/sqt/ - Stupid Questions Thread

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How do I deal with having two unknown forces?

How many ways do I place two queens on an 8 by 8 chess board such that they don't attack each other?

Answer: {[28×(64−22) (Queen on edge of board)]+[20×(64−24) (Queen one away from edge of board)]+[12×(64−26)]+[4×(64−28)]}/2

No clue how they got that.

I know next to nothing about genetics. But people always say that blonde hair and blue eyes are recessive genes.
Yet I know a couple where the girl has reddish-brown hair and brown eyes, and the guy has blond hair and blue eyes. And their child turned out to be a girl with blonde hair and blue eyes.
Is that because the guy had strong nordic genetics, and his testosterone-ridden masculine body "conquered" hers?

>>9146421
Case: Queen on edge of board:
You have 28 edge fields, you place the first queen on one of them. How many fields are now blocked for the second queen? 7 horizontally, 7 vertical and 7 diagonal + the 1 where the first queens stands, so 7+7+7+1=22, so there are (64-22) fields for the second queen, total: 28*(64-22).
Case: Queen one away from edge of board: left as an exercise.

>>9146493
The brown-brown girl has one dominant brown-brown gene and one recessive blonde-blue gene. Then she rolled the dice and got the recessive genes on her child.
In truth, eye and hair colour are not single genes anyways, and are apparently quite difficult to predict.

Thinking about pursuing a PhD in physics and going into research, but I keep seeing all the talk about oversaturation and how hard it is to find a job. Is it a good idea? or would I be better off just going into finance or something else business related.

>>9146393
Two classic ways:
• some forces cancel out so you can write their sum as [math]\vec0[/math];
• project the problem in an adequate coordinate system in which you don't need to bother about them (or can apply the first method on the projection).

>>9146571
Depends where you want to end up. If you want to end up in academia, you better go to a top 25 school and work for a well known PI, and publish a lot in your PhD, in a hot topic. Choices currently include anything "clean" energy, military applications, and things the media can meme.

After PhD, you better hit a sweet postdoc and continue publishing like crazy, and then you'll be competitive for tenure-tracked faculty positions.

e.g. My current PI went to Cambridge for Physics, then MIT to post-doc, bother under famous PIs, and now has a tenure-tracked position at the top school in my country (not USA).

If you want to go to industry, do your PhD in something with transferable skills, e.g. Computational Physics. A lot of finance jobs are now being filled by Math/Phys majors because of their ability to use mathematical models and program.

If you want to go into industry and work a Physics-related job, you'll probably end up as a research associate/research scientist, and have to climb up a ladder. The problem is, earnings are capped unless you want to jump to management, and that will most likely require an MBA.

Not the worst, but don't expect to be using that PhD in most outcomes.

>>9146355
I've been reading a bit about surreal numbers, and I'm wondering...
Beyond [math]\omega[/math] days we reach a point where we should be able to construct a number:
[eqn] \bar\omega=(\{0, 1, 2,\dots \}, \omega-\{0,1,2,\dots\}).[/eqn]
Now obviously this number is larger than any finite number yet smaller than anything that can be reached "going backwards" from [math]\omega[/math]. Then what is it? Or should I just go check it's algebraic properties?

If IQ is hereditary and individuals lose IQ over time does your offspring end up more intelligent if you have them when you're younger?

>>9146493
>his testosterone-ridden masculine body "conquered" hers?
Kill yourself

Can I calculate the limit of a multivar function in a point where the function is not defined in a direction?

>>9147024
> Can I calculate the limit of a multivar function in a point where the function is not defined in a direction?
No, the limit definition requires the function be defined in some neighbourhood around the point

>>9147067
That's what i thought, but the thing is the limit seems to be possible to calculate.
It's the limit of sin(x*y)/y as as (x,y) approaches (0,0)
If you do lim sin(xy)/y = lim x/x * sin(xy)/y = lim sin(xy)/yx * lim x = 1 * 0 = 0

>>9147078
>If you do lim sin(xy)/y = lim x/x * sin(xy)/y = lim sin(xy)/yx * lim x = 1 * 0 = 0
Doesn't tell you about approaching from x-axis.

>>9146393
Could someone check my answers:
Force from BC is 230.69 pounds
Force from AC is 172.73 pounds
sorry I'm a brainlet

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Here's a good one, how do fucking electrodes work? I have a cathode and an anode as stimulation electrodes and another two for recording the signal. How do I position those, why do I even need two of each? I'm supposed to be measuring action potentials.

>>9146964
Yes, but not for the reason you think.

Losing IQ as you age doesn't actually change your genes, so your offspring wouldn't end up more intelligent if you have them younger, however, having children too late can actually lead to less intelligent children, among other problems associated with having children late in life, although it's mostly a concern with an older mother rather than an older father.

>>9147188
>having children too late can actually lead to less intelligent children, among other problems associated with having children late in life, although it's mostly a concern with an older mother rather than an older father.
I know this is a thing for women because down syndrome rates start to skyrocket but are there any standout issues for men?

Would multiplication in the visualization of dots in rows & columns for something like 3*8 be stated as three rows & eight columns, or three columns & eight rows?

Does it even fuckin matter? I don't know, I'm fucking terrible at mental math and I'm trying to just start back at ground zero by using mental visualizations & then manipulating those visualizations in order to complete the mental math.

>>9147255
>Does it even fuckin matter?
no

>>9147255
3*8 = 8*3. So even if it mattered it wouldn't matter.

Until you get to Matrices. Fucking Matrices.

>>9146355
If all false statements became true and vice versa, would the resulting system be consistent?

Can we use Quantum Entanglement to create some form of instant communication? If two particles can perform the same/inverse functions at any (virtually infinite) distance, can't we build two rings that hold quantum entangled particles and then use those particles to read off a Hexadecimal language?

Assume I know next to nothing about Quantum Entanglement (but can understand that math of it all), what am I getting wrong here? Or if I'm not, why aren't we looking into it?

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In the solution he didn't consider the atmospheric pressure. Can someone explain me why?

>>9147370
Nevermind, I didn't read the question properly.

>>9147356
Only extremely fringe interpretations of Quantum Entanglement claim that the quantum particles are actually in communication with each other and among them an even smaller fringe states that that communication will continue if either particle is altered in any way.

It's more like a particle will decay into two particles in two different directions and if you learn something about one particle it will tell you something about the other no matter how far away it is. It's just really weird on paper because technically the other particle should still be relying on the fact that it's unknowable. Though I'm not going to pretend I know the mathematical ins and outs.

>>9147373
Even if you don't know the mathematic magic, what you said actually makes a lot more sense and now is making me wonder, "Why the fuck is there any hype about Quantum Entanglement anyways?" I realise I definitely had a misinterpretation of how this worked. There's a reason why I dropped this in the /sqt/, thanks anon.

>>9147398
>Why the fuck is there any hype about Quantum Entanglement anyways?
Because those fringe interpretations DO exist and they sell journals and inspire science fiction stories, so they're more popular than the more subtle interpretations.

>>9146705
>Or should I just go check it's algebraic properties?
Let's start with that.

What's a good template for making (personal) notes in latex?

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the criteria for this question in pic related seems a bit vague to me. anyone have a clue?

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>>9147753
ah shit wrong pic. check this one. what do they mean by "simpler function?"

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>>9147755
>>9147753
Nevermind. Much easier than I had thought.

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How did we transition from 2Re(z*w*) to 2|zw| in the 4th step?
Taking real analysis and so far everything seems alright though I can't understand all definitions from the first time.

>>9147774
Re(a) <= |a|

I've found that in real analysis, if you don't understand a definition properly you should look at theorems which prove that the original definition is equivalent to another possibly more intuitive one. Eg. Compactness in terms of finite subcovers vs. Compactness as being closed and bounded in metric spaces.

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>>9147758
is this u?

>>9147774
It's wrong. Should be 2 Re( zbar w )

Why do people say stock prices are perfect when there are obvious price fluctuations over nonsense?

Do stock prices ultimately correct or what?

Why is it when I am drinking mineral water it doesn't feel that heavy compared to tap water?
Is it pH levels or is it something else to it.

>>9148227
Yeah my bad

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Are peeps still here? Dumb-bum reporting in.
What, if any, is the name for the lower leg? From the knee to the ankle (circled in blue)

>>9148545
crus or cnemis
In common folk term, the front is called shin the rear is called calf.

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>>9148552
Thank you for the specificity; that did not help me figure out my confusion though. I will try again with more information.
As 'foreleg' is not a common term used in describing human legs.... I am having no success on Google.

" the disproportion in my build is that my forelegs are too short. Like the kangaroo, I have very short forelegs and tremendously long hind legs. Ordinarily I sit quite still; but if I move, the tremendous leap that follows strikes terror in all to whom I am bound by the tender ties of kinship and friendship."

I am having trouble understanding if the author means the 'foreleg' as the half of his leg above or below the knee?????

>>9148614
That describes front and rear legs.

>>9148419
>Why do people say stock prices are perfect when there are obvious price fluctuations over nonsense?
Shouldn't you be asking those people that question?

This one had me kinda stumped (yes, I'm dumb).
[math] \lim_{x\to0}x^2=0 [/math]
Given [math] \epsilon \gt 0[/math] we wish to find [math]\delta [/math] such that:
[math] 0 \lt |x| \lt \delta \Rightarrow |x^2| \lt \epsilon [/math]
[math] \Rightarrow |x||x| \lt \epsilon [/math]
https://s.4cdn.org/image/buttons/burichan/cross.png
Is delta supposed to be epsilon over x or equal to delta? The former makes no sense, the latter I'm skeptical of. Maybe 2 times epsilon?

>>9148727
I'm a complete brainlet but isn't delta just sqrt(e)?

You're probably right.
[math] |x^2| \lt \epsilon [/math]
[math] |x| \lt \sqrt{ \epsilon } [/math]

Not sure if you can square root... well.
[math] |x^2| = |x|^2 [/math]

So [math] \delta = sqrt{ \epislon } \Rightarrow |x^2| = |x|^2 \lt \delta^2 = (sqrt{ \epsilon })^2 = \epsilon [/math]

Is that it?

>>9148857
That's what I was thinking, yeah. Why wouldn't you be allowed to square root here? Nothing here that would exclude that. Also no funny business with negative roots since we have absolute values. But then again, I'm a pretty big brainlet so don't trust me.

I remember the wiki having recommendations books for html5 and I can't find them now, was that section deleted or I'm just imaging things and it never existed at all?

What's the best youtube lecture series for ODE?

>>9148857
The square is a monotone function on either side of 0, so let f(x)=x^2, then 0<a<b => 0<f(a)<f(b), now use a=x, b=d and presto.

d/dx ((x^3)/(f(x)))
at point x=4 and where f(4)=1 and f'(4)=2

please tell me the answer is -20

>>9148913
Nope, sorry.

>>9148928
what is it then

>>9148883
MIT lectures are decent:
https://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/

>>9148934
Just use the quotient rule and plug in the numbers. It's not that hard.

>>9148939
did that and got -20, but the answer was wrong and i can't see where i fucked up

>>9148947
figured it out now

>>9148947
You probably divided by the wrong number. You said yourself that f(4)=1, so you need to divide by 1^2=1.

Just started Partial Diff Eq, can anyone help me with this problem?

For the Hydrogen atom, if [math] \int |u|^{2} dx = 1 [/math] at [math] t=0 [/math] show that the same is true at latter times. (Hint: Differentiate the integral with respect to t, taking care about the solution being complex valued. Assume that [math] u [/math] and [math] \bigtriangledown u \rightarrow 0 [/math] fast enough as [math] |x| \rightarrow \infty [/math] ).

>>9148958
https://math.stackexchange.com/questions/189809/hydrogen-atom-in-partial-differential-equations
Literally the first google result.

What is the probability of randomly choosing a permutation of the 10 digits 0, 1, 2, ..., 9 in which 5 is not in the first position and 9 is not in the last position?

A: {(1×9×8!)+(8×8×8!)}/10!

Wtf, why? My idea was to calculate all the permutation and subtract out ones starting with 5 and ending with 9.

( 10! - 8! ) / 10!

Why is this not right? And why is what is right right? fuck nigga

>>9148958
>Just started Partial Diff Eq, can anyone help me with this problem?
differentiate as the hint says. use the schroedinger equation et voila

Hey people, i'm stuck with these two :

"Consider the differential equation [math]\ddot{x}
= \sqrt{x} [/math], with initial condition [math]x(0) = \dot{x}(0) = 0 [/math]. Is the solution unique ? If not why is the exemple pathological ?"

and

"Is it true that a once differentiable function [math] x(t) [/math] is a solution of [eqn]m\ddot{x} = -ax [/eqn]
ifand only if it is a solution of [eqn]\dot{x} =
\frac{2E}{m} - \frac{a}{m} x^2 [/eqn]? If not, find a non trivial counterexemple."

So it's classical mechanics but I must admit my math skills are rusty, I suppose that I obviously don't have to solve the nonlinear ode-s in order to answer the questions. But I've forgot how one can prove the existence/uniqueness of a solution of ode aswell as that it's a pathological solution.
Can someone help me to get on the tracks pls ?

Why is the Earth's core still so hot? I read its still the approximate temperature of the surface of the sun and is supposed to remain so for billions of years., it'll be hot and liquid long after the sun converts to a red giant, for example.

Seems like an improbable thermal flywheel to retain such heat energy for so long. Why does it take so long to dissipate when most rocky objects around are at such lower energy states throught?

Is stating "Q is a necessary condition for P" synonymous with the contrapositive of P -> Q?

Could anyone help me finish up a proof I'm working on? Or suggest a different approach to proving it?

"Prove that if [math]a \equiv b (mod~n)[/math], then [math]a[/math] and [math]b[/math] have the same remainder when divided by [math]n[/math]."

Here's what I've got so far:

Suppose [math]a \equiv b (mod~n).[/math] Then [math]n | (a - b)[/math] and [math]a -
b = nk, k \in \mathbb{Z}[/math].

Let [math]a = qn + r, 0 \leq r < n[/math] and [math]b = pn + t, 0 \leq t < n[/math]. Thus
[math][(pn + r) - (qn + t)] = nk[/math]
[math]r - t = n(k - p + q)[/math].

Since [math](k - p + q) \in \mathbb{Z}[/math] we have that [math]n | (r - t)[/math] or in other words [math]r \equiv t (mod~n)[/math].

After that I'm stuck. Intuitively I "know" that since neither r nor t are divisible by n them being congruent to each other mod n means that they must equal each other, but I'm not sure how to actually show that. The proof in general also seems a bit long for something so simple.

Repost to fix the latex.

>>9149162
Yes, but it's also synonymous with P -> Q.

>>9149168
Right, whereas the "sufficient condition" only refers to [math]P \rightarrow Q [/math] and not [math] \neg Q \rightarrow \neg P[/math], correct?

>>9149185
No, for two reasons. P -> Q is synonymous with ~Q -> ~P, and saying "Q is a sufficient condition for P" means Q -> P.

>>9149165
Your whole proof is shit and you've basically ended up back where you started.

That said, use the fact that both r and t are between 0 and n to conclude that they are equal.

>>9149194
Ah, okay, was confused on the grammar of the statements, that's fairly straightforward then.

>>9149207
I actually don't end up where I started, and I figured out how to end my proof (even if the proof is admittedly, shit).

[math](1) r - t = n(k - p + q) = ns, s \in \mathbb{Z}[/math] and [math]0 \leq (r - t) < n[/math]
[math]0 \leq \frac{r - t}{n} < 1[/math]. Since [math]\frac{r - t}{n}[/math] is an integer from (1) we conclude that [math]r - t = 0[/math] and [math]r = t[/math].

It's still an ugly proof, I agree, and I'd love to see your take on it.

>>9149252
My take on it: a-b has remainder 0

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nuclear detonations in atmosphere or solar flares:
will disconnected hard drives and electronics survive fine?
what about hard drive in ESD-bags?
ESD-bags wrapped in aluminium foil?

electromagnetism is not one of my stronger topics

>>9149257
Ah, OK. I feel stupid now. So how about this?

Suppose [math]a \equiv b (mod~n)[/math]. Then [math]n | (a - b)[/math] which means that [math]a - b = nk, k \in \mathbb{Z}[/math].

Let [math]a = qn + r, 0 \leq r < n[/math] and let [math]b = pn + t, 0 \ leq t < n[/math]. Then [math]pn + r - qn - t = (p-q)n + (r-t) = kn[/math]. Since [math](r - t) < n[/math] we have that [math]p - q = k[/math] and thus [math]r - t =
0[/math] and [math]r = t[/math].

Was that better? Could you simplify it even further without losing formality?

>>9149290
Mixed up p and q there, but you get what I mean.

I want to know how I can concentrate muriatic acid from the 31% jugs to as concentrated as possible. Can I just boil off the other liquid that comes in the jug.

>>9149303
>I want to know how I can concentrate muriatic acid from the 31% jugs to as concentrated as possible
Hydrochloric acid has a maximum concentration in solution of about 38%. You can't concentrate it further than what you can buy at the store, boiling it is just going to cause poisonous vapors.

>>9149303
"As concentrated as possible" is ~42% at 20C. It's rarely made above 35% because the evaporation rate increases dramatically as you approach saturation.

Heating it will reduce the concentration: the boiling point of HCl is -85C, versus 0C for water.

>>9149376
> versus 0C for water
Um ....

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>>9149376
>Heating it will reduce the concentration: the boiling point of HCl is -85C, versus 0C for water.

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>>9149376
>Heating it will reduce the concentration: the boiling point of HCl is -85C, versus 0C for water.

And to think I had shame to ask my stupid question.

A number x is in the subset of Reals which is (0, 1). How do I construct another number in the set smaller than it? I want to do 1/x but that makes it > 1...

Is there anything that will take away the overwhelming desire to not exist?

>>9149447
Have you tried the double chalupa?

>>9149449
No

>>9149447
Maybe reading some books by Jean-Paul Sartre?

>>9149440
>How do I construct another number in the set smaller than it?
just think about it...

>>9149454
Sure, recommend one?

>>9149455
x / 2, I'm dumb

>>9149457
"Being and Nothingness" is supposedly his seminal work. Never read it myself though.

Link to the pdf
https://libgen.pw/download.php?id=360461

>>9149465
Sorry, that's a link to class notes about the book. Here's the actual book.

https://libgen.pw/download.php?id=531452

>>9149451
well there's your problem

How far away are we from creating the virus that only kills all white people?

>>9149475
Thanks anon, I'll check it out

>>9149480
Somehow I don't think a fried tortilla filled with meat and cheese will help. Chalupas worked when I was younger but now I just hate myself after eating that stuff

>>9149484
>How far away are we from creating the virus that only kills all white people?
About 50 years ago, it's called multiculturalism

>>9149520
kek

>>9149484
already here and it's called BIG BLACK DICK

how do I prove that falsum and implies is functionally complete?

>>9149290
>>9149290

your proof is too mechanical. proofs aren't supposed to look like long division, they're supposed to reveal something about the intrinsic structure of whatever it is you are "proving." Stop copying the writing conventions you see in textbooks. Think for yourself, write like you speak, show don't tell, etc. remember that proofs are for other people to read.

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By uniform (since [math]K[/math] is compact) continuity, there is a [math]\delta>0[/math] such that [math]\|x−y\|<\delta[/math] implies [math]|f(x)−f(y)|<\epsilon[/math]. By compactness we can cover [math]K[/math] with finitely many, say [math]N[/math], such [math]\delta[/math]-balls. Since the image of [math]K[/math] under [math]f[/math] is compact, can we do something like cover the image with finitely many [math]\epsilon[/math]-balls? I'm just not sure how I can get a bound in terms of [math]\|x−y\|[/math].

There's a quote I'm looking for (Descartes, I think), that goes something along the lines of:

>We live in a universe predictable enough that life can exist but unpredictable enough to keep things interesting
Any clues?

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What does [math]s_\overline{x}[/math] mean?

I've found it in an ecological statistics math referencing Barford (1985) but I can't find the original paper. There's nothing that I can think of which makes sense in context.

I'm a swede and my name contains an ö, but when I write it directly in LaTeX it comes out as Ã˝u in the pdf

How do I fix this?

Could somebody explain to me what's the theory behind why an approximation will get less accurate the closer the input values are to it's interval of convergence?

>>9149778
Let [math] \displaystyle A \geq \sup_{x,y \in S} \frac{|f(x) - f(y)|}{\delta} [/math]. The RHS is finite because [math] f(S) \times f(S) [/math] is compact and the distance function is continuous.
If [math] |x - y| < \delta [/math] then [math] |f(x) - f(y)| < \epsilon [/math] because of the selection of delta and uniform continuity. If [math] |x - y| \geq \delta [/math] then [math]|f(x) - f(y)| \leq A \delta \leq A |x - y| [/math] by the selection of A.

>>9150114
Either create the source file in ISO-8859-1, or tell the converter that it's in UTF-8.

given that a length of electric wire creates an orthogonal field of magnetism, could not a Planck length of time create an orthogonal field ,separate from this universe but mutually effected by its presence?

>>9149454
Why would reading complete garbage somehow fix his problem?

>>9149852
There is actually evidence to suggest that they did.

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>>9150114
>I'm a swede

>>9149708
How would you go about proving it then?

>>9149290
Here's what I'd write:
a≡b(mod n)
<=> a−b=kn for some k
<=> a=qn+r and b=pn+r for some q, p and r.
Thus a and b have the same remainder.

Stupid question threads should be called brainlet question threads tbqh.

>>9150453
Why does
>a−b=kn for some k
imply
>a=qn+r and b=pn+r for some q, p and r.
?

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I have no idea how oxidation states nomenclature work. To boot, the teacher won't let us use the periodic table or any chart for the exam, so I can already feel my rectum trembling. What do???

>>9150569
>he hasn't memorized the periodic table
You might as well drop out.

>>9150716
I do have it memorized but not perfectly, the cations and anions chart much less so. And the fact some compound names don't seem to follow any logic doesn't help much.

>>9150453
You can't define a and b as having the same remainder, that's what you're trying to prove.

What are some good books for learning computing-related maths?
Stuff like matrices, sets, algorithms, probability etc

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>>9150989

>>9150525
>>9150759
In primary school you guys (hopefully) learned that r-r=0. This is what's being used here.

>>9151248
>In primary school you guys (hopefully) learned that r-r=0. This is what's being used here.
Elaborate, how does this take you from
>a−b=kn for some k
to
>a=qn+r and b=pn+r for some q, p and r.
?

>>9151248
Well?

If I have a general solution to a differential equation and it has an arbitrary complex constant in it, can I choose to look the subset of solutions where this constant is real only?

Do I have to do anything extra to do this?

>>9150989

finite math will cover some matrices, probability. discrete math will cover sets and a whole lot of other foundational stuff, directly leading to algorithms (if you are doing this in uni you will eventually need to know how to do induction proofs for your algo classes and above, ex)

>>9150993

this is fine but it depends on how dumb they are to begin with. i don't know that text in particular but jumping into matrix algebra might be a turn off without a baseline understanding

>>9151448
Why do you want the constant to be real? If that's because you want real solutions, there might be more to do since the rest of the function could be complex.

>>9151469
Yes, I want real solutions. Everything in my solution is real except for this constant

>>9151477
Then it's enough to just take the real constants.

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>>9146355
I'm doing an assignment where I have to keep subtracting the absolute value of differences between values until they all cancel out and get zero.

Can anyone explain why these four quantities are all equal to eachother?

How do I find the angles from axes x,y, and z given a vector in unit vector notation?

>>9151572
Dot product formula

>>9150114
Murricanize your name like the rest of the civilized world.

How do you turn studying from being a horribly stressful torture into an engaging and fun activity?

>>9152024
just stop yourself from ever thinking of the words 'study' or 'work' if they already carry such negative connotation

>>9147633
My question got dubs, someone answer it plz.

Assume [math](x_n)_{n=1}^\infty[/math] is a cauchy sequence in [math](E,||\cdot||)[/math] and [math](x_n)_{N=1}^\infty[/math] is a subsequence, of said sequence, which converges in [math](E,||\cdot||)[/math]. Does these two assertions imply that [math](x_n)_{n=1}^\infty[/math] converges in [math](E,||\cdot||)[/math]? How would I show this?

Given two independent random variables X and Y with identical distribution, how do I find out the distribution of Z=Z(X,Y), specifically for Z(X,Y)=|X-Y|?

If guy A punches guy B who has aids, hard enough to injure guy B and guy A's own hand, so that wounds leaking blood are clearly visible on both of them, will this exchange be enough to pass on the HIV virus to guy A?

what are some nice /sci/ documentaries to watch?

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I'm currently taking a real analysis course, and I feel like I've hit a spiky wall. I can barely understand anything written in the book, and I don't know how to approach the exercises and how to prove them.
Though I understand everything covered in class.
The book we're using is Principles of Real Analysis by Rudin and Apostol's Mathematical Analysis as a reference.
I borrowed a "workbook" today that was supposed to be supplementary to the book by Rudin, but it turned out to be made for another book by the same name but different author (By Aliprantis). My question is, is there any such book by/for Rudin? Couldn't find anything online.
Also, any tips would be greatly appreciated.

>>9152539
n*(-1)^n

>>9152562
n*(-1)^(n+1)

*

Can I have some feedback on this proof of the following theorem:

Let [math]E_1, E_2[/math] be two vector spaces, let [math]f:E_1 \rightarrow E_2[/math] be continuous and let [math]S\subset E_1 [/math] be compact. Prove that [math]f(S)[/math] is compact.

Proof: Let [math](x_n)_{n=1}^\infty[/math] be an arbitrary sequence in [math]f(S)[/math]. Let [math](y_n)_{n=1}^\infty[/math] be a sequence in [math]S[/math] such that [math]f(y_n)=x_n, \forall n \in \mathbb{N}[/math]. Since [math]S[/math] compact there exists a subsequence [math](y_{n_k})_{k=1}^\infty[/math] which converges in [math]S[/math]. But [math]f[/math] continuous and so, by definition of continuous mapping of vector spaces, the image of said subsequence also converges in [math]f(S)[/math]. But this image of said subsequence is a (convergent) subsequence of [math](x_n)_{n=1}^\infty[/math] and so [math]f(S)[/math] is compact. [math]\blacksquare[/math]

>>9152099
This is as much a learning exercise for me as it is for you, so this may be faulty.

Since [math](x_{n_k})_{k=1}^\infty[/math] is convergent with limit [math]x \in E[/math], the following applies: [math]\forall \epsilon > 0 : \exists k_0 \in \mathbb{N}[/math] so that [math]\forall k > k_0 : ||x_{n_k} - x|| < \epsilon[/math].
Similarly, [math]\forall \epsilon > 0 : \exists n_0 \in \mathbb{N}[/math] so that [math]\forall m,n > n_0 : ||x_{n} - x_m|| < \epsilon[/math]
Let [math]N := min(n_{k_0}, n_0)[/math]
Thus, for any [math]\epsilon > 0 : \forall n > N : \exists k > k_0 :||x_n - x|| = ||x_n - x_{n_k} + x_{n_k} - x|| < ||x_n - x_{n_k}|| + ||x_{n_k} - x|| < 2\epsilon[/math], which proves that [math]\lim_{n \rightarrow \infty} x_n = x \in E[/math]

>>9151254
>>9151384
Try assuming
a=qn+r and b=pn+t,
then
a-b=(q-p)n + (r-t)
and since both r and t are less than n, this can only be equal to kn when r-t=0.
Thus, a=qn+r and b=pn+r.

As I said, you should have learned this in primary school.

Need notation clarification. Every element of polynomial ring [math]R[x_1,...,x_n][/math] can be written uniquely in a form [math]\sum{r_{x_1,...,x_n}}x_1^{i_1}...x_n^{i_n}[/math]. I don't really understand what [math]r_{x_1,...,x_n}[/math] means. Is it just [math]r \in {r_1,...,r_n} [/math]? If so, wouldn't it mean that there are only [math]n[/math] elements that can be coefficients(i.e. restriction to subset of a ring)?

>>9152843
>[math]r \in r_1,...,r_n[/math]
[math]r \in {r_1,...,r_n}[/math]. Fast fix

>>9152843
It should be [math]\sum {{r_{{i_1}...{i_n}}}} {x_1}^{{i_1}}...{x_n}^{{i_n}}[/math]


They are just indices labeling the coefficients for each monomial.

>>9152852
Oh, thanks.

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What's the name of those "weak" microscopes? Like when you look at your finger under one you can see every groove of your finger print very clearly? I thought it was monoscope but googling that only brought up hunting gear

>>9151528
Because they're all equal to 1119/350-pi.

Eliminate the modulus operators (replacing them with either their argument or its negation, depending upon sign), replace 3.2 with 32/10 and 3.14 with 314/100, then simplify.

At masters level in the UK, does a grade above distinction exist like at undergrad at Oxford, Cambridge and UCL?

>>9152971
Stereo microscope/ dissecting microscope.

>>9152971
You mean a magnifying glass?

>>9152666
>[math]\in \mathbb{N}[/math]
No such thing.

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I'm trying to solve for what regions have unique solutions.
How do I write out the answer? I know that x and z should not be the same, but how what is the proper way of writing this?

>>9153116
Why are you so sure there is a even a solution, let alone a unique one?

>>9153121
I think it's assumed. The question asks "determine a reqion of the xy-plane for which the differential equations WOULD HAVE a unique solution"

>>9153136
>I think it's assumed
Then you can prove that absolutely anything is a solution, since anything follows from a contradiction.

>>9153142
lol i'm dumb. thanks

is a tablet like surface or ipad pro a decent alternative to paper for working through problems?

>>9153153
No.

>>9152746
That's literally what I wrote here:
>>9149290
So I'm not sure what you're complaining about.

>>9152971
A loupe?

How does the science field look like to you all?

I decided to study Wildlife Ecology. I graduated a year ago and was able to obtain some temporary jobs in environmental sciences. I couldn't find permanent jobs where or when I wanted so I decided to get a Master's in biology.

Today, in plant physiology, I was working with another graduate from my lab and some other student. The graduate in my lab is working with genetics of a genus of snails. I am doing ecology and population assessments of snails in Texas.

He made a joke that he was doing the real work. Of course, genetics (doing PCRs or primers or CRSPR etc) is important. At least, I believe so I haven't done these processes myself. It did make me feel insecure.

Are there ecology jobs out there? Will I find a permanent job in what I enjoy? Do all biologists (excluding medical workers) need to know how to run genetics in the lab?

>>9153153
the only substitute for pen and paper is a blackboard.

>>9153153
If you have stylus, yes.

What is K?
I have 2 equations:
Ce^(10K) = 70
Ce^(5K) = 90

>>9153322
What's the subject?

>>9153330
Physics. It's supposed to be newton's cooling law.
I keep getting ln(7/9)/5 but it doesn't fit for both.

>>9153330
I should also note that 70 was the room temp, so it would be Ce^(10k)+70 = 140 and Ce^(5k)+70=160.

I'm trying to find the initial temp.

>>9153337
This was actually the correct answer. I'm dumb.

>>9153322
Divide the first equation by the second, take logs and divide by 5 to get
[math]K = \frac{ln{\frac{7}{9}}}{5}[/math]

>>9153376
That isn't necessarily well defined though.

>>9153379
Why not?

>>9153387
The answer might not be a number which can be shown to exist.

>>9153390
But the only pair (C, K) for which those two equations are true is
[math]C =\frac{810}{7}[/math]
[math]K = \frac{1}{5}ln{\frac{7}{9}}[/math]

Hello, been playing Kerbal Space Program recently and just wondered if I understood a few things correctly, if anyone has a spare moment.

As I understand you can write acceleration as e.g 9.8m/s^2 and that means that after one second i'd be going 9.8m/s and after 2s i should be going 19.6m/s and so on.

My question is really about gravity and i just wondered if I drop a ball from a 9.8m ladder it takes 1 second to hit the ground travelling at 9.8m/s on impact? I think this is correct but i just wanted to be sure, mainly because i just explained it to a friend like this and i don't want them to have walked away dumber than i found them. thanks

>>9153402
>if I drop a ball from a 9.8m ladder it takes 1 second to hit the ground travelling at 9.8m/s on impact?

no, think about it like this if it was travelling at 9.8mps at impact that means that the fastest it was ever moving was 9.8mps so there was a good amount of time (the entire duration of the fall) that it was moving slower

to solve for how long it takes to hit the ground use the equation
[math] x=v_0t+\frac{g}{2}t^2 [/math]

where x is the overall displacement (9.8m) and initial velocity is 0

your first statement is true though so you can use that concept and the time value you found from solving the equation to determine the actual final velocity

>>9153402
Literally take a physics class

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>>9153435
>>9153437
Thankyou for your explanation, in return i have found (you) a relevant gif.

I have heard I can mix urine and wood ash to make a homemade fertilizer my question what does this mixture yield?

>>9152746
>Try assuming
>a=qn+r and b=pn+t,
>then
>a-b=(q-p)n + (r-t)
>and since both r and t are less than n, this can only be equal to kn when r-t=0.
>Thus, a=qn+r and b=pn+r.
Right, invoking the division algorithm is the actual work needed to be done in the proof, the way your "proof" was originally written would most likely get a 0 if handed in as a homework solution

>>9153471
Ash and piss

The fucking colle kikes are forcing me to buy this chemistry software from cenegage called owlv2. Is there any way to get it free or at least cheaper than the regular 100 dollars price.

Lab teacher is asking us what's the composition of a glass tube we put under a flame. It gives off a bright yellow so I gather it has sodium, and the only glass with sodium I could find was sodium silicate. Is that it, or could it be something else?

>>9153677
Disregard that, found out it's soda-lime glass.

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*sigh*

How do I plug in 1/(x+5) ?

>>9147794
No idea. She is just some Jewess I've seen posted on pol by Israelis. Most of her pics are NSFW.

>>9153802
u put into function

>>9153817
yes, but I don't remember how that first step should look. should it look something like
( (x+deltax) / (x +5) - 1/(x+5) ) / (deltax) ?

Sorry that looks so autistic — I'm a complete knub.

simplify plox

sqrt( (64x^(3/4))^(1/2) / 2x^(-1/4) )

>>9153835
I'm pretty sure you could just input that on symbolab and they'd show you how to do that with steps.

Can /sci/ tell me if I got this right

[math]
f(n) = { if n > 100: n-10; if n \leq 100: f(f(n+11)

f(99) = f(f(n+11) = f(f(110) = f(100)
f(100) = f(f(n+11) = f(f(111) = f(101)
f(101) = 101 - 10 = 91

f(99), f(100), f(101) = 91
[/math]

>>9153862
>>9153862

I thought [math*] contained newlines

I'll write it out in English

If n is greater than 100, f(n) = n-10
If n is less than or equal to 100, f(n) = f(f(n+11)

Find f(99), f(100) and f(101)

My answer was that all three equal 91.

>>9153802
All right, you sons of bitches. Pulled myself up by my bootstraps. For anyone who's curious, look up the "difference quotient."

>>9153928
good job anon! do you know what that limit means?

>>9153107
Why not?

>>9153938
The limit in that equation is actually the easiest part for me to grasp since we're covering limits in class now (Calculus I, as I'm sure most of you know). I just forgot about the difference quotient over summer.

If z+z* = 2Re(z)
Then what is z*+z? Is it the same as above?
What about xt*y* + x*ty?

I'm currently struggling through a master's in physics and honestly I've just lost all interest.

Can I don anything with my bachelor's or should I just become a bus driver

Let [math]f(X)=a_nX^n+a_{n-1}X^{n-1}+\cdots + a_1 X +a_0[/math] and [math]g(X)=b_mX^m+b_{m-1}X^{m-1}+\cdots + b_1 X +b_0[/math], The sum of f and g is defined as [math]f(X)+g(X)=c_kX^k+c_{k-1}X^{k-1}+\cdots + c_1 X +c_0[/math]
where [math]c_i=a_i+b_i[/math] and [math]k=\max\{n,m\}[/math].
Can someone explain that? I don't understand the k part

>>9149035
In short, youre finding the probability of choosing a permutation where NOT("5 is first" AND "9 is last"),
but the question is asking for the probability of choosing a permutation where (NOT "5 is first") AND (NOT "9 is last")

Now let [math] s [/math] be the universe of discourse and the set of all permutations of the elements of {0,1,2,...,9}.
Let also [math] q [/math] and [math] r [/math] be the sets of all permutations where 5 is first and 9 is last, respectively.

(To understand this better, your answer becomes [math] \displaystyle\frac{|(q\cap r)'|}{|s|}=\frac{|s|-|q\cap r|}{|s|} [/math]. )
What we want to find is [math] |q'\cap r'|/|s| [/math] or equivalently, by de Morgans law, [math] |(q\cup r)'|/|s| [/math].
Clearly [math] |(q\cup r)'|=|s|-|q\cup r| [/math] and by the inclusion/exclusion principle [math] |q\cup r|=|q|+|r|-|q\cap r| [/math].
Combining these, the probability is [math] \displaystyle \frac{|s|-(|q|+|r|-|q\cap r|)}{|s|}\,. [/math]

As youve already worked out, the set sizes are [math] |s|=10!\,,\ |r|=|q|=9!\,,\ |r\cap q|=8! [/math] so the probability is [math] \frac{8!\cdot 73}{10!} [/math], which is the same as the answer

>>9153862
>>9153872
maybe im misunderstanding, but
[math] f(n)=\begin{cases}n-1, & n>100\\ f(f(n+11)),& n\leq 100\end{cases}\,. [/math]

[math] f(99)=f(f(99+11))=f(f(110))=f(109)=108 [/math]
[math] f(100)=f(f(100+11))=f(f(111))=f(110)=109 [/math]
[math] f(101)=100 [/math]

>>9154004
> what is z*+z? Is it the same as above?
Addition is commutative.
> What about xt*y* + x*ty?
Note that a*b*=(ab)* and ab*=(a*b)*
So xt*y*+x*ty
= x(ty)*+x*(ty)
= x(ty)*+(x(ty)*)*
= 2*Re(x(ty)*)

>>9154160
>Addition is commutative.
Prove it.

>>9154180
>Prove it.
"no"

>>9153872
Apologies, I'm no good with the Latex syntax on sci.

[math]
f(n)=\begin{cases}n-10, & n>100\\ f(f(n+11)),& n\leq 100\end{cases}\,.
[/math]

n - 10 not 1

>>9154185
>>>/lit/ might be a better board for you then. We demand rigor here.

Would you address all PH.D professors as "Doctor"?

>>9154190
>We
Speak for yourself.

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I need help to find alpha. Knowing the fact that the sum of all triangle's angles is equal to 180° i managed to find most of the angles but not alpha.

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>>9154203
Here are the ones that i've found. Hope you can help (or at least give me a clue).

>>9146393
180-33-30 = 117 degress for angle 'c'

from there it is easy to break down the 330lb (go SI already, jesus.) into x and y axis forces so you can find out what is needed

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Can someone explain how substituting 2k for m gives 4k2
Surely it should be 2k2
pic related

>>9154319
[math]m^2 = (2k)^2 = 2^2 * k^2 = 4k^2[/math]

>>9154319
Substituting [math]m = 2k[/math] in [math]m^2[/math] yields [math](2k)^2 = (2^2)(k^2) = 4k^2[/math].

>>9154328
>ninja'd to the tune of less than a second
Fuck your shit m8

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>>9154319
>"real" line
No such thing.

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>>9154203
>>9154206
Help me please ! Is it even possible to find Alpha or am I being tricked here ? Somebody tell me

> Was a discussion between me, O, M and D
> O said we should kill newborn with chromosomal deseases because it is a logical action, because animals do it and logic is the behavior of the most, the common sense behavior.
> D said we shouldn't because it was cruel and they have the right to live.
>O and M said it was irrational and a non logical behavior, and M tried to support that the behavior of common sense was based on the surviving of a society.
Do you think to say an argument is irrational is enough for to say it's not valid? Do you think that logical behavior is really logical in the context that it's an abstraction of a common behavior? Does the argument of O really based on statistic data while if we say that humans behave in both ways we are saying that not every animals behave in the same way? Can we really say that we are acting logically while we really don't own our notions of our nature? Can we define our nature for to act like that and say we are acting logically? Is logical behavior really logic or just an expresion of a pragmatic true beyon our interpretations? Is mathematical logic process really used to analyse this case?

>>9149484
There are hundreds or thousands of rich white people around the world working on a virus that kills all non-whites as we speak.

We'll let you know when we figure it out.

if there are 15 dumplings in one big plate of soup (let's say 400 milliliters), what is their molar concentration?

>>9154394
You'll never get us whitey. AIDS didn't work and neither did ebola, we only came be stronger.

>>9154379
Define mathematically what "logical action" and "logical behavior" mean or fuck off to >>>/lit/

>>9154418
acting and behaving w.r.t. logic

How does one grow biological flesh tissue without flaying cloned bodies?

How does one change the color of the sclera and iris?

Can an embryo be altered genetically to make offspring look differently or take the traits of another ethnic group?

Now that hot plasma fuel for nuclear reactors exist, will plasma reactors directed energy cannons soon arrive?

>>9154418
That's exactly what I mean. Those "variables" are not mathematically representable (I think no, because I can't imagine a way to) and for that maybe the "logical" of the arguments is just a pragmatic truth but not a real logical one. I posted just because maybe there's a way I'm not realised.

>>9154421
Which logic?

>>9154447
>Which logic?
Whichever you want

Is there no Book of Proof even problems solutions handbook? I'm struggling with one of them and I can't find anything online. Most I got was a half assed Chapter 4 solutions .tex

How to survive a bad math professor?

>>9154494
Skip lectures, read book and solve problems

>>9149035
An alternative to >>9154116, more combinatorial approach:

There are two cases in which 5 is not in the first position:
Case 1: 5 is in the last position. Then there are 9 remaining positions for the number 9 and 8! ways to distribute the remaining numbers to the remaining positions, i.e. 1*9*8! such permutations.
Case 2: 5 is not in the last and not in the first position. Hence there are 8 options for the number 5 and then 8 remaining positions for the number 9 and, again, 8! ways to distribute the remaining numbers, i.e. 8*8*8! such permutations.

As your probability distribution is the Uniform over [math]S_{10}[/math], the probability is (1*9*8! + 8*8*8!)/10!.

>>9154494
What do you mean by "bad"?

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Phone poster here need help i am home schooled and have a test tomorrow can someone help me with these questions please

>>9154494
>>9154498
And make sure you have a good book. Stack Exchange has good recommendations for every subject. Have a book for reading and use the classes book just for the homework problems (unless the class book is good).
Of course a study group is nice. If your TA has office hours go to them every week.

>>9154528
Dude literally read the book. The answers are in there.

>>9154337
Fuck off, Wildberger

If [math]s[/math] is any element of a ring [math]S[/math], then there is a unique ring homomorphism [math]\phi: \mathbb{Z}[x] \rightarrow S[/math] sending [math]x[/math] to [math]s[/math] and 'extending' the unique ring homomorphism [math]\imath : \mathbb{Z} \rightarrow S[/math]. I don't get why there is no assumption [math]s[/math] commutes with every [math]s' \in im \ \imath[/math]. Can't prove [math]\phi[/math] preserves multiplication otherwise

>>9154596
>Can't prove ϕ preserves multiplication otherwise
Why not?

>>9154596
the image is isomorphic to a quotient ring of Z[x] by the first isomorphism theorem, and quotients of commutative rings are commutative, so there shouldn't be any issue

>>9154604
Because [math]\phi(\sum \sum_{i+j=k}a_ib_jx^k ) = \sum \sum_{i+j=k}\imath(a_i)\imath(b_j)s^k = (\sum_k \imath(a_k)s^k)(\sum_k \imath(b_k)s^k) = \phi(\sum_k a_kx^k)\phi(\sum_k b_kx^k)[/math] assumes that [math]s[/math] commutes with image of [math]\imath[/math]. It is forced by definition of polynomial ring, that is, [math]x[/math] commutes with ring elements.

>>9154617
Yeah, the image itself is commutative, but this [math]s[/math] mustn't be an element of it and there's not guarantee it commutes with the image

>>9154633
s commutes with the i(ak)'s and i(bk)'s since those are just sums of the multiplicative identities, some shit like

s(1+1+1+1+1)=s1+s1+s1+s1+s1+s1=1s+1s+1s+1s+1s=(1+1+1+1+1)s

>>9154633
> the image itself is commutative, but this s mustn't be an element of it
But phi(x)=s?

>>9154643
this must be some next level of blindness from me, thanks.

>>9154650
np, the path to becoming a brainiac is a long one

I need to show that if two linear operators [math]T, U: V \rightarrow V[/math] commute then they're simultaneously diagonalizable.
If they commute, then let [math]v \in V[/math] such that [math]v[/math] is eigenvector of T, so:
[math]TUv = UTv = U \lambda v = \lambda Uv \implies Uv \in E_{\lambda} : E_{\lambda}[/math] is eigenspace of T in respect to
that [math]\lambda[/math].
If the eigenspace is unidimensional, then [math]Uv_j = \lambda^{'} v[/math], thus [math]v_j[/math] must also be
eigenvector of [math]U[/math]. Now if [math]E_{\lambda}[/math] has more than one
eigenvector in it, then [math]Uv = \alpha_1 v_1 + ... + \alpha_k v_k[/math] where each v are eigenvector in the eigenspace and
each [math]\alpha[/math] is a scalar. That linear combination of eigenvectors is still eigenvector of T, but how do I show it
is eigenvector of U?
I've looked it up on Google, but they only talk about the unidimensional case.
Sorry for being a brainlet.
Thanks!

>>9146393
>>9146421
This is my first time on /sci/ and I am already creeped the fuck out because I don't know what any of this means.

>>9154686
>If they commute, then let v∈V such that v is eigenvector of T
Why do you assume T has an eigenvector?

>>9154703
Sorry, I forgot to mention that they're diagonalizable.

Long story short, had to give up studying just before getting into university to work, and now I can go back to it, any place where I can find some math textbooks from early highschool to just before college level? I've also checked Khan academy but I'd rather have text based info thanks in advance

Why exactly do degrees of freedom matter when we are calculating a t-statistic or f-statistic?

I understand what dofs are nominally, but I don't really get why they matter or what their power is as an object

>>9154750
I think the sticky might have what you need.

>>9154688
Welcome to combinatorics nigger. Enjoy your stay in a hell where there is no learning and only building intuition from doing a shitton of problems

SOS

True or false and why? If [math]A_1\supseteq A_2\supseteq A_3\supseteq ...[/math] are all finite, nonempty sets of real numbers, then the intersection [math]\bigcap^{\infty}_n A_n[/math] is finite and nonempty.

Pls help

>>9155233
I should stipulate that, according to the prof, "finite" does NOT mean bounded. It means a finite amount of points on the number line.

>>9155233
true, the intersection has to have somewhere between 1 and |A_1| elements

>>9155236
Can you explain? I'm not sure how to even come up with a finite, nonempty set of real numbers, nested within eachother...

>>9155237
>I'm not sure how to even come up with a finite, nonempty set of real numbers, nested within eachother...
because they're all finite and non-empty there exists some n such that A_i = A_j for all i,j>n

a short example is [math] \{1,2,3\} \supset \{1,2\} \supset \{1\} \supset \{1\} \supset \{1\} \cdots [/math] where every set after the dots is also {1}

>>9155243
>because they're all finite and non-empty there exists some n such that A_i = A_j for all i,j>n
intredasting thought. Thanks

>>9155243
>because they're all finite and non-empty there exists some n such that A_i = A_j for all i,j>n
the non-emptiness isn't actually important in this part, can rewrite it as
>because they're all finite there exists some n such that A_i = A_j for all i,j>n

>>9155260
That particular statement is still true, but the idea was we wanted to show the intersection was nonempty, so we had to stipulate its constituents were nonempty

I'm not very knowledgeable of "formal math writing"
Like that sideways fork thing that means "x is the domain of y", it's seriously fucking with my ability to research further into harmonic analysis
Any way to get familiar with it and how to characterize and read back formulas work with them?

>>9155380
>Any way to get familiar with it and how to characterize and read back formulas work with them?
Read a textbook on logic and set theory. It should not be difficult.

>>9155051
Yeah you are right thanks mate

brainlet here, I have a question about syntax for ODE45 in matlab.

I have a DE of [math] \left[ \dfrac {dC}{dt}\right] =\left[ C\right] \left[ \wedge \right] [/math] which is a 3x3 matrix. [math]\left[ C\left( 0\right) \right] [/math] is known (3x3) and [math] \left[ \wedge \right] [/math] is the angular velocity matrix (skewsymetric with time dependent variables in the off-diagonal positions.)

I'm looking for the variation of Cij (it maps the coordinization from one reference frame to another as one tumbles relative to the other) over the time interval, which I'd like to do by solving that DE and then integrating the 9 solutions.

I just dont know the damn syntax to put the piece of shit into ODE45, I've never used it for something like that.

[t,C] = ode45(@(t,C) C*A, [timespan], C(0));
Where C is a 3x3 matrix full of symbolic places holders, eg syms C11, C12, etc?
I'm stumped.

Find all functions A(t) such that u (x,y) = A (x^2+y^2) is harmonic

Wot de fok? I assume t is complex? Idk mane

>>9155582
>Wot de fok?
>Idk mane
>>>/b/

>>9155211

I thought I finished highschool.

Why is that if I have a complex rational function of degree n , say f, then for every complex bumber "w" we have that there are exactly n solutions (up to multiplicity) of f(x)=w

File: 20170908_095949.jpg (1MB, 3264x1836px) Image search: [Google]

1MB, 3264x1836px

guys I feel like a complete and utter brainlet in basic probability... could you help me solve this for P(A)? please show the steps so I could figure out where I got lost.
this is the problem:

thanks in advance!

>>9155611
the problem is in pic related in case it's not clear haha

>>9155603
f(x) = w
=> g(x)/h(x) = w
=> g(x)-w.h(x) = 0
where g,h are polynomials of degree n. So the LHS is also a polynomial of degree n, which has n roots.

>>9155750
>So the LHS is also a polynomial of degree n
except when leadingcoefficient(g)-w*leadingcoefficient(h)=0

>>9155611
seriously no answers to this stupid question?

>>9154187
>n - 10 not 1
my bad. in that case
[math]f(99)=f(f(110))=f(100)=f(111)=f(101)=91[/math]
[math]f(100)=f(f(111))=f(101)=91[/math]
[math]f(101)=91 [/math]
in fact id also bet that [math]f(n)=91[/math] for all integers [math]n<102[/math]

>>9154206
The small triangle containing alpha and the medium triangle are mirror images of eachother.

>>9154528

I dont care that i am not gonna learn anything i don't care about this and the only reason i am is cause i forced to please help guys come one everyone else i turned to are assholes please help a brother out i know you have gone through this too

When passed-out / unconscious, does your body perform the same functions it does when you're asleep?

>>9146393
F(AC)=cos(50)x300lb= 1.9x10^2 Ib
F(BC)=cos(35)x300Ib=2.5x10^2 Ib

>>9153535
>butthurt about being proven wrong detected

>>9153185
I'm not complaining about anything. You asked for a shorter way to write the proof and I gave you one.

>>9156714
Being wrong about what?

>>9155582
Use the chain rule and the definition of a harmonic function.

>>9156724
>claims a proof is wrong
>the proof is actually correct
>"I would have given you a 0 since I didn't understand it"

>>9156754
>claims a proof is wrong
When did that happen?

Why is there something rather than nothing?
>context is that I'm developing a game based on this
>also I realize that this question varies extremely from person to person so I'm prepare for different answers

>>9156760
>called it a "proof"
>is now seriously backtracking

>>9156780
>says I claimed the proof was wrong
>is now seriously backtracking
I said "proof" because it included an implication that relies on another theorem, but without any reference to them or how the theorem gives the implication.

>>9155582
The answer should be pretty obvious. It's
A(t)=C*ln(t)+K

>>9156795
>has obviously used a specific theorem based on the conclusion
>"you didn't write down the name of the theorem, therefore your argument is wrong"

>>9156811
>"you didn't write down the name of the theorem, therefore your argument is wrong"
Who are you quoting?

The argument was lacking a calculation that showed the remainders were equal, which was the whole point of the proof to begin with

>>9156822
>still doesn't understand subtraction

>>9156824
>still doesn't understand subtraction
What do you mean?

>>9156825
>" argument was lacking a calculation that showed the remainders were equal"
>is still unable to do a subtraction

>>9156833
>is still unable to do a subtraction
Where did you get this implication? I already said the subtraction was clear here >>9153535

>>9156836
>is given the answer
>"yeah that's obvious, I could have done that"

>>9156843
>>"yeah that's obvious, I could have done that"
Who are you quoting? Your mind seems to keep generating strange quotes

Let [math]A,B,C[/math] be sets of the universe [math]U[/math].
I need to show that [math](A \times B)^c = (A^c \cup U) \cup (U \times B^c)[/math].
I can show that [math](A \times B)^c = (A^c \cup B) \cup (A \times B^c) \cup (A^c \times B^c)[/math]. How do I get that U there?

>>9156849
Its [math](A^c \times U)[/math] by the way, I mistyped.

>>9156845
>still backtracking

>>9156852
>still backtracking
Backtracking to what?

>>9156849
did you try just doing it element wise? like one direction:
(x,y) in (AxB)^c
=> (x,y) not in AxB
=> x not in A or y not in B
=> x in A^c or y in B^c
=> (x,y) in A^c x U or (x,y) in UxB^c
=> (x,y) in A^c x U union UxB^c

most of those steps are probably reversible

>>9156860
Yeah, I did it like that, but I don't understand this step:
>=> (x,y) in A^c x U or (x,y) in UxB^c
Why is it [math]A^c \times U[/math]?

>>9156866
because x in A^c and y in U

>>9156869
Alright, thanks.

>>9156719
Except your shorter proof loses some rigor, which I explicitly asked for. Regardless, the second proof I wrote was shorter than the first one, while still being acceptable.

>>9156854
>was proven wrong
>still trying to pretend he wasn't

>>9156890
Did you misread my post? Your greentext doesn't seem to answer the question

>>9156896
>not only unable to understand proofs, but also arguments in general

>>9156903
Which part of your proof did I not understand? I already said it was right

Also your "arguments in general" are simply non sequiturs, there's no depth to them to be confused by

>>9156911
>>9156843

>>9156916
That post doesn't seem to contain a part of your proof that I didn't understand, could you try again?

>>9156922
>>9151254

>>9156925
That post doesn't seem to contain a part of your proof that I didn't understand either, could you try again?

In fact your proof is in this post >>9152746, so I'm not sure why you continue to non sequitur by linking two other posts

>>9156931
>sees his own post asking about something he didn't understand
>"That post doesn't seem to contain a part of your proof that I didn't understand"

>>9156934
>>sees his own post asking about something he didn't understand
You seem confused, there wasn't anything misunderstood (which is why nothing in my post refers to something I did not understand), your "proof" just needed elucidation before being able to consider it a proof.

>>9156938
>>9156843
Also:
>"it's only a proof if I understand it"

>>9156940
>>"it's only a proof if I understand it"
Who are you quoting?

>>9156941
>"your "proof" just needed elucidation before being able to consider it a proof."
>"it's only a proof if I understand it"

>>9156945
>>"it's only a proof if I understand it"
see >>9156941

>>9156947
Well, looks like you just aren't smart enough to understand green-text. I'll explain the boring way then. The sentence:
>"your "proof" just needed elucidation before being able to consider it a proof."
has the same meaning as:
>"it's only a proof if I understand it"
Understand?

>>9156955
>Understand?
Still not totally, could you elaborate?

>>9156961
When you finish high school you'll learn that trivial steps in proofs are usually left out. Whether you personally understand a proof has no bearing on whether it actually is one.

>>9156966
>When you finish high school you'll learn that trivial steps in proofs are usually left out.
But your "proof" was simply stating what needed to be shown, which is why it was a "proof" and not a proof.

>Whether you personally understand a proof has no bearing on whether it actually is one.
This is true of formal proofs but not informal proofs. Though your "proof" was not even an informal proof and so you'll have to explain the relevance of this statement.

>>9156976
We've already established that you didn't understand it before it was explained to you. Your critique of it is therefore just you showing your own butthurt. As already explained.

>This is true of formal proofs but not informal proofs.
Nope, sorry.

>>9156983
>We've already established that you didn't understand it before it was explained to you
When was this?

>Nope, sorry.
When you finish undergrad you'll learn that peer review exists because whether you personally think an informal proof is correct or not has no bearing on whether it actually is.

>>9156987
>peer review
If you actually read a paper you'll learn the difference between peer review and "idiot who doesn't even understand subtraction" review.

>>9156991
>"idiot who doesn't even understand subtraction
Who are you referring to?

>>9156999
The only person I have been referring to in this thread is you.

>>9156999
Anyway, it's been fun. I have other things to do today, so I'm off. I wish you luck on finishing high school.

>>9154116
>De Morgan's Law
Getting an anxiety attack seeing this because I'm way behind in my Discrete Math homework.

I like the idea of burning things with sunlight and a large converging lens.
However, I don't like the fact that the burning point is a set distance away from the lens.

Is there any reason why I couldn't place a diverging lens just before the focal point or a converging lens just after it, and collimate the cone of sunlight into a "beam"?

>>9157005
>The only person I have been referring to in this thread is you.
What subtraction did I not understand?