m-n+1)}{n!(m-n+1)!} + \frac{m! n}{n!(m-n+1)!} = \frac{m!(m+1)}{n!(m-n+1)!} = \frac{(m+1)!}{n!(m-n+1)!} = {m+1 \choose n} [/math]

>>10322936
i'm sorry but I don't get how that's the common denominator. Excuse my brainletism
please m'anon

>>10322936
nvm I actually do, thank you for the help :)

>>10322939
[math] n! = n*(n-1)!
\\
\frac{m!}{n!(m-n)!} + \frac{m!}{(n-1)!(m-n+1)!} = \frac{m!}{n(n-1)!(m-n)!} + \frac{m!}{(n-1)!(m-n)!(m-n+1)}[/math]

>>10322939
[math]
n! = n(n-1)!
\\
\frac{m!}{n!(m-n)!} + \frac{m!}{(n-1)!(m-n+1)!} = \frac{m!}{n(n-1)!(m-n)!} + \frac{m!}{(n-1)!(m-n)!(m-n+1)}
[/math]

>>10322948
yeah I figured it, much thanks!

Simple chem question. During a double replacement reaction, such as CuCl2 + 2 AgNO3 Cu(NO3)2 + 2 AgCl, when the Cl2 separates from the Cu, does it return the electrons it accepted from Cu? Or does it give them back and accept the ones from Ag?

>>10322991
*not give them back, and form [Cl2]-2 [Ag]+2

what does "The exists a positive number A and an open interval (a, b) which contains t0, such that
|P(t) − L(t)| ≤ A(t − t0)
2 (2) for all t in (a, b)." mean? Come on brainlets!

>>10323244
> Come on brainlets!
Do you think that gets you a quicker or better answer?
> what does [...] mean?
What do you think it means? How about "The difference between P and L at point t is at most A times the distance from t to t0."

Why are girls bad at math

>anime tranny is triggered by the word "stupid question"
The state of your life.

>>10322991
>>10322993
aw sweaty, didn't they tell you? nobody actually does chemistry...

>>10322422
Answer me biofaggots

Can someone explain this to me as if i weren't half a year from my cs degree?

I get that you break out -1 and make -i into [math](-1 * i)^2[/math] but i don't really see why that is allowed. Like, when i write -i, does it always "mean" -1 * i?

[math](1-i)^2[/math]
[math](1-i)(1-i) = 1 - i - i -i^2 = 1 - 2i - i^2[/math]

Does [math]i^2[/math] mean
a. [math](-i)^2 = 1[/math] or
b. [math]-(i^2) = -1 [/math] and why is it the one and not the other?

I know i can brute force learn this from just googling the answer, but i want to actually learn it so i can apply the same principle to other stuff as well, if need be. Brackets and order of operation in math is no doubt the hardest aspect in math, it makes no sense at all to me, a lot of the time.

>>10323493
Does [math]-i^2[/math] mean: ***

>>10323493
You multiplied wrong at the beginning, i^2 is positive.
Also, order of operations is PEMDAS or BEDMAS or whatever.

>>10323493
is this schizophrenia?

>>10323504
Ah, ofc.

I figured it out also, sort of. It doesn't make any sense to have [math]-i^2 = ((-1)*i)^2=(-1)^2*i^2=1*-1=1[/math] since that would mean that [math]-i^2=i^2[/math], which seems highly unpractical. Someone must've disproved that in a purely mathematical way at some point. So [math]-i^2 = 1[/math], it's the only way which makes sense.

>>10323537
Maybe, the doctors couldn't really figure me out, so i stopped taking the pills and stopped asking for help, i just go with it and make sure I never hurt anyone but myself.

>>10323572
SIGH [math]1 * -1 = -1[/math], ofc.. I hate that there isn't a preview before posting stuff..

>>10323572
You should learn elementary school arithmetic

>>10323576
What did I do wrong (except the typo at the end which i corrected in another reply)?

[math](ab)^2=a^2*b^2[/math] last i checked and [math]-x=-1*x[/math].

>>10323575
There is: use The TeX button in the upper left corner of the reply window.

>>10323589
i'll spoonfeed you

-a^2 = -1 * a^2
(-a)^2 = (-a)(-a) = a^2

>>10323590
[math]Thank-you. Also, \LaTeX [/math]

>>10323599
[math]Use[/math] ~ [math]for~spaces[/math].

Hi i have two questions
1.I plan to take the SAT and I am using Khan Academy. Up to what grades of math should I master?

2.I have the leechblock addon for firefox and it is pretty good until i discovered that i can just disable the add on and do some unrelated surfing. Are there any other stricter application?

Thanks for you time.

>>10323596
Why did you do [math](-a)^2=(-a)(-a)[/math] instead of [math](-a)^2=(-1 * a)^2[/math]? How do i know which one i should use? They don't give the same result, but the only difference is the interpretation of [math]-a[/math], assuming that [math]-x = -1*x[/math], which I'm pretty sure is true (although I haven't seen proof of it I suppose).

>>10322422
>not constantly being in fourth gear thanks to amphetamines
never gonna make it

Jokes aside, I don't think there are any serious consequences to taking caffeine pills compared to a coffee with the same amount. Take a look at some nootropics like L-theanine and the various herbs.

>>10323639
They do give the same result. The second one still has the exponent to it and the first one already explicitly wrote that out

>>10323639
Wait... if [math]-x = -1 *x[/math] and [math]x=-1[/math] wouldn't that recursively become [math]-x=x^ \infty[/math] since [math]-x = -1 * x = -1 * (-1 * (-1 * x)) [/math] and so on, meaning that [math]-1= -1^ \infty[/math]? See this shit is why i never can learn math.. i always get too sidetracked..

How can i check if this curve intersects with itself or not?
(t^3+t, t*sin(2πt)) for t ranging between -1 and 1
I don't know how to solve the system of equations that comes out when applying the standard method

can someone tell me what I'm doing wrong
I think I have the wrong shell radius (I'm just using x) but I don't know how to find the correct one
pls help

>>10323645
I'm 3 years clean off meth so I'd rather not
thanks for the response though

We've been working in class with pic related as the definition of a measurable function. This is just some random pic I found but I guess regular X is the domain of f and bold X is the sigma algebra of the measure space. What I want to know is why a measurable function is defined like this in the first place. As far as I know, a measurable function is simply a function for which the preimage of a measurable set in the codomain is also a measurable set in the domain. So if the function between measure spaces where [math] f : (X, \Omega , \mu) \longrightarrow ( \mathbb{R} , \Sigma , \nu) [/math], it would basically just mean that the preimage of every element in [math]\Sigma[/math] is also an element of [math] \Omega[/math], right? Then why is this not used as a definition instead of what is stated in pic related? Why work with specific intervals from some constant to infinity? That is basically just restricting the definition to the Borel algebra, right? So why use a more complex and less general definition? And even if it is just restricted to the Borel algebra, why not just say that the preimage of an arbitrary interval is a measurable set, instead of picking specific, unbounded intervals? I don't see the advantage of using this definition.

>>10323785
Using bold X for the sigma algebra is the blackest retarded gorilla nigger notation I've ever seen in my life.
But anyhow, the interval from alpha to infinity is not measurable.
Also, that definition implies that the preimages of closed intervals are also measurable. Proof is left to the reader.

>>10323819
Wait, nevermind, the interval was measurable. Fucking Lebesgue integrable functions making me think infinite values don't count.
But anyhow, the usage of that definition is linked to whether functions are also Lebesgue integrable. Nice theorems and stuff.

>>10323819
>>10323823
>Also, that definition implies that the preimages of closed intervals are also measurable
With the Lemma that's stated below that seems pretty reasonable. It's just confusing that the definition just picks one specific type of interval and gives 3 alternative statements instead of just saying that the preimage of any interval is measurable.

>the usage of that definition is linked to whether functions are also Lebesgue integrable.
So the definition is just stated like that to make the introduction to Lebesgue integrability more straightforward? In the end it should be equivalent to the statement about the preimage of all measurable sets being also measurable, right? Equivalent when the codomain of f is [math] \mathbb{R} [/math], at least

>>10323673
scratch that I've figured it out
can someone help me out though?
I need to find the volume of a solid formed by y=3x+4 and y=x^2 and revolved around the x-axis using the shell method
I'm using the functions in term of y, x=sqrt(y) and x=(y-4)/3 but I keep getting 11264pi/45 and apparently thats wrong

>>10323870
What is "the shell method"?
I don't understand why you want functions in terms of y instead of using the definitions you've been given -- if you revolve around the x axis, the radius is y(x).

I done can't remember probability. If something has x% chance of happening and y% chance of not happening how long until x^n (n times done) becomes 100% chance? Expected probability or something. Can you use logarithms to find n?

>>10324061
If the probability of an event is x%, it has probability p = x/100. The chance of the event not occuring is then q = (1-p), so the event does not occur once in n times with probability q^n. If p is not one, that does never become zero.
You can use logarithms to find out how large n needs to become for the event not to occur with any given probability:
Say p is 1/6, (rolling a 6 on a W6). Then if you want to find out how many rolls you need to do for at least one 6 occuring with 95% confidence, you'd calculate: [math] (1-1/6)^n \leq 0.05 \Rightarrow n \geq { \ln 0.05 \over \ln { (5/ 6) } } \approx 16.4 [/math]

>>10324130
Thank you this is exactly it. It's been a while since I've touched any probability.

sorry for homework questions
I'm a turbo retard and somehow completely forgot how to solve trig equations

how do I go about solving
2sin(x)-sin(2x)=(4/pi)

>>10323908
They're asking about the Method of Cylindrical Shells to find the volume of a solid of revolution.

It's important to pay attention to what direction the plane is rotated as it will form a completely different shape if rotated about another axis

>>10324578
https://www.quora.com/What-are-the-formulas-of-sin-2x

>>10323244
The error/difference is less than a parabola centered around the point t0 when near by (a<t<b). Since the parabola goes to zero, the error goes to zero so it is the limit.

Get a better calculus book that's not afraid of limits.

>>10323493
1 - 2i + (-i)^2

(-i)^2 = -1^2 i^2 = -1
-(i^2) = -(-1) = 1

which one is correct
the algebra yields the right one as correct but I can't imagine wolfram alpha fucking something as simple as this up

what sort of math is involved in theoretical computer science?

how do you find probabilities of stochastic functions involving absolute values?
[math]P(|X - c| \le d,\; x \in [a,b] [/math]
I have both the pdf and the cdf of X

a,b,c,d are all simple numbers

Do I have to manually just see that the lowest value X can take is t and the highest is s and then use that with the CDF?
This pretty much completely stumped me

>>10324720
>Do I have to manually just see that the lowest value X can take is t and the highest is s and then use that with the CDF?
Yes.

>>10324578

sin(x)+sin(x)cos(x) = (2/pi)
s + s(1-s^2)^.5 = y
(y-s)^2 = s^2(1-s^2)
y^2 - 2ys + s^2 = s^2 - s^4
y^2 - 2ys + s^4 = 0

solve the quartic
sin(x) ?= 0.327326, 0.945206
x ?= 0.333472, 1.238225, 1.903368, 2.80812
plug back and find only 2 work (we got more solutions because we squared)
x = 0.333472, 1.903368

System and signals is the application of what pure math subject(s)

I'm trying to write up some math in LyX for the first time. How do I do multiline blocks of equations and align on the equals signs? I tried making a new math block and going to new lines with ctrl enter which is supposed to convert it to either an eqnarray or align environment. I wind up getting two math blocks on each line. I don't get why I have two, and I can't figure out how to get rid of the second one.

>>10324712
A lot of linear algebra. You work a lot with vectors. If you're into animations and similar expect both imaginary numbers (with rotations) and polynomials. Also some probability and basic geometry/trigonometry if you do anything more front end than a static website.

>>10324742
Fourier Analysis
https://4chan-science.wikia.com/wiki/Mathematics#Fourier_Transforms

>>10324698
There's no difference between them. All logarithms are constant multiples of each other.

>>10324749
I figured out the two blocks on each line are sides of the equation, so I put the LHS and equals sign on the left and the RHS on the right, but now the spacing in the output is messed up. Anyone know the fix?

>>10323638
1. Underage unless you are taking it in college for some reason.
Anyways, the math on the SAT is simple. The most "complex" math it goes to is Algebra 2 and basic trigonometry. As someone who took it last year and got a perfect on math, just do the practice tests that are available on collegeboard. I went up from 1430 to a 1550 by spending a week reading and solving practice questions.
Basically, just do the practice SAT questions and you will do fine.

>>10324742
Fourier series - periodic waveforms can be said to be composed of other constituent even/odd periodic waveforms. Sometimes in infinite amounts to make square waves and such

Fourier transform - how much of each frequency is present in a time varying signal

>>10323638
I guess knowing your inequalities can't hurt

>>10323638
for 1.

I'd recommend you just buy a book that's specialized for that sort of stuff. For example, Weil's Basic number theory has been used by many to get the best grades.

Starting medschool in march. What should I expect? Do you like it? Are there a lot of people who give up?
I am a brazilian monkey, so cater to medicine and not university

I barely passed linear algebra by cramming everything in a week and then forgot it all, only for it to come and bite me in the ass years later since I need to learn it again now because it's actually useful.
I would like to think I'm a lot wiser now, studying better and I love learning. Which textbook should I study to learn it all from the ground up, but also get insights on how and why everything ties together like it does?
Also, can someone post the non-troll /sci/ math reading list?

>>10327410
I've looked around and from what I've seen, Lang & Axler's books are not for me.
I'm between Strang and Poole

>>10327410
>Which textbook should I study to learn it all from the ground up, but also get insights on how and why everything ties together like it does?

Most linear algebra books start from the ground up but the advanced ones move faster through the basics while expanding on them. I suggest you read a 2nd course book either theoretical or applied.
https://4chan-science.wikia.com/wiki/Mathematics#Applied_Linear_Algebra

>>10327522
Hmm. I read some reviews on the "Linear Algebra Done Right" book by Axler saying it's very "love it or hate it" because you might not understand it.
I will try to get into it and if I can't, I'll try a more introductory text.

Thanks.

I'm given an RL circuit and it is connected to an AC voltage generator.
I need to derive equations for magnitude and phase of current and the voltages on the resistor and inductor in the phasor domain.

V = i(R+jwl)
i = V/(R+jwl)
From here, how do I find the magnitude and phase of the current?
Then for the voltages for the inductor and resistor, it would just be jwli and r*i respectively?

>>10327410
Lang's Linear Algebra.
>>10327491
>Lang isn't for me
Lang's Algebra and Lang's Linear Algebra are two entirely unrelated books and only the Algebra is a meme.

fellas please help me

>>10327892
i've tried being more precise with my answer and I still keep getting it wrong

Is it correct to say that the elements of [math] \mathbb{Q} \left[ \sqrt{2} \right][/math], the smallest subring of the complex numbers that contains the rationals and [math]\sqrt{2}[/math], are all of the form [math] a + b \sqrt{2} [/math], where a and b are rational?

>>10327965
All subrings of the complex numbers that contains the rationals and √2 have to contain {a+b√2}. And {a+b√2} is a subring. Therefore it's the smallest.

>>10322930
Use the combinatorial meaning. If a subset of an m + 1 set doesn't contain the first element then it's a subset of the
m other elements.

>>10328022
Danke

>>10327567
Magnitude and phase is just rectangular->polar conversion. If you have a complex denominator, multiply numerator and denominator by the conjugate to get a real denominator, e.g.:
I=V/(R+jwL)
= V(R-jwL)/(R+jwL)(R-jwL)
= V(R-jwL)/(R^2+w^2L^2)
Also, |A/B|=|A|/|B|
So |I|=|V|/sqrt(R^2+w^2L^2)

>>10324741
You fucked up right at the start with sin(2x).

>>10328138
I'm a physicist, I'm not allowed to not forget a minus sign.

A friend told me to "solve this". I reckon a lot of you can easily solve this. Context: prove that f(x) is strongly monotone (without using differential calculations).

>>10322269
If I'm pushing an object up an incline slope of 45 degrees, how much less force is required to lift it 1 meter compared to lifting it vertically?

>>10327410

>>10329420
object of mass m requires a force of at least
[math] F_{inclin} = mg \sin(\pi/4) [/math],
which is the weight projected in the inclined plane.
lifting vertically requires at least a force of [math] F_g = mg [/math].

though, the inclusion of distance 1m implies your teacher is interested in the work done or energy, not force.

>>10329420
Do we consider drag?
You are actually doing doing more work 45deg way because you are also pushing it horizontally.

>>10329536
Assuming it's frictionless, and that the distance traveled is equal.

Is there any 4chan viewer app with math notation support?

I don't want to change my reptile's water bowl all the time, so I've started looking into test kits in order to assess water quality so I can change it only when necessary.

However, I probably don't have to test for all kinds of things. So what sort of compounds should I test for in a water bowl? There's everything from ammonia, nitrite, nitrate, and pH, to calcium, magnesium, iodine, etc, etc.

I'm guessing ammonia, nitrite/nitrate, and pH are the most important, right? Maybe just pH?

>>10329547
>>10329532
Work is
[math]
W = F \times d
[/math],

so
[math]
W_{inclin} = mgsin(\pi/4) \times 1
[/math]
and
[math]
W_{g} = mg \times 1
[/math].

you need [math]mg[1-\sin(\pi/4)][/math] less work to push it inclined. or [math]\sin(\pi/4)[/math]% of the vertical work.

>>10329410
can you use 2^x is strongly monotone? You need calculus to define 2^x anyways

>>10329570
>>10329547
if you meant the same distance as same distance vertically for both, then the distance you have to push in the plane is 1m/sin(pi/4), so the work done on both cases is the same (which makes sense: if there's no friction, there's only gravity and pushing something 1 meter high requires the same amount of work no matter the path it takes (gravity is a conservative force)).

>>10329410
I'd show that if y>x then f(y)-f(x)>0

>>10329585
Ah I just realized that I worded the original question wrong. Your response did answer the original question I had in mind though, so thanks for that.

V = 15cos(4x10^-4*t - deg120)
The magnitude of this is (15cos(120)^2 + j15sin(120)^2)^(1/2)?

I am unsure how to prove this claim. Should I take the the set of natural numbers, a closed subset of the real numbers, and infinite union together all signleton subsets of the natural numbers containing prime numbers? What should I do?

Also 1 more. Is there a density argument to be made or am I dumb? How should I prove this claim as well? ty /sci/ <3

>>10330799
I don't really understand what's your idea, but regardless you can always just use the definition, so you take the complement [math] \mathbb{R} \setminus \mathbb{P} [/math]. A set is closed iff it's complement is open, which is usually stated as the definition of a closed set in a topological space. And in this case the complement is just a bunch of open intervals. Showing it's not open is also pretty straightforward with the definition.

>>10330808
Yes, you can use density to easily show that [math] \mathbb{I} [/math] is not open. To show it's also not closed you can use the same reasoning, but just apply it to its complement.

How is the phasor technique used when the forcing function is a non-sinusoidal periodic waveform, such as a train of pulses?

>>10330894
Thank you so much. These make so much more sense.

>>10324752
what the fuck are you on about
>>10324712
theoretical computer science is about complexity and computability theory. so, what problems we can write programs to compute, and how efficiently (speed, space) we can compute them. it's all about efficiency, algorithms, and models of computing such as the turing machine.
really interesting stuff, especially uncomputability. if you were fascinated with the cantor's diagonal argument to prove that the reals are uncountable, you will love any and all computability theory.

>>10324822
>make one dumb mistake on the SAT math when i take it
>fucking 790 instead of 800
i got fucking 800 on every god damn practice exam, so obnoxious. it was probably some shitty non-math question like some statistics garbage too. god damn.

>>10323668
There must be an equality in the first cordinate
let there be t1!=t2 such that
t1^3+t1= t2^3+t2
t1^3-t2^3+t1-t2=0
(t1-t2)(t1^2-t1t2+t2^2+1)=0
so it follows that the second term must be zero
if t1t2>0
t1^2+2t1t2+t2^2>=t1^2-t1t2+t2^2>=t1^2-2t1t2+t2^2
ift1t2<=0
t1^2+2t1t2+t2^2<=t1^2-t1t2+t2^2<=t1^2-2t1t2+t2^2
the left side is a full square the right side is a full square so the thing in not zero unless both squares are zero. That would imply t1=t2 and t1=-t2 . That is t1=t2=0 which showed that there are no intersections for this curve whatsoever.
Basically the second cordinate is a red herring as x^3+x is monotone and increasing. Wchich leads to a better solution
Let there be two t1,t2 and t1<t2
x’(t)=3t^2+1
so x(t1)<x(t2) the end.

[math]y:R1 {\displaystyle \rightarrow } \rightarrow Rm.[/math]

What does this notation mean?

>>10331730
ignore the extra arrow

How do I stop forgetting stuff? I want to remember everything I read

>>10331744
https://www.gwern.net/Spaced-repetition

>>10331730
It means function y maps set R1 to Rm.

Now my question: I seem to have had a brain aneurysm and can't remember how to solve differential equations in this form

[math]dy/dx = y^2[/math]

How do you integrate this?

>>10332460
Ideally you would get it to some form of f(y)dy = g(x)dx so you could just integrate.

In this example:
[math]
\frac{dy}{dx} = y^2
\Rightarrow y^{-2}dy = 1dx
\Rightarrow \int y^{-2}dy = \int 1dx
\Rightarrow y = \sqrt[3]{- \frac{1}{3(x + c)}}
[/math]

>>10332516
Sorry the result is wrong

>>10332516
>>10332519
[math]
y = - \frac{1}{x+c}
[/math]

>>10332516
>>10332519
>>10332520
Ah yeah I remember now. Thank you.

I'm struggling to understand the definition in pic related. The span of several vectors [math] v_1,...,v_n [/math] in an [math] \mathbb{F}[/math]-vector space can be written explicitly as
[eqn] \langle v_1,...,v_n\rangle=\left\{\sum_{i=1}^n\lambda_iv_i:\lambda_i\in\mathbb{F}\right\} .[/eqn]
How do I express [math] [H,K]=\operatorname{span}\{[h,k]:h\in H\,,\ k\in K\} [/math] in a similar fashion (i.e. one that shows the form of the elements)? Am I right in thinking that
[eqn] [H,K]=\left\{\sum_{i=?}^?\lambda_i[h_i,k_i]:h_i\in H\,,\ k_i\in K\,,\ \lambda_i\in\mathbb{F} \right\}? [/eqn]
Is it possible to simplify further?

As one ages, their organs begin to age as well and eventually fail.
They can, at least theoretically, be replaced.

However, I've come to the realization that this must also be true for the brain, and even if we do expand our lifetimes to 100, 120, 150+ years, if the useful life of the brain is still only about 75-80 years, wouldn't that mean we would just be destined to become brain-dead once our brains begin to deteriorate?

Assuming one's other organs won't/cant fail won't one's brain age/decay, eventually rendering the person brain dead? Assuming an otherwise healthy brain.

>>10333049
Yes, you are correct in thinking that. Note that the summation you have in [H,K] should be i=1 to n for any natural number n. That is, the sum is always finite (but can be arbitrarily long or short). And without more specific knowledge about H and K, I don't think you reduce it further.

Up here in leafland, Rogers they operate most cell phones over 1.9GHz (1900MHz) frequency. But companies like Roger are on "Band 5", Bell on "Band 2", etc. What are these bands?

Need to show [math]C^{1}[a,b][/math] is not a complete metric space under [math]\displaystyle d(f,g) = \max_{a\leq x \leq b} |f(x)-g(x)|[/math] . Don't know where to start. Should I do contradiction? Or construct an example explicitly?

I don't know if this is a small question but would there be a theoretical top speed (besides c of course) where space walking would no longer be feasible?
I'm asking because I am a fa/tg/uy who is thinking of making our scifi android buddy hitch a ride on the outside of a space ship going thousands of kilometers a second through space.
I think since the android would have the same speed, he would be able to move normally relative to the space ship but would the minuscule forms of space shit (ie. radiation and particles of... stuff) in the "emptiness" of space fuck him up?

>>10334335
>In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M.

So you need a sequence of continuously differentiable functions that pointwise converge to a function that's not continuously differentiable. Didn't Cauchy get royally owned with this exact same thing in his Cours d'analyse by Abel.... [math]{}_{{\rm hint:} ~ read ~ your ~ history ~ book}[/math]

how am I supposed to search and read peer reviewed papers to form my own opinions if theyre all behind a paywall

>>10334390
Bang sorority girls
Get their log ins
Treat your stds

>>10334335
call c = (a + b)/2
[math] f_n(x) = sqrt{(x - c)^2 + \frac{1}{n}} [/math]
approaches abs(x - c)

>>10334335
look within

>>10334403
[math]
f_n(x) = \sqrt{(x - c)^2 + \frac{1}{n}}
[/math]

i always forget the fucking slash

>>10334403
Not C1

>>10334409
Don't spoon feed him

You fellas seem like a smart bunch, can i get some help on my finance hw

>>10334441
>>>/biz/

I have to use mesh analysis for this one, but I'm not sure how to go about this considering that the voltage sources are unknown.

>>10334524
[math] (V_O+V_{S1}) R_1 (V_O+V_{S1} - V_{S2})R2 + (V_O-V_{S2}) R_3 + V_O R4 = 0 [/math]

Solve for [math]V_O[/math]

>>10334524
[math]\frac{V_O+V_{S1}}{R_1} + \frac{V_O+V_{S1} - V_{S2}}{R2} + \frac{V_O-V_{S2}}{ R_3} + \frac{V_O} {R4} = 0[/math]

Solve for [math]V_O[/math]

>>10334542
That looks a lot like nodal analysis, and I'm specifically tasked with using mesh analysis for this one.

>>10334638
Your image has a super node tho....

[math]
i_1 R_1 +(i_1-i_s) R_2 = V_{S2} \\
i_4 R_4 + (i_4 - i_s) R_3 = V_{S2} \\
(i_s - i_1) R_2 + (i_s - i_4) R_3 = V_{S1} \\
i_4 R_4 = V_O
[/math]

[math]z_1 = x_1 + iy_1[/math]
[math]z_2 = x_2 + iy_2[/math]
[math]z_3 = z_1 \times z_2[/math]

Where does [math]z_3[/math] point? The complex room?

>>10323645
Namefag

did the matrix films by the wachowski brothers had anything to do with math?

>>10334691
cross product makes sense only in 3D. complex numbers are 2D

Can you give me an example of function [math]f(x)[/math] which inverse function is [math]\frac{1}{f(x)}[/math]?

>>10334917
1/x

>>10334919
[math]x[/math] isn't a reverse of [math]\frac{1}{x}[/math].

>>10334926
*inverse

>>10334917
Let f(x) be invertible. Then, f(x) is surjective. Thus, f(a)=0 for some a. Assume 1/f(x) is its inverse. 1/0 is not defined. Therefore, there's no invertible function whose inverse is 1/f(x).

>>10334917
1/f(f(x)) = x
f(f(x)) = 1/x
f(f(f(f(x)))) = x
f^3 = f^-1

...?

Why does having an unequal amount of lowering and raising operators give the expectation value of zero in ground state of a harmonic oscillator?

I need to make a windmill for a fantasy environment and looked through google for inspiration and came upon this one.
Question: does it make sense for a windmill to have two sets of superposed blades? If so, does it make sense for them to be completely different sizes?

>>10334638
Vs1 and Vs2 are independent variables.
Top loop (I1):
(I1-I3)*R3+(I1-I2)*R2+Vs1=0;
Left loop (I2):
(I2-I1)*R2+I2*R1+Vs2=0;
Right loop (I3):
(I3-I1)*R3+I3*R4-Vs2=0;
3 equations in 3 unknowns. Solve. Substitute I3 into Vo=I3*R4 => Vo=(1/3)Vs2-(1/2)Vs1

Why don't my muscles respond to weight training?

>>10330799
trivial
>>10330808
also obvious
>>10330922
think
>>10331730
look a few pages back in your book
>>10332460
is this a joke?
>>10333049
why could you?
>>10334335
check the obvious requirements of the counterexample
>>10334390
sci hub retard
>>10334524
? i dont know any physics
>>10334691
this is not well defined
>>10334813
i dont know
>>10334917
f(x)=1
>>10335182
because you're a tranny

>>10335320
/x

>>10335320
What is this shit? This is literally a containment thread for questions not deserving of there own thread. There are plenty of losers to shit on if that's what you're here for, but these are people who actually came to the right place, this is the place for trivial questions and so there is no point in calling them trivial.
>>>/g/et out

>>10335326
questions that are as trivial as that means the poster did not even try to think for 30 seconds before posting it, thus wasting everyone's time

>>10335320
>f(x)=1
Not even invertible

>>10335351
>>10335325

>>10335353
What do you mean?

>>10335358
f(x)=1/x

>>10335361
Its inverse is f(x) not 1/f(x).

>>10322269
when do you start applying for phd programs?

Hello Brainlet here with a high school tier question.

If we have a population of a 100 individuals with some being infected with virus A.

- 52 percent are girls
- 48 percent are boys.
- 23 percent of the boys are infected with virus A

- 17 percent of the girls are infected with virus A.

If you pick a girl randomly from the group what are the chance she has the virus?

>>10335387
17%, since 17% of the girls have the virus.

>>10335402
That would only make sense if the entire population was girls.

>>10335419
It makes sense since he picked a girl randomly.

>>10335419
>if you pick a girl randomly
If a female is certain to be picked then yes, it's 17%. However, the chance that any randomly sampled individual both has the virus and is a girl is 52% * 17%.

>>10335433
ah yea sorry i think the question was if the sampled individual happens to be a girl then what are the odds she has a virus aswell.

>>10334917
I don't think such a function exist, because
f(x)=y is equivalent to f^(-1)(y) = x = 1/y = 1/f(x)
then y = 1/x and f(x) = y means that f(x)=1/x
which because of f^(-1)=1/f(x) means f^(-1)=x
and that's a contradiction as 1/x and x are not inverse to each other

>>10335459
>f^(-1)(y) = ... = 1/y
f^(-1)(y) is supposed to be 1/f(y) though

When we say something like "this galaxy located 1.9 billion light years away", how do we know that object still exists? We're seeing the light that it emitted 1.9 billion years ago, but the object might not be there anymore. Is there a way to determine whether a very distant star or galaxy or planet or whatever still exists today?

>>10335563
you're right

how come so many climate skeptics are pro-nuclear, while climate change alarmists are so anti-nuclear when nuclear power is the best currently available solution for emissions-free power generation?

>>10335601
>but muh chernobyl!
>but muh nukes!
>nuclear bad!
That's basically it. They don't actually know anything about nuclear energy, and they don't want to know.

>>10335606
I thought people who were pro-climate science were supposed to be open minded for solutions.

>>10335387
>17% of the girls are infected with the virus

If 17% of the girls are infected with the virus, then a random girl will be infected with the virus 17% of the time.

If however, you meant that 17% of the whole population are girls infected with the virus, and rest of the girls in the population aren't, then the chance is 17/52, which can't be reduced because 17 is prime.

>>10335433

According to my computer, that equals 8.84%. However, computers aren't exactly great at floating point arithmetic so excuse me if it's not 100% accurate.

Anyhow, I think they meant 17% of the population are girls infected with the virus and you randomly choose one of the girls, so the correct answer is 17/52 which approximately equals 28.84%.

>>10335377
In the UK it's in early december

>>10335567
Well, you can tell if it's moving away from you and if it's accelerating too, and since there are no external forces usually, you can predict approximately where it will be in relation to where you see it now

>>10335567

I'm no expert so don't take my word for it, but I don't think so. At most we can gather as much information as possible about the state as is currently observed and try to simulate its time evolution in order to try to figure out its present state, but I don't think that's usually possible.

>>10335613
It's easier to understand "burning coal" and "wind turbines" than "controlled fission of uranium", especially for roasties, so a simple-minded person will always remain sceptical, on top of the aforementioned disasters completely sealing the deal for them.

>>10335650
>>10335652
Yeah but even if we could calculate where it will be (or rather where we will see it) say 900k years from now, we can't possibly know if it still "exists". Galaxies don't go anywhere but planets or stars could get swallowed by a black hole, or go supernova or whatever at some point and we'd never know
I guess it doesn't matter since we won't be around to see it and we'll never travel there anyway

Kinda sad to think all we see when we look at the stars is just the past and that we will never be able to go anywhere that far away

>>10335662
I've had this discussion with my parents a few times. They're hardcore anti-nuclear, and no matter how many times I explain to them that coal is far more damaging to the environment and that nuclear is perfectly safe if everything works the way it should, all they ever think about is
>but look what happens when nuclear goes wrong!

>>10335680
perhaps show them stats of how the radiation from coal plants is and has been more damaging (cancer rates, etc) to the local population than nuclear ever has, even including disasters

>>10322269
utter fuking brainlet here

can sombody explain me why the N-GG´s (here orange) are not Pareto efficient ?

I mean if you are by (2.2) you cant get any better while not hurting the other player.
So why is that not Pareto efficient.

>>10335674
it's hard for a galaxy to be completely "swallowed" by a black hole, and it's not like they spontaneously appear. And sure, supernovas are hard to gauge when they will happen, but they are still somewhat predictable with current data.

I don't know why you're thinking that nothing is predictable. If you throw a tennis ball at a wall and watch it, you're technically seeing the past as you receive the light from the ball by the same reason (speed of light is finite), however, you can see the trajectory, predict approximately where it's going to hit or if it will miss the wall completely. What you're thinking is (analogously) that perhaps at the same time someone decided to hit a golf ball from 50 yards away and coincidentally hit your tennis ball, making it change course completely. Sure, it could happen, but what are the chances? Very little. It's just that the cosmological scale is large enough that it might just happen.

brainlet AF here, not muslim BTW

Can someone tell me if it is possible to provoke a nuclear meltdown from outside?
By outside I mean usage of explosives or some shit,
what about maybe a Nuclear War scenario where a nuclear missile reached a nuclear reactor? Assuming the personnel dies product of the shockwave and the reactor is left in some kind of automatic mode

>>10335647
say im on my first masters year, that means if I intend to get into a program by 2020 (aug-september) I have to apply early december 2019?

>>10335790
Because A2B1 exists.

Is there a company offering DNA tests like Ancestry or 23andme, but instead of a bunch of useless information about my ancestry it offers me things like medical information instead?

>>10335867
elaborate pls

when player 1 locks down C1
player 2 cant get any better than C1,D2

when player 2 locks D2 down
player 1 cant get any better or equal without hurting player 2

so how has it to do with A2B1 ?

>>10335892
Reread the Pareto optimum definition. It's not about one player being able to change his choice to better both of them, it's about bettering both of them being possible in general.

>>10335866
In the UK, yes. Some EU institutions are a bit later. I would apply earlier if you can, since sometimes they do them as they come. It's just that december is the deadline. If you have a two year masters, then you should start sweetening your supervisor/lecturers about it to get an early start to them writing your letters.

However, if they don't do them on a rolling basis, then perhaps you can expect to wait till march or even may for a message back, so don't worry too much

>>10335895
you have my gratitude anon

need dating advice /sqt/
>doing phd in algebraic curves
>on tinder
>say if i unlock their secrets, i could probably hack any online server
>she asks if im gonna do it (unlock secrets)
Would it be a bad idea to say "im almost there, just need your number for the final step"

>>10335913
kys

>girl in my linear algebra class standoffishly declares that she "disagrees that a point doesn't have direction"
>debate ends up involving her, the professor, one sane guy, and three brainlets who back her up

Why the fuck are stupid people allowed in higher undergrad math courses? How are professors not able to kick someone out for that kind of shit?

>>10335921
Actually, there is a natural identification of points to vectors from 0 to that point in R^n. In fact, many proofs use that vector and the point interchangeably. So actually, the girl is right and the prof is wrong.

>>10335939
>R^n
>not working in general affine space

>>10335951
>being pedantic
retard
Every affine space is a linear space once you decide on the origin anyways.

>>10335961
>Every affine space is a linear space once you decide on the origin anyways.
exactly, and the "direction of points" like >>10335939 says kind of depends on this choice, doesn't it

>>10335971
No one actually cares, brainlet

>>10335904
thanks anon for the info

so far I've only seen people who were fast tracked into a program just because their msc thesis supervisors liked them, so they didn't have to go through the whole process of interviewing/sweet talking

>>10336005
np, if you've got any other question perhaps i can answer, since after all im doing a phd right now

>>10336013
mind if I ask you what is your field?

This isn't even a question really, but more looking to see if anyone can help me remember this thing
I was taking a math class last year on proofs, and the teacher used an example of a particular formula to show why just testing every number against a formula was a bad way to see if it works or not. It was something like nine hundred and something times x minus two is never prime, and the first case where this was false was some fifteen digit number or something along those lines. I know it's a huge stretch, but is that some well known thing or just a random example he came up with?

>>10336032
pure math

>>10336053
http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
not that but similar

>>10336056
cool, good luck!

>>10336117
>good luck
you're the one applying, not me, wtf?

>>10336123
was just trying to be nice, but then I forgot where I was

>>10336053
Random example.
A proper classical example would be say, Fermat numbers.

Is there a way to incorporate natural constants as functions into Excel/Google Sheets/OpenOffice Calculator/whatever? Kinda like "pi()" which most of these programs have.
I found one for excel but it was outdated and won't work.

Why do humans take so damned long to develop? Dear god we have the brains of parrots until we’re like 4 years old and then it takes another dozen years before we’re able to function unsupervised

>>10336624
Not a biologist or anything but I once heard on a documentary or someshit that we evolved this way because otherwise our heads would be too big for the birth canal of m'lady.
So while other chad animal babies already know how to walk, our retarded virgin babies need to learn it as their brain keeps developing as if it was still in the womb.

Makes sense don't it?

>>10325658
start reading human anatomy textbooks YESTERDAY!

>>10334311
i think they are different channels of the same frequency

Excuse my brainletism, but I'm trying to go through a problem in my intro to analysis class. If I take the infinite sum of 1/n^x, where x is a complex number, are there any zeroes other than numbers of the form 1/2 + ri or negative even integers?

>>10336690
nope, to prove this use taylor expansion

>>10335178
>Vo=(1/3)Vs2-(1/2)Vs1
how did you get this?

If I have two known, parallel lines a known distance apart, how do I find the diameter of the circle they would fit inside?

>>10336662
How does that work?

>>10323319
Math doesn't care about your emotional IQ

>>10336741
nvm, I just remembered perpendicular bisectors

(−2t −3)^2 +(−2t −2−1)^2 +(−2t −3)^2 = 24
3(−2t −3)^2 = 24
(−2t −3)^2 = 8
(2t +3^)2 −(2sqt(2))^2 = 0
t = (-3 - 2sqrt(2))/2 or t = (-3 + 2sqrt(2))/2


The following is wrong somewhere but I don't know where.
Could someone tell me please?
(−2t −3)^2 +(−2t −2−1)^2 +(−2t −3)^2 = 24
= (3 + 2t)^2 + (3 + 2t)^2 + (3 + 2t)^2 = 24
9 + 12t + 4t^2 + 9 + 12t + 4t^2 + 9 + 12t + 4t^2 = 24
27 + 36t + 12t^2 = 24
3 + 36t + 12t^2 = 0
Delta = 36^2 - 4 (3) (12) = 1296 - 144 = 1152
t = (-36 - sqrt(1152))/ 24 t = (-36 + sqrt(1152))/ 24
t = 12(-3 - sqrt(96))/ 2*12 t = 12(-3 + sqrt(96))/ 2*12
t = (-3 - sqrt(96))/ 2 t = (-3 + sqrt(96))/ 2

>>10336928
Oh I found it, sqrt(1152) = 12sqrt(8) and not 12sqrt(96).
Thanks.

Why do less denser things "go over" more denser things? Like, why do molecules do that? What is the basis for this behavior?

>>10336978
In many ways it comes down to either the difference in the mass of an element or molecule, or how the element or molecule is bonded together.
In the case of ice floating in water, even though its the same substance, the crystal structure of ice means that there's less matter per unit volume than liquid water, and is thus the ice floats.

>>10336992
I still don't get it.

For example, you get a balloon with helium in it. It will exert the force on the balloon just because the balloon(and air above it, if we're dealing with gravity.) is denser. In your example water exerts a force on Ice. But how does it do that?
I am wondering if this is by proxy just thermodynamics, and therefore matter's intrinsic need for equilibrium. "More matter = more pressure" if that makes sense. So a less denser object (and therefore containing less matter) would get "pushed" by more denser objects. Like when you expose air to vacuum, the more dense medium would travel to the other.

Why does matter wants to equalize so badly however is rather a metaphysical question unless there's some satisfying answer in some quantum physics or something.

Quick very retarded question: If someone says "plot A against B", does that imply which one I should take as the X axis? Or do I decide that?

Further details:
Asking because I'm doing this question where I have to rearrange an equation to show that some term is actually given by the gradient of two other terms. It says "Show that X can be determined from the gradient of a linear graph of A plotted against B". I first understood this as "X = A/B" but after playing around with the terms I got "X = B/A". I can't tell if I fucked it up or not.

>>10336978
It's entirely due to gravity. Denser particles are attracted more strongly towards the centre of gravity, and they've got more inertia. So they're able to "push through" the lighter particles, whereas lighter particles are manlets of the physical world and can't do shit.
I didn't think it would, but I believe this explanation holds up in the macro scale as well? Like a kilogram of wood won't be able to float on 500 grams of water I believe. I could be entirely wrong though. Whatever; at least it's true in the micro scale lmao I hope I helped with your intuition in regards to the physical world anon take care :^)

>>10337215
I case anyone's curious, here's my basic calculations[eqn]
C = \frac{B-A}{B+A} \\ C = \frac{B}{A+B} - \frac{A}{A+B} \\ \frac{B}{A+B} - C = \frac{A}{A+B} \\ B - C(A+B) = A \\ B - CA - BC = A \\ B(1-C) = A(1+C) \\ A = B \frac{1-C}{1+C}
[/eqn]
Statement: Plot (1+C)/(1-C) against B, slope will be A.
As you can see I didn't exactly get it right.

>>10336711
Tried this method but the numbers got messy. The book has several solutions but I don't know how they arrived at them.

>>10336732
> how did you get this?
By:
> 3 equations in 3 unknowns. Solve. Substitute I3 into Vo=I3*R4 => Vo=(1/3)Vs2-(1/2)Vs1
Once you substitute the values given for the resistances, the equations are
8*I1-4*I2-4*I3=-Vs1
-4*I1+6*I2=-Vs2
-4*I1+6*I3=Vs2
Vo=2*I3

I get that most of you are math fags or whatever so this is a shot in the dark:

So assuming pure phase saturation vapor pressure is e_(w)t=6.112*e^(17.62t/(243.12+t)) for the sake of clarity,
In the equation for calculating saturation vapor pressure, where does relative humidity fit in? And what the fuck would ambient vapor pressure be?

I apologize in advance for my retardation but there are absolutely zero resources for this that I can find on short notice.

why does it always seem like the higher the floor of the building you are in, the more advanced the class?

How do 2hus fly? For example, what kind of thrust does Reimu produce?

>>10322269
How do you find the smallest distance between any 2 functions?

>>10337896
Find critical points of (f - g)^2. If the minimum exists at an interior point, it should be a critical point.

This is a stupid question
In the FLRW model of cosmology we treat the matter and energy contents of the universe as perfect fluids with the following stress-energy tensor

[math] T^{\mu\nu} = \begin{pmatrix}
\rho & 0 & 0 & 0\\
0 & p & 0 & 0\\
0 & 0 & p & 0\\
0 & 0 & 0 & p
\end{pmatrix} [/math]

How do I get [math] T_{\mu\nu} [/math]?

Is it the exact same thing or is every element inverted?

>>10338034
[math]T_{\mu \nu} = T^{\alpha \beta}g_{\alpha \mu}g_{\beta \nu}[/math]
So, for example, to calculate [math]T_{00}[/math] you do
[math]T_{00}=T^{\alpha \beta}g_{\alpha 0}g_{\beta 0} = T^{0 0}g_{0 0}g_{0 0} + T^{1 0}g_{1 0}g_{0 0} + T^{0 1}g_{0 0}g_{1 0}+... = \rho[/math] where you sum over all possible indices (this is the 'Einstein summation notation')
It's easy to note that [math]T_{ij}=0[/math] for [math]i\neq j[/math]. Don't think of tensors as matrices (i.e 'inverting')

How can I build man muscle if I'm a man with a woman's body? I want to be tough but my muscles don't respond to weight lifting

>>10338305
https://en.wikipedia.org/wiki/Androgen_replacement_therapy
https://en.wikipedia.org/wiki/Growth_hormone#Replacement_therapy

should i transfer to a 'better' uni with more interesting classes, brand name value and stronger alumni, with the drawback being that I'll do have to do an extra semester?

>generally good at math, like number theory, linear and abstract algebra, real analysis and probability
>am absolutely fucking retarded when it comes to geometry, physics and applying math to physics
I ace most of my math classes, but basic kinematics just eludes me. I can't manage to understand the most straightforward shit like vector derivatives on an orthonormal basis to figure out velocity. What's wrong with me?

I'm trying to dopamine starve myself by avoiding all seeking behaviours.

Since I can't resist looking up medical factoids, I need to redirect this curiosity in a direction that doesn't give instant gratification (e.g. reading pubmed studies) and thus avoid tweaky and shallow forays into broscience that are more entertaining than edifying.

With this in mind, can anyone recommend me a few beginner's books on the endocrine system and/or the brain?

>>10338394
depends on your money situation and your major
if you're interested in grad school, well, you'll be in school for a while anyway.

>>10338750
an extra semester won't cost too much, and this other school seems to have much better grad school placements. so rationally, I should probably transfer, but at this other uni I'll be 22 when I graduate instead of 21 at my current uni. i don't know why but that aspect is really bugging me. it's dumb, right?

How do I take the squareroot of this equation? I’ve tried the distrubutive property, still end up with something like (a+bi)^1/2

>>10338305
holy fuck you're annoying

>>10338870
Compute the number inside the square root sign. Write it in the form Re^iz (polar form). Then the square root is plus or minus (sqrtR) e^(iz/2). Notice that there is a Re[ ] operator, meaning you take the real part of whats inside (ie: the a in the a+bi)

I don't understand the relationship entropy - bits.

Given
p(a) = 0.8
p(b) = 0.1
p(c) = 0.1
, the entropy is ~0.922, which means it takes 1 bit to decode 1 symbol, which is obviously bullshit. But all sources I found say that entropy * (length of sequence) is the minimum number of bits you need to encode it.

Am I dumb?

>>10338305
you're not enough, and you're not eating enough protein.and without fucking around with hormones you'll only build muscle half as fast as men do

>>10338870
nigga did u just take a picture of a screen with a phone..? what is print screen button?

0^0 is undefined

so if you have (x^0)/5 is it correct to say that for all values of x the value of the function is 1/5 except at x=0 where it is undefined?

So my friend is reading a pop sci book about artificial inteligence and i told him he needs math to optimize the genetic algorithm so it knows how to evolve "perfectly", instead of it just evolving/adding stuff randomly, he says that it doesnt matter because if stuff says then its good/helps to advance in the problem so it must stay there; can someone actually explain to me who is right? I saw a vid about this on youtube, basically a guy did artificial inteligence to solve a guy running or something, and it was pretty bad, but it worked, then google released their result and he compared and he said his was worse because he didnt do the optimization, like google did.
Bonus points if you can find the video

>>10339405
yes

>>10322269
What does the 2nd T in "QTTDTOT" stand for

>>10339206
you have no idea what it's like not to be able to build muscle since you are healthy, you would behave like me if you had my problem that I am desperate to solve

>>10339625
Questions that truly don't deserve their own threads.
>>10339405
0^0=1

In the context of quantum mechanics and things like the black hole information paradox, what exactly is meant by "information"?

>>10339715
no if you google it almost everywhere says 0^0 is undefined. half the people here have told that to me. im lost

>>10339625
QTs that don't deserve their own thread

>>10339758
Google is wrong, 0^0=1.

>>10339766
should have just wikied it in the first place.

real answer:

Jump to search
Zero to the power of zero, denoted by 00, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra, combinatorics, or set theory, the generally agreed upon value is 00 = 1, whereas in mathematical analysis, the expression is generally left undefined. Computer programs also have differing ways of handling this expression.

>>10329410
>streng
>strongly
kek


[math]f(x) =\frac{2^x-2^{-x}}{2^x+2^{-x}}[/math]

Let y, z in R such that y < z. We have to show that [math]f(y) = \frac{2^y-2^{-y}}{2^y+2^{-y}} < \frac{2^z-2^{-z}}{2^z+2^{-z}} = f(z)[/math]
or equivalently [math](2^y-2^{-y})(2^z+2^{-z}) < (2^z-2^{-z})(2^y+2^{-y})[/math]
or equivalently [math]2^y2^z-2^{-y}2^z+2^y2^{-z}-2^{-y}2^{-z} < 2^y2^z-2^y2^{-z}+2^{-y}2^z-2^{-y}2^{-z}[/math]
or equivalently [math]-2^{-y}2^z+2^y2^{-z} < -2^y2^{-z}+2^{-y}2^z[/math]
or equivalently [math]2*2^y2^{-z} < 2*2^{-y}2^z[/math]
or equivalently [math]\frac{2^y}{2^{-y}} < \frac{2^z}{2^{-z}}[/math]
or equivalently [math]2^{2y} < 2^{2z}[/math]
or equivalently [math]{2y} < {2z}[/math]
or equivalently [math]{y} < {z}[/math]
Which was our assumption

>>10338305
>my muscles don't respond to weight lifting
Lift heavier weights, do it more often and eat the right stuff. Literally nothing else matters, not even your retarded delusions about being trapped in a woman's body. Muscle is muscle, and women can be bodybuilders too.

>>10329410
>make up a problem
>figure out it has an obvious solution
>add "No don't use that" to make the problem harder
We multiply by 2^x/2^x=1 to obtain:
f(x)=(2^2x-2)/(2^2x+2)
You should be able to finish.

>>10339247
pls respond

>>10339748
A general quantum system is described by a density matrix. Pure states, a.k.a. wavefunctions, are rank 1 density matrices. Information conservation in this context means that a closed system that starts in a pure state will remain a pure state.

For black holes, the Hawking radiation is predicted to be thermal. Thermal states are not pure states. So the paradox would be that if you create a black hole from a pure state, then it seems like it would decay into an impure state.

>>10339405
the limit x^0 as x->0 is 1, while the limit 0^x as x->0 is 0. Any could do depending on the context

>>10339807
Why do you think the answer is obviously bullshit?

>>10339814
How would you decode 3 states (a, b, c) with just 1 bit (0, 1)? With two bits, it's easy (a = 0, b = 01, c=11).

>>10339784
I can't lift heavier weights without compromising either form or rep count, and I already lift for low rep counts. Any more and my sets are going to be like 1-3 rep each. I have tried upping the frequency to everyday and it doesn't make a difference. I already eat the right stuff. It just doesn't grow at all, no difference after years, literally the same nothing changed. The average joe would have changed significantly even if he did everything wrong in that time frame

>>10339820
5V, 0V, and NC

>>10339826
That's three states.

My algebra is bad. How can I solve for V? I've tried multiplying numerator/denominator by j, end up with something with j*v, which kind of fucks everything up.

>>10339820
Entropy is not about the minimum bits you need to encode a worst case message. It's the minimum expected number of bits you need per character, in the limit of large messages.

>>10339810
Can you explain that again but in really dumb layman's terms
my (likely incorrect) understanding is that a quantum state is like the probability of each particle in the system having a given degree of any observable property like its location or energy, and the problem with black holes is that the information going into it is all merged and then radiated in a random manner so when you measure/observe a particle radiated from it you can't know anything about its state prior to being swallowed by the hole

god I really like learning about physics but all this quantum stuff really fucks with my brain, especially since I lack the necessary knowledge of mathematics

Does anyone else crippling study guilt? I study 6-8 hours a day on top of my lectures but whenever I'm not studying I feel dirty and lazy. I literally don't feel like doing anything anymore because it all seems pointless and always feel like I don't study everyone else and the course is going to surpass me. The only respite I get is sleep or the three say a week I allow myself to get drunk.

>>10339845
>Entropy effectively bounds the performance of the strongest lossless compression possible, which can be realized in theory by using the typical set or in practice using Huffman, Lempel–Ziv or arithmetic coding.

>>10339847
That's good enough for a basic understanding. If you're not familiar with density matrices, I'd just suggest a quick look at the wikipedia page. They're basically just classical probability distributions over wavefunctions.

You can define an entropy for density matrices, but what's really important is that time evolution preserves the eigenvalues of a density matrix. For a pure state, there's one eigenvector with an eigenvalue of 1 (this is the wavefunction), and all the other eigenvectors have an eigenvalue of 0. One would expect to in principle be able to start with a huge pure state representing a system that will eventually collapse into a black hole. If the black hole evaporates, and the Hawking radiation really was thermal, then it seems like you have to accept that your density matrix is no longer a pure state, which means the Schrodinger equation wasn't enough to describe the time evolution. There's a lot of ways to avoid swallowing that pill, but we ultimately just need a good quantum description of black holes.

How do you define "operator". It's not just a function, is it?

>>10339911
And?

>>10335332
you are a huge faggot

>>10335913
do it

Damn I am having way too hard a time proving these two things. What should I do? I feel like I sometimes get close but also don't.. if that makes sense

Lets say I am trying to write a proof for (iii), I know why it is a basis for the euclidean topology on R^2, but I have no idea to write a formal proof to express this idea with as much rigor as possible.

I can write proofs all day long in my Analysis 2 class, but my topology professor treats topology like some willy-nilly hippy-dippy "perfectly natural" math subject and hasn't expressed what he'd like to see in our proofs. Any tips on writing proofs for topology/point-set topology would be greatly appreciated thanks

>>10340124
for (i), all you need to do is to prove that for every point in an intersection of two elements in the set there is an element contained in the intersection.

>>10340133
fuck, forgot the pic related

for pic related

>Lets say I am trying to write a proof for (iii), I know why it is a basis for the euclidean topology on R^2, but I have no idea to write a formal proof to express this idea with as much rigor as possible.

>I can write proofs all day long in my Analysis 2 class, but my topology professor treats topology like some willy-nilly hippy-dippy "perfectly natural" math subject and hasn't expressed what he'd like to see in our proofs. Any tips on writing proofs for topology/point-set topology would be greatly appreciated thanks

>>10340134
would the intersection of two elements in the set look like space between two functions that cross at some point? Im having trouble visualizing the situation. thanks for the reply

>>10340142
Say h is in M(f, e) cap M(g,e'). so int |h-f| =z < e and int |h-g| = z' < e', then if int |j - h| < min (e' - z', e-z), int |j-f|< int |j-h| + |h-f| < e-z + z = e, similarly for g.

>>10340137
The open squares are open in the max norm. Its trivial to show that the usual euclidean norm is equivalent to the max norm.
Alternatively, you can always show that any open set can be written as the union of infinitely many open squares.
From then on, you just refer to the previous result. Any open disk can be written as an union of open squares, and vice versa, thus they induce the same Euclidean topology. And so on.

>>10340142
you cannot visualize this situation, because the functions can be very weird, they don't necessarily have to cross anything. If you really want to imagine something, think of them as functions near enough to the given f, in the sense that the area between them is less than epsilon.

>>10340133
To prove that two bases give rise to the same topology, you prove that for every element in B1 and point in it, there is ane element of B2 containing that point and contained in the element and vice versa. In this case, the standard basis is open balls.

>>10340157
Is it really that simple? what about number 5? Same shit?

>>10340157
I forgot, but you can also show that any sequences that converge in one generated topology converge in the order.
"Assume that a sequence n converges to x but that, for some square l, there's no i that guarantees every element after is in l."

>>10340151
>>10340157
>>10340161
>>10340168
>>10340173
I dont know if youre one person or many. regardless, this advice is very helpful thank you. I meeting up with a friend at a building on uni campus with a shit load of black boards so I can get bigger and clearer pictures of what I'm doing. I'll post back later to see if i nailed it or totally missed the ball. no pun intended

Looking at a map of global wind temperatures.
Some places it is -5 C on land, but +5 C immediately off shore.
Is this accurate? And if so, how?

>>10339843

bump

>>10339843
Expand all terms, isolate Vo. j's should cancel.

>>10340379
How do they cancel? Only thing I can think of is multipling by all of their denominators to eliminate the fraction, but then I still end up with j’s

>>10339974
>>10339247
> the entropy is ~0.922, which means it takes 1 bit to decode 1 symbol
No it doesn't. It means it takes ~922 bits to encode a string of 1000 symbols where the occurrence of each symbol roughly matches its stated probability.

Creating a naive Huffman code for the 3^8 combinations of 8 symbols results in bit strings ranging from 3 bits for aaaaaaaa (0.375 bits/symbol, P=0.8^8=0.16777) to 26 bits for e.g. bbbbbbbb (3.25 bits per symbol, P=0.1^8=1e-8), with a weighted mean of 0.932 bits/symbol.

As the number of symbols grouped into each word increases, the probabilities get closer to powers of 1/2 and the compression gets closer to the theoretical limit given by the entropy. An optimal encoding has the length of the encoded string for a word equal to -log(p), where p is the probability of the word. Any practical implementation requires the lengths of the encoded strings to be integers; as the number of words gets larger, the probabilities get smaller, the difference between -log(p) and the nearest integer gets less significant, and the encoding efficiency gets closer to the theoretical limit.

At the other extreme, encoding individual symbols is highly inefficient. The encoding for a should use -log2(0.8)=0.322 bits while that for b and c should use 3.322 bits. Note that the weighted mean is 0.8*0.322+0.1*3.322+0.1*3.322=0.922 bits per symbol. But there's no way to actually have a fractional number of bits. Rounding the encoding of a up to a whole bit would triple the size of the encoded data.

>>10340585
> How do they cancel?
Solve for Vo. The imaginary part is zero.

(v-(15+20j)/-50j + v/150 + (v-(15+10j))/20j = 0
=> -6(v-(15+20j)/300j + 2jv/300j + 15(v-(15+10j))/300j = 0
=> -6(v-(15+20j) + 2jv + 15(v-(15+10j)) = 0
=> -6v+6(15+20j) + 2jv + 15v-15(15+10j) = 0
=> (9+2j)v + (90+120j) - (225+150j) = 0
=> (9+2j)v - (135+30j) = 0
=> v = (135+30j)/(9+2j) = 15(9+2j)/(9+2j) = 15
If you didn't recognise that (135+30j) can be factored into 15(9+2j), you'd do it the long way and multiply numerator and denominator by the conjugate of the denominator to make the denominator real:
v = (135+30j)/(9+2j)
= (135+30j)(9-2j)/(9+2j)(9-2j)
= (135(9-2j)+30j(9-2j))/(9(9-2j)+2j(9-2j))
= (135*9-135*2j+30j*9-30j*2j)/(9*9-9*2j+2j*9-2j*2j)
= (1215-270*j+270j+60)/(81-18j+18j+4)
= (1215+60)/(81+4)
= 1275/85
= 15
But since you're doing a contrived problem, you should be looking for simplifications. 135+30j is clearly a multiple of 5 => 5(27+6j), 27+6j is clearly a multiple of 3 => 5(3(9+2j)).

Retard here, why is heat death possible if energy can't be lost?

>>10340870
because heat death is thermal equilibrium, not the absence of energy

>>10339961
usually a linear map from a vector space to itself

>>10322269
what would be the immediate and long term effects of unsheathing the internal part of the human penis by splitting the Bulbospongiosus?

of course, a nutshell response is appreciated. but are there any articles available to the public?

>>10339423
anyone?

In what situations does quality=quantity?
One I found was ratings. E.g. 10/10.

>>10322422
Nothing serious, although it will extremely exacerbate the immediate "come down" effects of the caffeine (generally speaking, low blood sugar and dehydration will exacerbate these effects - both of which will always accompany consuming caffeine with food to some extent).

Of course you might say you dont feel any significant come down, but that'll only be true if either (1) youre consuming relatively small amounts (<150mg), (2) you're tolerance is really high, or (3) youre too retarded and unaware of your own body to notice the difference (much like people who eat 5lbs of greasy ass fast food a day and only drink 5oz of fluid, but dont seem to notice a difference compared to being hydrated and eating healthy).

I want to understand the ultimate nature of reality but I'm too lazy and undisciplined to put any work in it. What book will spoil it for me so I can understand the universe without doing any of the hard work?

PS I want a real understanding, not gay analogies from pop-sci faggots.

>>10342020
Sperm.

>>10342060
No, there can only ever be one sperm in a sperm. If you are talking about the amount of sperm in ejaculate, that means nothing to quality, unless your definition of quality here is "most likely to impregnate."

>>10342075
>your definition of quality here is "most likely to impregnate."
Yep. AFAIK the genetic quality inside the spermatazoa has no effect on its likelihood to reach the egg first, so shooting more is better.

How do I solve for i1 and i2?
Since the equations are linear, I added both of them and end up with -j50*i1 + j20*i2 = j10
Doesn't this have infinitely many solutions?

>>10342090
It does.

>>10342090
oh wait i'm actualyl fucking retarded

What is the concentration of contaminated water after 5 minutes?

And why on earth is this concept so difficult to grasp? It feels like it should be super easy to solve

>>10342089
Quality can be subjectively defined, but I don't think that's what most people think of.
>>10342020
Anyone have other examples? I am collecting them.

>>10342097
actually I still don't get it
>>10342093
but the answer is supposed to be i1 = -.4 and i2 = -.5

>>10322269
100 ms = 0.1 s

100^2 ms = 10000 ms = 10 s
0,1^2 s = 0,01 s

Must we only do calculations with the Unit of measurement?

Hello anons, I'm banging my head on this one. To find the derivative I use the quotient and the chain rules, is this correct? E would be my answer

>>10342267
[math]f(x) = \frac{1}{(3x^2+4)^{\frac{3}{2}}} = (3x^2+4)^{-\frac{3}{2}}[/math]
[math]f'(x) = -\frac{3}{2}(3x^2+4)^{-\frac{5}{2}}6x[/math]

They're all wrong lol, but (a) is only wrong by a factor of 2

>>10342267
You only need to use the chain rule if you consider the fraction as just [math] (3x^{2}+4)^{-3/2} [/math]. Not having to use the quotient rule makes it less messier, and also can be solved in just one step. Also there seems to be no correct answer here, it should be a but without the 1/2. A calculator is showing me the same result so I assume it's just a typo.

Do you guys like robots?

>>10342105
it's easier to think of this problem by considering y to be the volume of the contaminate rather than the concentration, you can easily find concentration by dividing by volume. To find the amount of contaminate coming into the tank, multiply concentration and volume of the input. To find the amount going out of the tank, multiply y with the ratio of the volume that is leaving the tank and the total volume.
[eqn] \frac{dy}{dt} = \textrm{In} - \textrm{Out} \\
\frac{dy}{dt}=0.2-\frac{y}{20+t} [/eqn]
this is a very simple differential equation to solve, not going to go through all the work, but there are plenty of resources online for ordinary differential equations

>>10342267
This can ruin your derivation skills. Use with caution.
https://www.symbolab.com/solver/derivative-calculator

>>10342302
You could also just enter "derivative of *formula*" into wolframalpha

>>10342314
It can be very messy for long formulas and you can't get steps

>>10342288
>>10342291
>>10342302

Damn I'm a brainlet, totally missed the negative exponent option. thanks frens

>>10342214
you need to square the unit and the prefix as well

What is the semi-direct product of Z ⋊φ Z, where φ is the negation automorphism x -> -x, isomorphic to? I barely know what a semi-direct product is

>>10342379
Oh ok, so you multiply ms^2 by 10^-6 to have second and you apply sqrt to s^2 to have second, thanks!

>>10340124
Okay how’d I do?
I’m pretty sure I proved the two conditions necessary for something to be a basis for a topology. However my classmates say I’m incorrect because I didn’t prove all 3 properties of a metric. However I disagree because I am given the literal metric in the definition of the thing that I want to prove to be a basis. Yes a metric defines a topology, but that’s not what the question is asking. Am I correct in my thinking or do I need to do more?

Bump

today my teacher said that chlorine adams want to gain an electron to complete their octet. she said that this makes them more stable and have a lower potential energy. However, this makes the charge of the chlorin(d)e -1. Wouldnt it have lower potential energy if it had a neutral charge? Doesn't it have electric potential now?

She said something confusing when I asked, but she also says that every calculator is a little different whenever she makes a mistake.

>>10335443
17%

lads, I need help with a continuity proof. I need to prove that if [math]f[/math] is continuous on [math]a[/math] then [math]|f|[/math] is also continuous on the same point. I was thinking of doing it with delta-epsilon, but I have no idea how.

>>10343413
Write out the delta-epsilon definition for [math] f [/math] first. What you want to show is that [math]||f(x)|-|f(a)||[/math] is bounded by an arbitrary epsilon, and that there's always a value for delta that allows you to do so. You already know that [math] |f(x)-f(a)| [/math] meets those conditions, because of the definition of continuity. Then you can use that expression to bound [math]||f(x)|-|f(a)||[/math] with the same epsilon, with the help of the triangle inequality (or its variation for differences, to be more specific). I think you can pick up and finish from there, the inequality basically does all the work.

okay, how do I find the answer to the second question?

>>10342090
> How do I solve for i1 and i2?
Simultaneous equations. If they didn't teach you this on your course, it's because they assumed you learnt it in high school. If you learnt it in high school then forgot, you're going to need to re-learn it, because it's going to keep coming up and you'll be expected to know it.

> Since the equations are linear, I added both of them
You're supposed to add (or subtract) scaled multiples, with the scale factors chosen so that one of the variables disappears. In the general case:
ax+by=c => adx+bdy=cd & aex+bey=ce
dx+ey=f => adx+aey=af & bdx+bey=bf
=> (bd-ae)y=(cd-af) => y=(cd-af)/(bd-ae)
=> (bd-ae)x=(bf-ce) => x=(bf-ce)/(bd-ae)
If bd=ae then the system either has no solution or infinitely many solutions.

On to your problem:

I1(150-j50)+I2(-150)=15+j20
I1(-150)+I2(150+j20)=-(15+j10)

First, we're going to divide everything by 5 to make the numbers smaller:

I1(30-j10)+I2(-30)=(3+j4)
I1(-30)+I2(30+j4)=-(3+j2)

Let's start by making I2 disappear. So multiply the first by the coefficient of I2 in the second (30+j4) and the second by the coefficient of I2 in the first (-30), then subtract:

I1(30-j10)(30+j4)+I2(-30)(30+j4)=(3+j4)(30+j4)
I1(-30)(-30)+I2(30+j4)(-30)=-(3+j2)(-30)
=>
I1(30-j10)(30+j4)-I1(-30)(-30)=(3+j4)(30+j4)+(3+j2)(-30)
I1(940-j180)-I1(900)=(74+j132))+(-90-j60)
I1(40-j180)=(-16+j72)
I1 = (-16+j72)/(40-j180) = 8(-2+j9)/20(2-j9) = -2/5

Now make I1 disappear similarly:

I1(30-j10)(-30)+I2(-30)(-30)=(3+j4)(-30)
I1(-30)(30-j10)+I2(30+j4)(30-j10)=-(3+j2)(30-j10)
=>
I2(-30)(-30)-I2(30+j4)(30-j10)=(3+j4)(-30)+(3+j2)(30-j10)
I2(900)-I2(940-j180)=(-90-j120)+(110+j30)
I2(-40+j180)=(20-j90)
I2 = (20-j90)/(-40+j180) = 10(2-j9)/20(-2+j9) = -1/2