/sci/ - Science & Math

what is the conspiracy behind everyone pretending [math]4\pi r^2[/math] was the surface area of a sphere for thousands of years?

>>14879697
Good job, sir. That is a very stupid question indeed. Thank you for setting the tone of this thread.

>>14879691
I asked this a few threads ago and never got a response.

Let's say you have a finite set of points, and you want to define two distinct topologies on this set. Is there a name for this combination of a set and two topologies?

>>14879748
If nobody can think of a name for this setup, I think that means you have your answer.

>>14879691
Hey, if you have questions on PDE or related topics please check out:
>>14879555

Unanswered questions:

Math questions:
>>14879073 >>14879079
>>14878291
>>14876298
>>14875745
>>14874946
>>14874877
>>14874682
>>14873475 >>14873495
>>14872725
>>14871508 (That's exactly what the axiom of extensionality is saying, duh)
>>14870747
>>14863090
>>14865209

Logic question:
>>14869187

Physics questions:
>>14877029
>>14868280
>>14873788

Biochemistry question:
>>14869383 (such calculations are not possible with current computational power, plus protein folding is complicated by chaperons)

Stupid questions:
>>14875677
>>14874822 >>14874834
>>14874544
>>14872929
>>14871329
>>14870744
>>14867486
>>14865959
>>14865661
>>14862328
>>14862046
>>14861347
>>14860730

Laugh at this guy:
>>14872153

R.I.P.:
>>14864837
>>14862127

I might have missed or duplicated few questions.

>>14878291
>Please give a short example of a vector space that isn't in Rn. Something that is easily memorizable.
The continuous functions from R to R.

scientifically speaking - why do I, a 6'5" and muscular man, have intense desires to be small, weak and subservient to stronger and larger men? why did these desires crop up in mind at 11 years old, 2 years before I ever discovered pornography? this is a serious question and I don't know where else to ask
outside of these desires my life is very normal and I've had two loving parents for my whole life

>>14879865
your ancestors were probably slaves for many generations.

>>14879865
kinks and fetishes don't have to have a reason, they just happen. that said many start during puberty when your body is flooded with hormones and your brain is wiring itself for sex.

>>14879761
Anon, I want you to know that I really appreciate your efforts in summarizing the unanswered questions each thread. It makes you one of the few people that makes this place worthwhile to hang around.

How do you prove closure of a + b + ab in Z\{-1} ? Trying to show it's a group

>>14879761
What's stupid about my >>14875677, faggot?

>>14878291
Do you mean is not in Rn or is not Rn, or over Rn? Either way, polynomials are not Rn but isomorphic to it. One example of vector space that is completely different from everything else is:

[math] (2^S, \triangle, \cdot, \mathbb Z_2)[/math] where [math] 2^S[/math] is the power set of some [math] S[/math], the vector operation is symmetric difference, [math] \mathbb Z_2[/math] is integers modulo 2, and [math] \cdot[/math] is identity or null set, depending on whether you are multiplying by [math] 0[/math] or [math] 1[/math]

>>14879866
you're actually not wrong but I don't think this is the correct answer
>>14879871
but why didn't my body want to sex girls?

>>14879907
Lmao (lol).
>>14879073
>>14879079
Pretty sure it's a typographical issue and it's supposed to be [math]z = p^{\pm h} r/s[/math]
>>14878291
Spaces of matrices, spaces of functions, etc.
>>14876298
Don't the sup and inf need to be in [math]M[/math]?

I'm wondering if it's possible to create a gas matrix that's good at maintaining an excited state. Specifically, I'm wondering if anyone here knows what, if anything, could hinder plasma from relaxation energy-level wise: like if certain gasses would hinder the relaxation of other, more easily excited gasses if combined. I'm probably just bastardizing and misunderstanding the principles of lasing, but if anything comes to mind that'd be neat.

>>14879907
I only did it for this thread, you should thank the guy that came before me who is probably here >>14879984
>>14879912
Telescoping series are just one basic concept that you can learn on its own, is there anything particular you want to know about telescoping series?

>>14879691
Why is this true:
[math]\dfrac{\Delta I}{I} = 1. [/math]
In a physics question I made, the change in current divided by the current, like above, was 1? How is that possible?

>>14880018
ΔI = 2I?

>>14880010
>is there anything particular you want to know about telescoping series?
Exercises

>>14880027
Or actually, ΔI = 2I - I

>>14880034
>>14880027
Fucking confusing, I asked in the last thread as well. It was an exercise about electromagnets. Basically paraphrased:
---
A current of I = 1A flows through an electromagnet (coil) with N = 10^3 windings. Its length is l = 0.4m and it has a cross-section of A = 100 cm^2. The whole wire has a resistance of R = 5 Ohm. Inside the magnet, there's an iron core with a magnetic field strength of B = 1T.

Calculate the induced voltage U_ind, when the magnet is turned off for [math] \Delta t = 1 ms. [/math]
---
Pic related is the solution, I got the same, except at the end. If you do some proper calculations for L, you get the following, [math] L = \dfrac{NBA}{I} [\math], which they've substituted for the final solution. I just don't get why the current and change in current disappears.

Here's what they get at the end with L subsituted:
[math] U_{ind} = -L \dfrac{\Delta I}{\Delta t} = \dfrac{NBA}{I} \dfrac{\Delta I}{\Delta t} [/math]
and continued from there, somehow the current disappears completely (see pic's solution). How?

>>14880138
Sorry, I fucking hate shitting up the thread because of that mistake. When you subsitute L you get:
[math]U_ind = \dfrac{NBA}{I} \dfrac{\Delta I}{\Delta t}. [/math]
Then they somehow cancel out Delta I / I? How?

>>14879697
>>14879737
But you never answered?

>>14880010
>I only did it for this thread, you should thank the guy that came before me who is probably here >>14879984
Please redirect the appreciation appropriately, lads.

>>14879691
What is the union operator with exclamation mark here called? A disjoint union?

>>14879860
>>14879912
>>14879984
Thank you anons

>>14880265
I've never seen this (and so it's not standard/not used in praxis), but I think this should be to Exclusive Or what the standard union is to Or.

It's not a "disjoint union", since that term is already used for the tagged union (the categorical plus).

>>14879910
[math] ab+a+b = -1 \\ ab+a+b+1=0 \\ (a+1)(b+1)=0 [/math]
Therefore [math] ab+a+b [/math] will be equal to [math] -1 [/math] if and only if either [math] a [/math] or [math] b [/math] are equal to [math] -1 [/math]

>>14879691
why do homosexual pedophiles who masturbate to children's cartoons insist on spamming the science board with their masturbation material instead of using one of the many 4chan boards dedicated to post pedophilic cartoon masturbation material for that purpose? why do /sci/ have to be spammed day in day out with pedophilic eriotica? why does this board have to be incessantly proagandaized by this unwanted material from unwanted people?
why are the homosexual pedophiles who masturbate to children's cartoons so proud of their deviancy? what explains the anime pedophile's unhinged, aggressive exhibitionism?

>>14880510
Can science explain this one?

>>14880525
yes, this is what happens when you don't take your meds

>>14879691
Whatever happened to Yumemi et al? Her group used to publish all sorts of funny papers on ArXiV and then vixra, but then they just stopped. Can't find anything by her colleagues either.

What would be an example for (c)?

The closest thing I found is
[math]A = (-2,-1) \cup (-1,0] \cup ([0,1] \cap \mathbb{Q}) \cup \{2\} [/math]
this gives
[math]\overset{\circ}{A} = (-2,-1) \cup (-1,0) \\
\bar A = [-2,1] \cup \{2\} \\
\alpha(A) = (-2,1) \\
\beta(A) = [-2,0] \\
\alpha(\overset{\circ}{A}) = (-2,0) \\
\beta(\bar A) = [-2,1]
[/math]

but this still has two set inclusions too many.

>>14880138
>>14880146
Are they clear about how the magnet is turned off? It could be just a formula translated into a badly written question. That is, they mean to suggest that the current drops to zero in 1ms. What's the source?

>>14880722
I'd be much more willing to help you if you told me what are the two extra inclusions and I didn't have to spend half an hour hunting them down.

>>14880850
[math] \alpha(\overset{\circ}{A}) \subset \alpha(A) [/math] and [math] \beta(A) \subset \beta(\bar A)[/math]

>>14879761
>That's exactly what the axiom of extensionality is saying
Wrong. a=b does not imply b is an element of c if a is one.

Do photons accelerate? Or do they come into existence already at full speed?

>>14880862
Both of those are always true, the author just forgot to include them.

>>14880785
It is from one of TUM's experimental physics problems (the first one here https://www.ph.tum.de/academics/bsc/break/2009s/fk_PH0002_03_exercise.pdf)), sadly it's German, so I doubt it would be of help. I've thought about it dropping to 0 too, if that were the case then Delta I = I_after - I = 0 - I = -I. Which does make sense at first, but the problem is, the sign of the answer would be flipped.

Fuck it anon, I'll just assume this is a badly worded question and move on.

>>14880872
>>14879761
for the record, I'm saying the axiom of extensionality is needed for that to be true. Hence why just a definition may not suffice but I could be wrong.

>>14879691
In simple electrical generators like pic related, in real life, how do they make these spin? If you put a current through it, wouldn't the thing start spinning solely by magnetic forces? Obviously that isn't possible and I'm making a retarded mistake, they're turned by mechanical forces; does the Lorentz force then assist it in turning?

By energy conservation, there have to forces that stop the thing from turning, otherwise it'd infinitely turn by its own induced current.

>>14880872
That is part of the axioms of equality, which are what the ZF axioms build on.

>>14879752
Then henceforth such a configuration shall be known as "bosom buddy topologies."

>>14881061
I want to turn this into an >open balls are touching< joke somehow.

>>14881074
No homotopy.

>>14880944
>does the Lorentz force then assist it in turning?
No, it opposes it. That's why you need to put mechanical power in; you can't just start it spinning and extract electrical power. If a generator isn't attached to anything, it doesn't require much torque to spin it, but as soon as you start drawing current the torque required to keep it spinning increases proportionally.

Similarly, if you use it as a motor, it doesn't need much electrical power to make it spin unless there's some kind of torque opposing the spin; the more effort it takes to make it spin, the more current it draws.

What are some low powerlevel, over-the-counter vitamins/medications to improve focus? Other than caffeine and nicotine.
Yes I have ADHD, no it isn't medicated.

does anyone have a video lecture on this topic?
https://openstax.org/books/university-physics-volume-1/pages/14-introduction
Chapter 14: Fluid Mechanics
i tried reading the textbook but i dont get it
can someone link me like a video lecture or something

>>14873788
theyre not always depicted like that.
youre right that the energy levels of an idealized "particle in a box" should go as [math]n^2[/math], but you should understand that it takes like 60 million assumptions before you arrive at thinking a cluster of atoms constitutes a nice box of potential. even just one (nonhydrogen) atom is already making assumptions when you go to solve its energy levels. slapping hundreds of (different) atoms together makes weird stuff happen. the band gap splitting in the first place is an example of this weird stuff.
all this to say, you cant take the particle in a box thing too seriously with sold-state physics. here, its mainly used to give plausibility when saying that "smaller particles have bigger gaps". spoiler: prefect crystals dont actually exist, and even if they did, perfect band gaps wouldnt exist either.

>>14880510
i don't masturbate to cartoons.
i just thought AOT was kind cool till the third season

>>14881128
Thank you anon, much appreciated. All makes sense now.

Why am I absolute shit at solving logic/brain teaser problems that are commonly found in IQ tests or job interviews? I don't think I'm completely retarded as I graduated with a STEM degree at a top 20 university in the US and have a successful career as an ML Engineer. However, I can't help but feel retarded when around my friends as they can easily solve logic/puzzle problems while I fumble for hours.

Anons is pic related true or false? And why?

>>14881435
Since [math] h [/math] is continuous then it has some anti-derivative, let [math] H [/math] be one such anti-derivative.[eqn] \frac{d}{dx} \left( \int_{3}^{x^2} h(t) \; dt \right) \\ =\frac{d}{dx} \left( H(x^2) - H(3) \right) \\ = 2xh(x^2)[/eqn]

>>14879691
Source on OP image ?

>>14881442
Ohhh that makes sense. Anon you are amazing. Can you help me this one as well?

>>14881450
Use the chain-rule.

>>14881452
I forgot how to use it.

>>14881453
jesus christ faggot don't expect people to hand hold you this much

>>14881450
Come on dude, this exercise isn't hard, just take the derivative of h(x) like it's a normal function with the chain rule and see what happens, i'm going to give you a minute before i post

>>14881455
please man its for a quiz I last took calculus 2 years ago lmao

>>14881453
>>14881457
[eqn]\frac{d}{dx}f(g(x)) = g'(x) \cdot f'(g(x))[/eqn]
Derivative of the inside times derivative of the outside! Now apply it yourself.

>>14881457
google, retard.

>>14881472
too much adrenaline, sorry anon.

>>14879691
Can someone help me solve this?

i assume i have to find a normal vector first just not sure how to get there

>>14881470
I tried solving it but I don't think I got it right. I'd post my work but I don't want some TA that browses 4channel.org to flag me for bullshit.
I have no idea when I'm supposed to use f(0)=e and f′(0)=1 and I believe I did the chain rule and product rule correctly.

>>14881537
[eqn]h(x) = u(v(w(f(3x))),x)[/eqn]
with
[eqn]
u(x,y) = xe^y \\
v(x) = -x^2 \\
w(x) = \ln(x)
[/eqn]
The derivatives of those functions are
[eqn]
\nabla u(x,y) = (e^y, x e^y) \\
v'(x) = -2x \\
w'(x) = \frac{1}{x}
[/eqn]
With them you can just repeatly apply the chain rule
[eqn]
h'(x) = e^x (-2 \ln(f(3x))) \frac{1}{f(3x)} f'(3x) 3 - (\ln(f(3x)))^2 e^x \\
= \left( -6 \frac{\ln(f(3x)) f'(3x)}{f(3x)} - (\ln(f(3x)))^2 \right) e^x
[/eqn]
Now plug in x=0

[eqn]
h'(0) = -6 \frac{\ln(f(0)) f'(0)}{f(0)} - (\ln(f(0)))^2 = -\frac{6}{e} - 1
[/eqn]

>>14881563
Thank you so much, anon. What confused me was that I thought I couldn't have f(3x) = 0
I'm gonna study properly from now on this was too much stress on my heart.

>>14881152
bump can someone answer me

>>14879697
they weren't pretending
they were just retarded
there is no secret society of people who know real math
there is no conspiracy
humans just don't pay attention, and take things for granted

>>14881282
>till the third season
Based. Everything after it is so overrated.

When astronomers make parallax measurements how do they know the background stars haven't shifted all at the same time somehow, thus skewing the distances they measure?

>>14881988
usually you either pick something that's so far away that its motion can't be observed in the timescale of the experiment, or something whose motion you understand well and can calibrate to
it wouldn't really make sense to use your "reference" background as something you also don't understand well

>>14882018
How do we really know the background is far away though and not all moving together giving the illusion of being a fixed background?

>>14881444
learn 2 reverse image search dummy
https://images.google.com/
https://tineye.com/
https://saucenao.com/
https://iqdb.org/

>>14881988
they lie about everything because they know you don't have a space ship to go out and check to see if they're lying

[math]M := \{\{\{1, 2\}, \{3, 4\}\}, \{4, 5\}, 6, 7\} \\ (1)\ \bigcup M = \{\{1, 2\}, \{3, 4\}, 4, 5, 6, 7\} \\(2)\ \bigcup M = \{1, 2, 3, 4, 5, 6, 7\}[/math]

Is it (1) or (2)?

>>14881344
Because you can't solve logic problems by spinning the letters around in your mind.

>>14882060
Because depth-of-field and red-shift are a thing.

>>14882354
Neither.

>>14881344
Maybe you're subconsciously insecure about your performance and this insecurity prevents you from performing better. Try and take it easier. These tests don't test your intelligence as much as more your capability to work under pressure and stress.

>>14882380
So what's the solution? Is it the [math]\bigcup M[/math] operation not defined with this set? If so, why?

>>14882392
What the fuck do you even mean with [math]\bigcup M[/math]?
If you mean something like
[eqn]\bigcup M = \bigcup_{A \in M} A[/eqn]
then you have to explain what types of sets 6 and 7 are. If you use the von Neumann ordinals where each finite ordinal number is the set of all smaller ordinals then
[eqn]\bigcup_{A \in M} A = \{ \{1,2\},\{3,4\},0,1,2,3,4,5,6 \}[/eqn]

>>14881527
We choose [math]t = 0, 1[/math] to obtain the points in the line [math](1, 5, 0)[/math] and [math](3, 4, 1)[/math]. So any point in the plane can be expressed as [math](0, 0, 1) + u ((1, 5, 0) - (0, 0, 1)) + v((3, 4, 1) - (0, 0, 1)) = (0, 0, 1) + u (1, 5, -1) + v (3, 4, 0)[/math]. The normal vector to the plane is orthogonal to both [math](1, 5, -1)[/math] and [math](3, 4, 0)[/math]. Then you can take the difference between [math](1, 2, 3)[/math] and any point in the plane (i.e. (0, 0, 1)), project the difference onto the normal vector and compute the norm of the result to get the distance.

I don't remember if there was a simpler way to do this.

How can you have a sequence eith infinitely many terms when each term has a finite position in the sequence?

>>14882615
Consider the infinite sequence 1, 2, 3, 4, ...

How do you draw things using Fourier series?

>>14882667
1. parameterize your curve (doesnt have to be algebraic)
2. perform the Fourier transform on both the x and y coordinates
the circles orbiting around each other is akin to summing the sine waves, im sure you can fill in the details. however, for each frequency it is likely that the x and y amplitudes (which correspond to the radius of the circles) won't be identical, so you need it to orbit farther in one direction than the other. this can be accomplished with two circles, rotating at the same frequency but in different directions, with different radii. this will trace an ellipse.
at least this is how i assume you do it.

>>14882667
Get an array of x,y points on the curve. Treat each point as a complex number z=x+yi. Perform FFT on the array of points. Optionally discard (set to zero) any elements whose magnitude is below some threshold (conversely, select only those elements whose magnitude is above some threshold). An inverse FFT (i.e. sum of sinusoids) will reconstruct the path. Changing the parameterisation affects the series without affecting the path. Some parameterisations may require fewer frequencies than others.

for NLP bros, got this question at an interview, i think i didn't shit myself on this one, but it was pretty interesting i think, how would you answer it?
"If transformers are in essence a model that processes texts and outputs statistical probability of each word occuring next, how would you prove that they're better than just using a huge hidden markov model?""

>>14883026
and to make it clear, it was right after i explained the architecute, how attention works and every technical stuff like that, so it wasn't about that

if [math]\sum_n ||f_n||_2 < \infty[/math], where the f_n are L^2 functions on some measure space, does this imply that the series [math]\sum_n f_n[/math] is absolutely convergent pointwise almost everywhere?

If I finish Amann & Escher, would I need a separate book on undergraduate Complex Analysis?

Can someone motivate the definition of a morphism of varieties? I understand that regular functions on each open set are meant to pull back to regular functions on the preimage of that open set, but what information or underlying structure is this meant to capture? Even the degree of a variety isn’t invariant up to isomorphism, so what will even be the same about two isomorphic varieties?
I feel like I’m also not really asking the right questions about this so if you have anything to add that I didn’t really ask about feel free to explain.
Thanks a bunch

I'm a non-STEM economist and I'm reading a paper with terms like "supermodular function", "convex lattice", "semi-lattice valued", "quasi-convex difference", etc. This is clearly outside my mathematical comfort zone. What subfield of mathematics is this (so I can Google more) and what are some textbooks I can read to update my knowledge?

>>14883266
In case this is too vague, the paper I'm reading is related to "Minimizing a Submodular Function on a Lattice" by Topkis (1978). It has a lot of citations so maybe some anon knows of it. I don't seem to have access to it though.

>>14880510
>aggressive exhibitionism

>>14883212
Depends on if you care about Complex Analysis.
Amann-Escher does include the residue theorem which is the only thing most people care about in Complex Analysis but it does not have enough Complex Analysis for a full class.

>>14881152
>>14881630
bro can someone answer me
does anyone have a good physics lecture playlist or something

>>14883288
https://www.youtube.com/watch?v=A4ZDyzPqnT4

>>14883266
>supermodular functions
Basically that's not really mathematician mathematics, that's economist mathematics. You should pick it up through mathematics for economists, microeconomics texts and related articles.

The other terms are kind of part of convex analysis/optimization tho.
>>14883235
Giving you a shitty answer in case nobody gives you a good one, a variety's intrinsic geometry is entirely encoded in its ring of regular functions, and isomorphisms between varieties are specifically maps that induce isomorphisms between rings of regular functions.

>>14883301
Thanks, I'll look into that. I found the original Topkis paper on SciHub and after skimming it it looks like he defines most of the terms I'm hazy on. I love SciHub.

I'm confused about the binary operation [math] a * b = \sqrt{a b} [/math]. If you have [math] a * (b * c)[/math] would you have that as [math] \sqrt{a \sqrt{bc} } [/math]? Does that mean if bc is a square number that you would then be multiplying a by that number. I know it's a binary operation but the notation just confuses.

I'm a CS student in a security degree and I need to catch up on cryptography. Do you guys know a book that would teach me all the maths I need to know in order to understand what a fucking LFSR has to do with a polynom ? I don't know shit about polynoms. I need a book that covers this kind of things from zero. Thanks.

what if you posted kemono friends images rather than touhou images?

at what point do you stop doing the exercises and move onto the next section of a book?
I'm currently going through a number theory and have been grinding through a section of exercises for about a week now (10 questions in total, but I work full time so only have an hour or two a day to work on them. I also don't look up hints/answer online as a rule, unless I spend more than a week on a problem).
I can definitely feel that these questions are making me better at math and improving my understanding of the material, but I'm getting a little impatient now (I'm selfstudying so don't really have a schedule/deadline I need to follow).
Plus, I've found that some of the exercises implicitly introduce topics that are explicitly taught later, so it seems to me that the author intends to get the reader familiar to the ideas through the exercises before diving deep into the theory later on.
What should I do? Just autistically do every problem?
In the end, I'll probably push through it and do all the exercises but part of me can't help but wonder what is the opportunity cost

>>14883535
>what if you posted kemono friends images rather than touhou images?
I'd need to post way more duplicates.

I have the following thermal circuit where energy is passed from T1 to T2 and T3. The problem is that the areas don't match (A1 is equal to A2+A3). How do I make this consideration in the following equation?

[eqn]mc\frac{dT}{dt}=UA\Delta T[/eqn]

>>14883586
Label the center node T4.
Express the heat flow through each element:
q1 = U A1 (T4 - T1) etc.
Assuming it is a steady-state system, the node (T4) and reservoir (T1, etc.) temperatures don't change. Also, the sum of the heat flows at T4 is 0. (All heat entering the node must also leave.)
q1 = q2 + q3
(For this I'm saying that positive heat flow for each element is right to left.)
Finally, include your area info: A1 = A2 + A3

You now have five equations, but six unknowns: A2,A3,T4,q1,q2,q3. So you'll need a bit more info to solve it completely. I'm assuming you haven't provided all the relevant info.

not sure how to go about this

>>14883765
I am comparing the results obtained in the equation with the ones I obtained experimentally for a PVT+PCM system (T1 is the panel, T2 is the tip of the fins used to better distribute the heat with the PCM and T3 is the temperature of the PCM itself). The actual (well, still a bit simplified) equation for the panel would be the one written bellow, forming a system with 3 other equations for the variation of temperature of the fin, the PCM and the thermal system bellow the PCM reservoir, which I believe is not relevant for now. I is the irradiance received by the panel. The system is not in steady state and the areas are known. My main problem with it is, since the areas are different, I don't know how to merge the resistances and using a fourth temperature node is not viable, since I don't have the measured data for that part of the system.

[eqn]mc\frac{dT_1}{dt}=I-(\frac{1}{R_1}+\frac{1}{R_2})*A*(T_1-T_2)-(\frac{1}{R_1}+\frac{1}{R_3})*A*(T_1-T_3)[/eqn]

How do I get this derivative to this problem I tried using mathway but I got a different answer that I can't make sense of even with factoring differently I get 24 = 6 *4 it's the factored x variables I don't get

>>14883854
sry

>>14883856

>>14883859
>>14883856
These are the same.

[eqn]4(5x^6+2x^3)^3(30x^5+6x^2)=4*x^{3^3}(5x^3+2)^3*6x^2(5x^3+1)=24x^{11}...[/eqn]

>>14883849
Do you still have the TeX for this?

>>14883880
oh wait I need to raise x^3 to ^3 cause its on the outside of paranthesis. I was just getting x^3 okay thx that makes sense

>>14883881
By this do you mean the system of equations? I can write it down and scan it, will probably be easier.

RR tech here, I'm in Alabama for a few days with the family while Ian passes by. Is there really no way to shut this live wire off saw it on the news.

How can I prove magic is real to my university? Last time I tried to explain my encounter with it in Gensokyo I got kicked out.

>>14883889
Study hard, anon!

>>14883980
Come up with a formal definition of magic, and then ask other people if there's anything that they know of that fits that definition.

>>14883490
>polynoms
A polynom is a polynomial as perceived by ESLs. Do you remember what you learned in middle school algebra?

>>14881145
>Yes I have ADHD, no it isn't medicated.
Medicate it

What is the most ethical way to test whether certain drugs are teratogenic in human test subjects? The drugs in question are already category B, so animal testing is redundant, but I'm not sure how to progress from this point.

>>14884256
Am I autistic for even asking this or would a professor actually get on my ass for saying "do it the direct way", basically?

>>14883266
Why are you reading it? Mathematical """economics""", is nonsense. Don't bother.

Any reason I can't just use
[eqn]f(y) = \frac{d(x,y)}{1 + d(x,y)}[/eqn]
?


I guess the hint wants me to construct functions [math]f_k[/math] with [math]f_k(x) = 0[/math] and [math]f_k(y) = 1[/math] for [math]y \in F_k[/math] and then consider
[eqn]f(y) = \sum_{k=1}^\infty \frac{f_k(y)}{2^k}[/eqn]
but is this really needed?

am i retarded? i have to pick a choice but literally none of them are right

Can someone give me a hint on how to prove reverse inclusion? I've been messing with this for a while and nothing's popping out.
My original plan was to just set up a net in S converging to an arbitrary point in the intersection, but it seems like getting something well-defined requires essentially assuming that point is a limit point of S in the first place. Trying to get a contradiction by assuming there's a neighborhood of a point of the intersection which is disjoint from S hasn't gotten me anywhere either.

any japanese speaker here?
What does this mean in relation to insects?
無効分散(むこうぶんさん)

>>14884433
you could argue that a reflection is just a 180 degree rotation in the y axis

>>14884547
https://dictionary.goo.ne.jp/word/無効分散/
https://dictionary.goo.ne.jp/word/死滅回遊魚/
From looking at the entry on online dictionary, it is a new name for 死滅回遊(しめつかいゆう), possibly having a broader meaning. For your case, I am guessing the insects got carried away to some other area and they cannot survive there.

>死滅回遊 (lit. extinction migration): young tropical fish that were brought from Pacific Ocean to Japan Sea through Kuroshio current in early summer. In autumn as water temperature decreases, these fish will die. Seasonal migratory fish.
>無効分散 (lit. invalid dispersion): non-migratory/non-schooling species that are relocated outside of normal habitat through ocean current. New name for "extinction migration". Although the species will perish in the destination area/body of water as season changes or other factors, considering the possibility that the environment will change in the future and the species can settle there, the current dispersion is seen as "ineffective/invalid".

>>14883839
The distance between [math]Q[/math] the plane containing [math]P[/math] with orthogonal vector [math]n[/math] is norm of the orthogonal projection of [math]P - Q[/math] onto [math]n[/math].
So normalize [math]n[/math] for [math]\hat{n}[/math] with unit norm, then take the norm of the inner product [math]| (P - Q) \cdot \hat{n}|[/math].
>>14884386
>Any reason I can't just use
None.
>>14884495
What's the reverse inclusion? [math]\bigcap \{ S + U : U \text{ is a neighborhood of 0}\} \subseteq \overline{S}[/math]?

>a hint
Use regularity for topological vector spaces.

Full proof below:

If [math]x \in \bigcap \{ S + U : U \text{ is a neighborhood of 0}\}[/math] but [math]x \notin \overline{S}[/math] then there's an open neighborhood [math]x \in U[/math] such that [math]U \cap \overline{S} = \emptyset[/math] (because topological vector spaces are regular).

[math]U' = - (U - x)[/math], is an open neighborhood of the origin, hence there's some [math]s \in S[/math] such that [math]x \in s + U' = s - (U - x) = s - U + x[/math]. We translate both sides by [math]x - s[/math] for [math]-s \in -U[/math], then [math]s \in U[/math], a contradiction.

>>14884609
So it's a doomed migration where they're transported or migrate to a place where conditions will prevent them from reproducing?
does it not have an english term?

>>14883980
Look at the bottom right corner of OP pic
[eqn] \bigcirc \kern-0.75em 9 \; \beta \alpha \kappa \alpha [/eqn]

[math]\exists\ a\ \exists\ b :\ ...[/math]
[math]\exists\ a, b :\ ...[/math]
[math]\exists\ b\ \exists\ a :\ ...[/math]

Are these three statements equivalent?

How you induce precocious puberty in male children?

Pump them full of gnrh?
Gene therapy to induce familial male-limited precocious puberty or congenital adernal hyperplasia?

And how would get approval of ethics committee?

>>14884936
Yes.

>>14883490
Something which covers finite (Galois) fields. Strings of bits are often treated as polynomials over GF(2) (the field consisting of 0 and 1, where multiplication is AND and addition is XOR). Other cryptographic topics will use larger finite fields (e.g. AES uses GF(2^8)).

>>14879691
How would you guys go about calculating the capacitance between 12, 34 and 24, 12? I have no fucking clue.

>>14881282
>i don't masturbate to cartoons.
doubt

can someone explain to me what is going on here. I didn't think you could remove exponents from a term and just multiply all terms by it but thats what happens with 1/7

(3+4^1/2) = 5
1/2 * (3+4) = 3.5

How did I miss this in hs

>>14885566
bottom right buddy

>>14885599
man I keep on forgetting everything why are there many rules and formulas that I need to memorize.

>>14885626
For integer n, the third one follows directly from the first.
m^n = m×m×....×m (n times)
log(m^n) = log(m)+log(m)+...+log(m) (n times)
= n log(m)
Extending it to rational n follows:
x=m^(a/b) => x^b = m^a => log(x^b)=log(m^a) => b.log(x)=a.log(m) => log(x)=(a/b)log(m) => log(m^(a/b))=(a/b)log(m).

>>14884882
>So it's a doomed migration where they're transported or migrate to a place where conditions will prevent them from reproducing?
https://www.jstage.jst.go.jp/article/engankaiyo/46/2/46_85/_pdf/-char/ja
https://www.jstage.jst.go.jp/article/nkpmnh/2017/38/2017_29/_pdf/-char/ja
https://ir.lib.hiroshima-u.ac.jp/files/public/2/28725/20141016165200802632/BullHiroshimaUnivMuseum_1_85.pdf
I think that's all it means so maybe it doesn't need a specific term. I found a few Japanese sources and it seems like they use 無効分散 as a general term for any involuntarily dispersed population that can't sustain itself in the new area. (the first link suggests that for the metapopulation of a species, this unsustainable dispersion can be meaningful if it can contribute positively for other population)

>does it not have an English term?
https://www.jstage.jst.go.jp/article/biogeo/22/0/22_16/_pdf/-char/ja
https://www.oki-geopark.jp/en/episode/ecosystem/marine/migration-fish/
I can only find a few English sources describing the term, 死滅回遊 translated as abortive migration. I am too lazy to find more English resource.

hey guys, asking here since /pg/ isn't on the catalog

i'm about to learn qm, and i'm wondering if I should spend time reading vol. 3 of the feynman lectures on physics. People shill it all the time, is it really worth reading?
I'm planning to use shankar's book, btw. Does FLP contain/emphasize stuff shankar doesn't?

>>14885401
There are two parallel paths from node 1 to node 2: one path through C_D, and one path through a series of three capacitors: C_C, C_B, C_A.

First, find the equivalent capacitance of the three caps in series:
1/Ceq = 1/C_C + 1/C_B + 1/C_A

Then, find the equivalent capacitance of the two parallel paths:
Ctotal = C_D + Ceq

Look up "capacitors in series / parallel" if you want to know more.

Biology anons please advise me on my mercury blood level test.
>get tested
>get "<6,73 nmol/L"
>month passes
>get tested again
>get "<6,73 nmol/L"
So those results mean my Hg levels are constant and/or below the scale?
I'm asking because 2 exact same results feels a bit weird.

tl;dr I split mercury in my bedroom. I cleaned it, but was paranoid I missed something, and I'm breathing mercury vapors so I tested myself 2 times to see if my levels are increasing over time.

>>14885024
Thanks mate

>>14879691
I have somewhere near me that sells lots of antiques, including what they claim to be is uranium glass. I understand you can test for uranium by shining a UV light in to it, and it will fluoresce
I want to get a UV light to test this, but most places sell lights that emit either 365nm or 395nm, but they don't state what exact wavelength you need.
Will either work or will it only be one?

>>14886149
Either will work. Fluorescence isn't particularly sensitive to wavelength.

>>14883288
sorry bro, don't know of any video lectures, if you can't understand it then look for another book/text explaining the same subject, maybe a different author can make the explanations click for you.
Look for book lists in the OP
https://4chan-science.fandom.com/wiki/Physics_Textbook_Recommendations#Fluid_Mechanics

If there's something you don't particularly understand then just post it here

Why is this the case?

"No [D]og [L]ikes any [C]at"
~ExEy(Dx & Cy & Lxy)

I read it as "It is not the case that a dog likes every cat", because No = Not some, Any = All/Every.
So i got ~Ex(Dx & Vy(Cy -> Lxy))

Why does Any mean Some here?

>>14886033
Note that it says "less than 6.73 nmol/L". It could be that the test is less accurate below a certain level, so they just report that your level is below a threshold. So you could have two different results, both below 6.73 nmol/L.

You might expect such a threshold to be a rounder number like 5 nmol/L: It could be that the test was developed using ug/L or some other unit, and the threshold is a "neater" number when expressed that way.

I'm no expert-- I've just tracked down the meaning of my own blood tests a few times.

>>14885991
Fuck, it was that easy. It was on my experimental physics exam today and I had no fucking clue, because it looked so confusing and odd. Lost a shit ton of points on that question as well, otherwise I'd have an A. Now it'll be a B if I'm lucky, but most likely a C. That shit pisses me off anon.

Thanks anyways.

>>14886183
thank you

>>14886229
The shirt is no longer available in all colors:
You may still be able to purchase a black shirt or a blue shirt, but don't expect the full range of colors to be offered.

The shirt is no longer available in any color:
It doesn't matter which color you happen to want, we don't have it.

Unsure if this'll help.

>>14886332
Fortunately, it's the kind of thing that will only catch you off-guard once.

Am I missing something? why is this plain?

>>14886229
>>14886229
Define [eqn] D(x) \Longleftrightarrow x \text{ is a dog} \\ C(x) \Longleftrightarrow x \text{ is a dog} \\ xLy \Longleftrightarrow x \text{ likes } y [/eqn]

Logic is really just symbolic manipulations, language can sometimes be confusing. Intuitively "No dog likes any cat" means "All dogs dislike all cats".
Which can be represented as [math] \forall x \forall y : \left[ D(x) \wedge C(y) \right] \longrightarrow \neg (xLy) [/math] which you can prove is equivalent to [math] \neg \exists x \exists y : D(x) \wedge C(y) \wedge xLy [/math]

If you're still confused then think about the difference between these two statements
"No one can kill anyone" (this proposition is false because there exists at least one person who killed at least one person)
"No one can kill everyone" (this proposition is true because we would all be dead)

>>14886427
>we would all be dead
meant to complete to
>we would all be dead if it's negation was true

>>14886435
>>14886427
thats very helpful, thank you anon, and thank you for the cat!

>>14886422
Unironically prove that the inequality holds for [math]2[/math], [math]3[/math] and [math]4[/math] the direct way and then for anything above [math]\pi(x) \geq 3[/math] and [math]\log \log x \leq \log \log e^{e^3} \leq 3[/math]

>>14886667
Wait you can estimate [math]\log \log 4 \leq \log 2 \leq 1[/math] just from [math]2 < e < 3[/math] which gets you 2, 3, 4 automatically since [math]\pi (2) = 1[/math]

>>14885985
shankar is a comprehensive but more difficult first introduction. I would recommend Townsend for your first QM go-through, and then Shankar or Sakurai
Feynman isn't worth it for QM. I TA'd intro QM at the place that Feynman taught and they don't even use his notes as the main reference

YOU ARE ALL STUPID

>>14886703
THE ONE WHO CALLS OTHERS STUPID IS THE ONE WHO'S REALLY STUPID.

>I have a unit lower-triangular matrix [math]L[/math]
>I apply QR decomposition to obtain [math]L=QR[/math]
>I then run LU decomposition on the orthogonal matrix Q, to obtain [math]Q=PL'U[/math].

Assuming correctness and stability of the decomposition algorithms, will I always get [math]L=L'[/math]? How about [math]P=I[/math]?

Was looking for the images of the two fellas in the ghetto with speech bubbles explaining calculus, etc. Came across this, and I don't get it, which I suppose is some form of irony.

I understand the difference between the two expressions, and that they both evaluate to 1. But there's some finer point I don't get that makes this amusing. Or maybe it's just not funny at all.

>>14879691
How many 4 digit pins are there which do not use the digit 2? Pin digits can repeat

>I know total possible pins of 4 digits 0-9 is 10^4
>Dont know how to find how many 4 digit PINs have 2

>>14886823
4 of a kind has 1.
3 of a kind has 4*9 (you should know why).
2 of a kind has (4C2)*9*9.
1 of a kind has (4C3)*9*9*9.

>>14886798
>"definite" integral
>infinity as a bound
shiggy
The second one makes more "sense" and is implicitly what we mean by the first (I think; I didn't study Calc very hard)

>>14886823
You’re overthinking it. You know the number of possibilities with 0-9. If no digit can be 2, then what are you left with?

>>14886918
Thanks anons, I think the answer must be 9^4

>>14886798
Both are correct. It's just differences in notation.

Anyone has the pdf to Tokaty's History and Philosophy of Fluid Mechanics? I've already searched for it on all the links in op and other sites.

>>14887092
Forgot pic

>>14886427
Anon how do you type in those symbols

What is the function f such that f is a bijection from [math]\mathbb{N}[/math] to the set of prime numbers?

>>14885932
It's conceptually interesting, if conditions did happen to change enough at the dispersion site such as a climatic change or foodsource enough that some of the population could sustain a breeding pool then this would be a successful territory expansion.

>>14887151
latex

that's all i know

>>14887264
I think complete prime generating functions are still an unsolved problem. There are plenty that are injections.

>>14887293
i'm not that anon but how do you make an injective function, dont you already have to know the prime numbers or have a way to calculate them for it to be an injection?

>>14886904
Thanks, I think you've got to the heart of it. As it turns out, definite integrals with infinity as a bound are called "improper", and those with finite bounds are "proper". Hence the queen, I suppose.

>>14880944
The primary mover moves the shaft, then, the change in the magnetic field strength over time from the magnets surrounding the armature induces voltage in the coil thus moving electrons to one side, which is an electric current, which will change in intensity and orientation as the armature rotates, producing an alternating current.

https://youtu.be/jSVF-atWWZk

>>14886427
>>14886575
I realized just now that i made a typo a retarded typo, C(x) should be "x is a cat"
I hope that didn't confuse you

>>14887305
Injection from natural to prime. There are equations that generate prime in random order, so a lot of it is skipped over.
https://en.m.wikipedia.org/wiki/Formula_for_primes

i don't fucking get what an KPI is
if i got a document with a set of requirements, is KPI everything that's wrote in there?
or is KPI every requirement that has some numerical values?

>>14886740
https://www.wolframalpha.com/input?i=qr+decomposition+%7B%7B5%2C+0%7D%2C+%7B7%2C+2%7D%7D
https://www.wolframalpha.com/input?i=lu+decomposition+%7B%7B5%2Fsqrt%2874%29%2C+7%2Fsqrt%2874%29%7D%2C+%7B-7%2Fsqrt%2874%29%2C+5%2Fsqrt%2874%29%7D%7D

tl;dr no.

is a set of transitive sets transitive. I intuitively think it is but can't formulate why.

need help≧ ﹏ ≦

>>14887664
??????? Just sum it

>>14887664
start by posting that bussy since you wanna use emoticons like a bottom in heat
anyway, just sum the energies required for:
heating to melting temp -> melting -> heating to boiling temp -> steaming
then sum them

>>14887683
im assuming for b is just divide the heat output from a

>>14887711
yes

>>14879691
How do I make a joke about vaccines and autism that involves pic related and the etymology for vaccine itself?

Is it just me or have (You)s been particularly scarce lately?

>>14887615
Isn't a singleton containing a transitive set is a counter example?

>>14882388
I think this is it, thank you for the insight anon.

>>14887762
You can have a (You) from me any time, just ask. Scientifically and mathematically speaking, of course.

Getting into chemistry at 30 because I wanna know wtf the stuff around me is. Seems like I'll eventually want to learn organic chem based on my wikipedia searches.

I remember in highschool everyone saying organic chem is really difficult and challenging. What makes it difficult and challenging?

>>14887825
No, no, I want proper (You)s because people have understood and accepted my answers to their questions, not pity (You)s. I can get the latter from /wsr/ whenever I want.

>>14883283
Thanks.

>>14887888
if you can find those Putnam problem touhou images that were posted ~4 years ago then I'll give you a (You) for each one

Someone to give me a simple explanation to solve the following problem?

(I already know that 2π represents the circumference of the circle.)
(I already know that α = b mod 2π)


(Yet I can't figure out how to do solve the problem even with the correction and the theory.)

The problem :

It is noon. On an analog watch, the hour and minute handsare superposed.


At what times (hours, minutes, seconds) will they be superposed again (the hands of the hours and minutes) ?

>>14887901
>>/sci/?task=search2&ghost=&search_text=&search_subject=putnam&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=all&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=post

>>14887903
During one complete rotation of the hour hand, how many overlaps do you expect?

Compare one overlap to another: Imagine the overlap which occurs between 1 and 2 o'clock. Rotate the clock face such that this overlap points directly upwards, like the overlap at noon. Should you expect a similar interval before the next overlap? And the next?

>>14887762
they certainly have. maybe if someone gave satoko friend some (You)s every now and then he wouldnt have ran off to join that neo-nazi monastery.

>>14887615
You already posted this in /mg/ and got an answer.

Is this a real math/coding problem? Show is called Pantheon.

>>14887851
>>14887851
>>14887851

guys?

In first order logic, what is the symbol that looks like < but the lines are curved inwards so it looks like a sideways banana peel?

>>14888220
i dont know if learning university chemistry will really help you know what is around you

i suggest this book if you're interested. theres 2 more after this, molecules, and chemicals or something. i have all 3, the first was my favorite

if you want to be more rigorous, maybe material physics or materials engineering or materials chemistry?

most university chemistry stuff is wet, mixing clear badly smelling liquids with other clear badly smelling liquids, which occasionally change to some other color and smell even worse. weighing things, boiling things, and in the end you are left with either a clear liquid or a white powder of something you cant really do anything with

its focused on reactions, its a massive amount of memorizing things, and if you arent concocting shit in a lab (and even if you are), it really doesnt have much meaning in the practical world.

the theoretical part of chemistry involving bonds, elements, and all that stuff sits on the more physical side, but can probably be better explained with rigorous physics or engineering

knowledge of materials rather than "chemistry" sounds more like what you might be interested in, but its hard to tell

>>14888094
I don't have any questions he can help me with.
>>14888287
[math]\prec[/math]?
I don't recall that one having any meaning in first order logic.

>>14887908
I saved 54
would you like your remaining 53 (You)s now or would you like them randomly distributed amongst your future posts?

>>14887851
>>14888220
As >>14888298 pointed out, material science might also be an area worth looking into.

To know what the stuff around you is requires only a very basic level of chemistry knowledge - but it depends on how deep you want to dive into the subject. In either case, university level chemistry would probably be only useful for the first or so year (which should be high school level chem) for you. After that it rapidly diverges from everyday applicability. Unless you are genuinly interesting in the nitty gritty technical details.

Organic chemistry is mostly difficult and challenging because of two reasons. It is usually taught not all that well, so people aren't interested in it and put less work into it. Secondly, there are exceptions lurking everywhere and remembering a lot of rules and exceptions is just hard on its own.

You can tackle both issues. The first one by finding good courses, lecturers, books, websites, etc. Something that works for you. And by being genuinely interested in chemistry. Reading random articles on wikipedia for example in your free time. Watching chem YouTube videos. At least I learn the best when it doesn't feel like learning at all.
You will create a web of knowledge, and so reading about new things you are able to relate it to things you already know. This way remembering stuff is easier.
And practice, of course.

Look around for an introductory chemistry text book. Look for videos on YouTube. Read wiki when you're bored. And don't be discouraged too easily - it can and does get confusing at times.

>>14888359
I'm good with just this one (You).

Why can't i do:
VyEx(Axy)
1. Ex(Axy) Universal Instantiation of y
2. A(ay) Existential Instantiation of x to constant a
3. Vy(Aay) Universal Generalization of y
4. ExVy(Axy) Existential generalization of x

I know step 3 is not allowed, but i'm not sure the rigorous, formal reason why.

>>14888481
If you insist

>>14888298
Hell I dunno, I'm just starting with an anki deck of the periodic table.

I actually took chem once in highschool and once in college but I was tuned out pretty hard both times and got a C in the classes and labs.

>>14888465
>And by being genuinely interested in chemistry. Reading random articles on wikipedia for example in your free time. Watching chem YouTube videos. At least I learn the best when it doesn't feel like learning at all.
Yeah, this is me. I don't have any set date for "gotta know it" I just want to know about it. IDK how nitty gritty I'll get, just find it interesting and wanna see what I can learn.

>The first one by finding good courses, lecturers, books, websites, etc

lol hows Martin Shkreli and zumdahl? I've listened to his lectures as background while working out and thought they were kinda decent.

>>14888311
>I don't have any questions he can help me with.
you dont need questions, all you had to do was say "cute bika <3" or some shit once every thread or so. it goes a long way. it sucks typing up an essay that gets completely ignored.

What is the correct implementation of matrix vector calculation in numpy python? I always do weird shit. For example to compute I want to compute
[eqn] x^T A x. [/eqn]
Input [math]x [/math] is an array of size ((m,)) and A of size ((m,m)). Then I would type

y=x.reshape((1,m)@A@x.reshape((m,1)
y=y((1,))[0]

because they decided that for whatever reason a (1,1) is different from a scalar

How would someone who dropped out of high school and never got past Algebra II learn Fourier analysis (and other fields related to DSP/radio communication)? What's the path this person would need to take in order to learn such subjects? This person's end goal is to become knowledgeable about software-defined radio.

...asking for a friend.

>>14888541
I could do that but it would have to be over matrix or discord or whatever, I really dislike that sort of ritualposting on 4chan.

>>14888514
Also, how do i eliminate quantifiers when they cant be combined

VxAx v VxAy is not logically equivalent to Vx(Ax v Ay)

i am trying to get Vx(Ax v Ay)

>>14888578
you first gotta learn algebra and trig. then calculus. there's no shortcut

What is the most advanced technology in existence?

>>14888535
>hows Martin Shkreli and zumdahl
both of these names don't ring a bell, sorry.

but this guy https://www.youtube.com/c/ProfessorDaveExplains/playlists?view=50&sort=dd&shelf_id=4 had a cool video on quinine that I remember, so it might be worth checking out the other ones too.
https://www.youtube.com/user/periodicvideos is a classic for learning about the elements and inorganic chemistry.

https://www.youtube.com/c/ThatChemist2/playlists?view=50&sort=dd&shelf_id=4 has some nice playlists on organic chemistry. His other videos are bit too meme-y in my opinion, but maybe you like them. The linked playlists are fairly academic and are similar to what you would find in an intermediate university chem course.

Regarding books I sadly don't know a lot of good introductory ones as I read them in my native language which isn't English. That being said I liked the book by Mortimer which has an English translation: https://archive.org/details/chemistry00mort (You can borrow it there for free or download it on libgen).

Finally, here is a page redirecting to a random wikipedia page related to organic chemistry: http://tools.wmflabs.org/magnustools/randomarticle.php?lang=en&project=wikipedia&categories=Organic+chemistry&d=1
I have a few of these set as bookmarks for when I am bored.

Best of luck for your chemistry endeavours!

>>14888615
>>14888578 here, any recommended reading?

>>14888660
For algebra and trig? Just get any book from the library and do exercises. It doesn't matter what book you use there's nothing complex to explain. If it has examples and problems you can use it.

>>14888663
And for calculus?
Btw thank you for your help anon, I honestly didn't expect anyone to seriously answer my retard-level question

(for a friend, of course)

>>14888629
What is your native language? Not german or spanish by any chance? Anyway, awesome list of resources, thank you!

>>14888669
My first language is indeed German!
In case you speak that as well, I can recommend the German version of the book I mentioned (Chemie by Mortimer and Müller, I have the 12th edition) and Anorganische Chemie by Riedel and Janiak (I have the 9th edition). For inorganic chem history I also enjoy reading through the first section of each of the Gmelins Handbuch der Anorganischen Chemie (8th edition, should be present in most university libraries. Huge series with several books on each of the elements and usually starts part A with a history section.) And actually old books shouldn't be underestimated either; I have a copy of Lehrbuch der Organischen Chemie by Fieser and Fieser (3rd edition 1957) which I enjoyed a lot as well. Of course, for modern mechanistic insights you should look to something like Organic Chemistry by Clayden but I wouldn't start with that one.

>>14888514
The statement [math] \forall y \exists x : A(x,y) [/math] means that for every [math] y [/math] we can find a [math] x [/math] such that [math] A(x,y) [/math] is true. The important point here is that for EVERY [math] y [/math] the [math] x [/math] that exists might be different, let me make this example more concrete by letting [math] A(x,y) \Longleftrightarrow y < x [/math] so the statement becomes [eqn] \forall y \exists x : y < x [/eqn]This statement is basically saying for every number there exists a number which is bigger than it.
So let's try to follow the logic you presented with this particular [math] A(x,y) [/math] [eqn] 1. \quad \exists x : y < x \quad \text{Universal instantiation of y} \\ 2. \quad y < x(y) \quad \text{Existential instantiation of x to a constant DEPENDENT on y}[/eqn]Your second step is actually invalid, if [math] x [/math] was not dependent on [math] y [/math] then you're basically saying there's a constant that is bigger than any arbitrary number which is clearly false (if we are working with a number system that does not include infinite numbers)

Bill Shillito has an excellent lecture on predict logic which you're studying, i highly recommend it:
https://www.youtube.com/watch?v=YbNmPievBak

>>14888702
vielen dank! Ich wiess noch nicht die ganze Sprache, aber es geht ziemlich gut zu weit.

>>14888736
Kein Problem, ich freue mich helfen zu können!

now kïss

>>14888820
nur ob du zusammen mit uns

>>14886798
The first one (an improper integral) is a shorthand for the second.

You have to be careful with improper integrals because sometimes
[eqn]
\lim _ \limits {t \to \infty} \int_{a(t)}^{b(t)} f(x) \, dx \\
\text {where} \\
\lim _ \limits {t \to \infty} a(t) = - \infty \\
\lim _ \limits {t \to \infty} b(t) = \infty
[/eqn]
can produce different results depending upon the definitions of a() and b().

E.g.:
[eqn]
\int_{-t}^{t} \sin(x) \, dx = 0
[/eqn]
for all t, so
[eqn]
\lim _ \limits {t \to \infty} \int_{-t}^{t} \sin(x) \, dx = 0
[/eqn]
but
[eqn]
\int_{-t+a}^{t+a} \sin(x) \, dx = 2 \sin(a) \sin(t)
[/eqn]
so the limit
[eqn]
\lim _ \limits {t \to \infty} \int_{-t+a}^{t+a} \sin(x) \, dx
[/eqn]
is undefined.

>>14888721
bless you anon, i appreciate it very much

>>14888856
don't mind if I do

I'm phone posting, sorry for no latex.
I'm a bit turned around with discrete systems theory. I'm aware (or at least, thought) that there's a direct correspondence between differential equations and difference equations. I thought difference equations used the shift operator instead of differentiation. But, I don't know how that can be, considering the direct analog of differentiation would be the finite difference.

What's the deal?

>>14888196
/g/entooman here. Syntactically, it looks like a bizarre mix between the programming languages COBOL and APL. Definitely not any language in existence today. Mathematically I have absolutely no idea.

>>14888921
Difference equations can be expressed using the difference operator, (Δf)(n)=f(n+1)-f(n). There are some fairly direct correspondences between differences and differentiation.

But difference equations can also be solved using the Z-transform, which is similar to the Laplace transform, but with shifting taking the place of differentiation.

Laplace transform:
L{f(t)}=F(s) => L{f'(t)}=sF(s)-f(0)
=> L{f^(n)(t)} = (s^n)F(s) - Σ_k s^(n-k)f^(k-1)(0)

Z-transform: Z{x[n]}=X(z) => Z{x[n-k]}=X(z)/z^k
Corollary: Z{x[n]-x[n-1]} = X(z)-X(z)/z = (1-1/z)X(z)

>>14888921
https://www.youtube.com/watch?v=4AuV93LOPcE

>>14879691
Entropy precludes truth. So long as entropy increases, which it must, any answer to any problem becomes either redundant or incomplete, and every attempt to solve a problem always comes with collateral that prevents the problem from being truly 'solved.' Thus, truth is an adjective of veracity -an emotion - and has nothing to do with 'reason.' As such, there's no question about whether science is actually a 'good method' or not - science is the necessary result of entropic processes that will continue to be increase their entropy. The only sensor we have for truth is that which can defy any attempt to appear true: 0.99999999... = 1. Thus, to reconcile truth and reality, consciousness is instinctively foreclosed from being 'solved,' (by another consciousness) thus founding the basis for any possible knowledge, as god once did. Consciousness is a black box that always gives you the answer you don't want except for when you totally embody it, and become the decision arbiter itself.
In this scenario, can this statement be true? Is it possible to make a reflexive, 'meta' statement at all, if it weren't true?

How do i do a direct proof on
Vx(Px v Qx) -> Vx(Px) v Ex(Qx)
1. Vx(Px v Qx)
2. Pa v Qa //Universal elimination
and now i'm guessing:
3. Ex(Pa v Qx) ?? //this feels illegal skipping Pa
4. Pa v Ex(Qx) ??
5. Vx(Pa v Ex(Qx)) ??
6. Vx(Pa) v Ex(Qx) ??

i can do contrapositive i think:
~(Vx(Px) v Ex(Qx)) -> ~(Vx(Px v Qx))
1. ~(Vx(Px) v Ex(Qx))
2. ~Vx(Px) & ~Ex(Qx)
3. ~Vx(Px)
4. Ex~(Px)
5. ~Pa //existential elimination
6. ~Ex(Qx) //from 2
7. Vx~(Qx)
8. ~Qa //universal elimination
9. ~Pa & ~ Qa //from 5 and 8
10. Ex(~Px & ~ Qx)
11. Ex~(Px v Qx)
12. ~Vx(Px v Qx)

Am i doing any of this right? I am struggling especially with distributing both quantifiers over disjunctions

>>14887484
Thanks for looking into my problem (and sorry for the delay, it's my exam period now), but in the first step [math]L=QR[/math], I'm requiring that L is unit lower triangular, so that (if my conjecture is correct) [math]Q=LR^{-1}[/math] exists as the unique LU-decomposition of Q, and this should turn the two decompositions into an isomorphism for converting between L (the unit lower-triangular matrices) and Q (the orthogonal matrices for which an LU-decomposition exists, which I think means that all its leading principal minors are positive).

Re-using the matrix [math]L = \begin{pmatrix} 1 & 0 \\ -7/5 & 1\end{pmatrix}[/math] in your example, when I feed it into WolframAlpha's QR factorizer:
https://www.wolframalpha.com/input?i=qr+decomposition+%7B%7B1%2C+0%7D%2C+%7B-7%2F5%2C+1%7D%7D
it indeed returns the same Q (well, actually [math]Q^\dagger[/math] for some reason, but once you undo that, it becomes consistent with my conjecture above).

I was integrating a definite integral and this was my resulting indefinite integral. The bounds I have to integrate with respect to are -infinity (lower bound) to e^2x. I'm not sure how to simply the result after plugging in the definite integral bounds.

>>14889119
integrating with respect to y

>>14887092
>>14887099
not him but bump for this if it's a cool book

I'm interested in fluid mechanics

can anyone help me out with this?
i am just doing 2n x Fa + 4n x Fb to get the moment about the origin but i dont know if the moment about point B affects it as well.

So wait If I have a variable with a negative exponent fraction in the numerator I can just move it to the denominator and it becomes positive right

The opposite is true too right if I have a variable with a positive exponent fraction I can move it to the top and make it it negative

Can someone post the names of these rules I forgot them

I decicided to watch a old youtuber I used to watch named brewstew it was the video he had on mathmatics pretty funny. Anyway in the video there was the quadratic formula -b +-sqrt(4ac) / b^2 I think

I remember learning that in middle school and how annoying it was due to all the parts but now in college we just use the what numbers add to constant and multiply to the variable coefficient. Why do we never use it, why did they make me learn it. And is it still used for anything anymore??

>>14889385
yes and if its negative in the denominator, it can go to the numerator and be positive

What's particularly stupid about the following question is that I'm asking for career advice on a board made for sharing Chinese cartoons. Still here I go: I want to research aging, and I want to help produce useful technologies to prevent or reverse aging. How the fuck do I do this? Personal background: I'm a 29 year old factory worker who has wasted about 10 years since high school. I want to finish my god damn college degree and work on aging research. How do? inb4, "lol kys," I'm looking for something a little more productive. I really do want to help everyone and myself live long, healthy lives.

I haven’t taken a shit in 4 days and the scale says I have put on 3 pounds even though I’ve been having trouble eating enough food to not faint. I’m scared of what will come out

>>14888287
I have only seen it in rational choice theory.

My linear algebra class was fucked up because the prof was brand new and the scheduling was all messed up by covid (half online classes, half classes where he had to teach to people online and in person at the same time). Can someone explain what the significanceof a determinant and eigenvector is?