/sci/ - Science & Math

Unanswered questions:

Maths questions:
>>15067897
>>15068865
>>15069359
>>15071771
>>15075842
>>15077525
>>15077863

/g/ questions:
>>15068168 [He nvmed his post so you should probably disregard this one.]
>>15069335
>>15073021
>>15074690
>>15076785
>>15083220

Engineering questions:
>>15082920

Biology questions:
>>15081785

Stupid questions:
>>15070410 [He explicitly rejected all answers given.]
>>15070585
>>15075246
>>15075812
>>15077215
>>15077885
>>15077889
>>15079336
>>15081057
>>15081189
>>15081290
>>15084091

>>15085518
How many ways can I sum the absolute value of n integers such that the sum is equal to a positive integer, namely m?

>>15085599
That is related to the partition function of some integer. Specifically the partitions of m with distinct parts of length n. I'm unsure if there is a direct formula (or function) for the exact value since the count of partitions for some integer requires the use of a generation function. So to obtain the value probably requires some brute force coding effort.

>>15085518
Good Morning /Sci/entists!

I am finishing Kurumi MaidCard and I have space in my character set for 151 more characters. Please tell me characters you want in the character set. I am trying to focus on characters used for programming, math or formatting like bullet point. I have a thread with more details and the existing character set here.

>>>/g/90582947

Two of the characters appear to be empty. They are crosses but for some reason the dra/g/on maid board filtered them so it looks like 2 empty strings instead.

Thank you /sci/entists for reading my post.

>>15085453
I don't know I guess I got scared about if I realyl wanted to do computer science for the rest of my life

>>15085518
When scientists and engineers will stop being massive retard faggots that worship kike bullshit?

>>15085716
I don't think most believe in it but they still have to work in Universities where the administration is very leftist, they remain silent and the few that do share beliefs with the administrators.

What is the link between mathematical, ethical/moral, and emotional maturity under the sense of adulting? Especially neuronally?
Does it have to do with mental illness/autism?
Why do nuns do this?

>>15085518
small o notation: for x->x0, f(x)=o(g(x)) if [math]lim_{x \to x_0}\frac{f(x)}{g(x)}=0[/math]

so in intuitive terms, can i think that f(x) is under the graph of g(x) for x approaching x0?

>>15085518
Serious question. How do I reliably know if someone has planted a bomb in my car? Any tools I can use?

>>15086082
Loan your car keys to your least favourite friend.

>>15085716
When geniuses like you come up with better bullshit.

>>15074690
what is "wafer resolution"?

What's worse? Incompetence or apathy?

>>15086584
Incompetence. Apathy can be fixed.

>>15086584
Apathy. It doesn't matter how competent you are if you can't be motivated to act.

Apathy also seems to be somewhat infectious. Apathetic people lower the energy in the room and demoralize others in their proximity.

My first question:
Let
[math]\Phi : G \times M \to M[/math]
be a group action with group G and set M. Is
[math]\forall_{p\, \in\, M} : \Phi_{g}(p) = p \iff g = e[/math]
then a correct characterization of a faithful group action?

My second question:
Is there a keystroke combination for latex code? Like the one for spoilers on /tv/?

>>15086584
Incompathy. Apathy can be fixed and incompetence at least isn't infectious.

>>15086683
I'm going to use this word

You are not a little girl. You're a homosexual pedophile who masturbates to children's cartoons.

>>15086584
apathy inevitably leads to incompetence

>>15086678
your notation is not clear. The group action is faithful when:
(gp = p, for all p in M) iff (g = e).
This is not the same as:
(gp = p iff g = e) for all p in M.

>keystroke
alt+m, but this might be a 4chanx thing

>>15086717
To clarify, I meant
[math]\forall_{p\, \in\, M} : (\Phi_{g}(p) = p \iff g = e)[/math].

I also made a mistake in the translation. What I meant wasn't faithful group actions, but free group actions. Is the definition above a correct characterization of such free group actions?

>keystroke
Unfortunately doesn't work without 4chanX. At least it does spawn a [math]\mu[/math].

can black holes become no longer black holes

>>15086739
yes, that is correct. Note that free is a stronger condition than faithful

>>15086750
yes, these objects do decay. But I don't know how

>>15086760
Great, thank you very much!

>>15085518
what causes a flock of pigeons to keep flying in circles for five minutes?

>>15086014
>What is the link between mathematical, ethical/moral, and emotional maturity under the sense of adulting?
None. Having a strong sense of morality is not tied to being good at understanding abstract mathematical structures and objects, which is not tied to being good at appropriately dealing with difficult situations. People call them "maturity" because they wouldn't expect a young person, or a person who's not very bright, to possess them, but really they do not emerge all at once nor do people who possess one type of "maturity" necessarily have the other types of "maturity" well developed.

>>15085518
How do you tell someone's IQ based on the smell of their butthole?

>>15082920
I'm guessing the multilevel wavelet transform is the same as the 2D wavelet transform.
If you only reduce the L1 norm of the upper left corner, then you are only working on part of the data, so you reduce the L1 norm of the whole matrix. The upper left portion corresponds to the low frequency and low spatial resolution pieces and the rest corresponds to high frequency and high spatial resolution information. A large wavelet is used for the low frequencies because it needs to be multiplied by a large part of the image to see the low frequencies. Steve Brunton on Youtube has a lecture series on wavelets which I found usefull.

>>15077889
Seems like you have a high caffeine tolerance, so you sleep easily after drinking coffee. If you drink a lot before bed, your need to piss wakes you up, and you are more likely to remember your dreams if you are woken up by something sudden that causes adreneline release (like having to pee). Maybe the dreams are caused by caffeine too, but I doubt it.

i want to completely change my body and psyche. like straight up cure aging, fix my mental illnesses, and transfer or transform myself into a completely different body
what fields of research should i study and how do i generate the most impact in this cause?

>ywnbaw blah blah blah
not relevant to the question. at least give me a field of research so i can at least have a cope to keep me going until i die a bitter old man

there is no medicalgen up rn

Sometimes when I blow my nose (usually when I have been doing it repeatly) I get a pain in the right side of my neck while I am blowing my nose. Googleing it only brings up stuff about how neck pain can be related to sinus infections.

I am just curious of the physiology being neck pains from blowing your nose too much. Its not so much neck pain, but I feel something being pulled or strained in the right side of my neck

is it worth relearning all of mathematics to form a good foundation if you were an absolutely lazy shit student growing up

if so, where is a good starting point/general guideline for where to proceed and in what order

>>15087429
No unless you enjoy it.

[math]\lim_{x \to \bowtie } \sqrt[3]{(3s^7-4s^5)/(2s+1)}[/math]
How to evaluate this?

>>15087498
x doesn't show up in the expression so it is just that expression

>>15086802
pigeon A sees danger and takes flight
pigeons B, C, D, etc. see pigeon A take flight, assume danger, and take flight
pigeon A sees that danger has abated, but assumes that B, C, D, etc. have good reason for remaining in the air
B, C, D, etc. are looking for the danger and assume that A has good reason for remaining in the air
this cycle continues until one or two birds are tired enough to risk landing again
the remainder of the flock wonders what the fuck they're doing in the air, and lands, too

source: Mavis Goodall, Jane's dimwit sister

Brainlet question:

Show that [math] T - I [/math] is a Hilbert-Schmidt operator if and only if [math] T T^* - I [/math] is a Hilbert-Schmidt operator.

Any hints?

>>15087498
>>15087520
Sorry, my bad. It's actually s approaches infinity , not x

>>15087498
rewrite so that it's the cube root of the numerator over the cube root of the denominator instead and apply l'Hôpital

>>15087738
Reduce to [math]T[/math] self-adjoint.

>>15087792
Thanks, but it is supposed to hold even if [math]T[/math] is not self-adjoint. See pic for context. Sorry for missing the obvious :(

>>15087799
It's not true in general.
Define [math]T: l^2 \to l^2[/math], [math]T(e_n) = e_{n + 1}[/math] if n is odd and [math]T(e_n) = e_{n - 1}[/math] if [math]n[/math] is even. The operator is clearly unitary, hence [math]TT^* - I = 0[/math]. But [math]T - I[/math] obviously has infinite Hilbert-Schmidt norm, since the sum has an infinite number of equal [math]\| (T - I)e_1 \|^2 = \| e_2 - e_1 \|^2[/math] factors.

>>15087817
I see, thank you very much! I guess I'll have to figure out what's meant in the book then...

>>15087817
Actually, I've just realized my example shows you should need at least positive self-adjointedness for this.

>>15085518
Let X be the set of all solutions to a polynomial of degree n such that all of its coefficients less than k. Is x=k in X ?

>>15085518
What's the mechanism here?
The first two steps are obviously just the Schiemman reaction, but what happens during 3?
It looks like a Friedel-Crafts acylation, but I can't figure out what cation is formed and why the ring opens/where the carboxy group comes from.

>>15087950
Wrong picture, whoops

>>15087950
>>15087952
Nvm, I got it.

>>15085518
Good Morning /Sci/entists!

I discovered that there is a dra/g/on maid from touhou called Yachie. I don't know what this means yet, but I am happy to have found her.

Last time I posted here someone told me a lot of books about Numbers, Counting, Shapes and Colors. I was able to get them and also a lot of books about combinatorics. I have to walk to the store to get it though and the weather is bad so probably won't have physical books until next week, but that is acceptable. If you know more nice books about these topics, please tell me.

I am debating buying Forth books because I am losing faith in LISP's ability to match it's usefulness and power, especially for the amount of effort it takes to make a Forth variant vs a LISP. I have about 15 LISP books and I feel like I might've picked wrong when I got them instead of APL or Forth books.

I want to get better at algorithms so I can make my Computer Programs go faster. Does anybody know good books about algorithms? I would be interested both in reading about the math and seeing a lot of pseudocode examples. Dead languages are also acceptable as they approximate to being pseudocode most of the time.

I have to make a lot of multidimensional arrays full of booleans go faster and get bigger.

Wikipedia said somebody called Grzegorczyk made Grzegorczyk Hierarchy and that it uses Successor Function to make arithmetic operators. Does anyone know good books about Grzegorczyk Hierarchy? I like Successor because it uses the letter S a lot.

Thank you /sci/entists for reading my post.

are you afraid of aliens?

>>15088363
I'm not afraid of things that do not exist.

>>15088374
why'd you think the don't exist?

>>15088380
Say they do exist the laws of physics means we will never interact with them so it's pointless to be scared either way.

If [math]\Phi : G \times M \to M[/math] be a free and transitive group action, then [math]\Phi_{p}: G \ni g \mapsto \Phi_{g}(p) \in M[/math] is a bijection.

I have to show that by using left multiplication this mapping translates the canonical action from G to itself to the action from [math]\Phi[\math] to M. Do you understand this, anons? If so, can you give me a tip?

>>15088450
>Do you understand this, anons?
no. do you have a picture or a screeny of your reference?

>>15088550
I could take a photo of the book, if you want. But it's in German.

>>15088580
what book?

>>15088662
Lineare Algebra I, author is Stefan Waldmann.

>>15088662
it's a part of an exercise from this book

>>15084135
>Have you tried not drinking anything?
I have, I often masturbate in the morning after urinating and I still need to use the toilet no matter how empty I felt before doing it just after urinating.

I must add, I'm pretty sure I have a problem with saliva production in my mouth. I usually can't swallow food without drinking water to wash it down. And because there isn't enough saliva in my mouth I feel thirsty a lot more. Certain drinks manage to make me not feel thirsty, usually fruit juices. So obviously I drink a lot more than the average person and use the toilet a lot more, but I wouldn't think I would still need to go after urinating after sleeping because obviously you I don't drink while sleeping. I'm still too lazy to talk to a doctor about all this.

>>15088820
Another thing, urinating after masturbating is usually really painful and difficult to do.

Is there any research into music learning methods?
I've looked into it and all I can find is articles about the benefits of learning to play a musical instrument
Is there the equivalent of SLA research for music?

So do any of you guys know how to deal with convolutional networks and ragged tensors.

https://stackoverflow.com/questions/74953779/ragged-rank-for-tensorflow-ragged-constant-and-ragged-stack-not-retrieving-shape

Need help dealing with this , docs suggests it should work but it doesn't and want to check if its me or a bug

>>15088820
>>15088823
By itself pissing after cumming isn't too much of
a problem, but painful urination is. It could be one
of the things listed in the link below, and it's
something worth discussing with a doctor or
urologist.

https://www.bensnaturalhealth.com/blog/sexual-health/painful-urination-after-ejaculation/

https://mathb.in/73718

Just a curiosity I had.

>>15089675
The point of an infinite series is to closely
approximate the trig function as a form of a
polynomial of some degree (the more terms/higher
the degree of polynomial, the better the graph).
This is not needed here...unless you like playing
with potentially infinitely many terms.

By the property you have used, you recovered
the same sine term as what the equation was
equal to. In that case, expand and group that
sine term. You will then have:
[eqn] {1\over 2}\sin(3\theta) = {1 \over 2}\sin(\theta)+\cos(2\theta)\sin(\theta) [/eqn]
Swap out [math] \cos(2\theta) = 1-2\sin^2(\theta) [/math] .
Then, you'll have:
[eqn] {1\over 2}\sin(3\theta) = {1 \over 2}\sin(\theta)+\sin(\theta)-2\sin^3(\theta) [/eqn]
Complete the rest and you got it.

Pic related is the infinite series of sine and
cosine for reference. You may probably see why
switching one or all parts to infinite series could
be troublesome in proving the identity.

If you have a signal that is just white noise, how many samples do you need in order to capture the characteristics of that signal?

For example, if you had just one sample; well that's just a single data point, a number. It's nothing.
Obviously you need more than one sample before the data set begins to show that it is just noise, but what is the minimum number of samples you need?
Also, does this change depending on the color of noise? White, pink, blue, brownian etc.?

Let [math]\mathcal{A}[/math] be an associative unital algebra over a field [math]k[/math]. Suppose [math]\phi: \mathcal{A} \to k[/math] is linear and satisfies [math]\phi(uxu^{-1}) = \phi(x)[/math] whenever [math]x[/math] is arbitrary and [math]u[/math] is invertible. Under what 'reasonable' assumptions can we conclude that [math]\phi[/math] satisfies the tracial property [math]\phi(xy) = \phi(yx)[/math] ([math]\forall x,y[/math])?

(This holds e.g. when [math]\mathcal{A}[/math] is [math]M_n (\mathbb{C})[/math], and by 'reasonable' I mean to exclude trivial solutions such as requiring [math]\mathcal{A}[/math] to be commutative or [math]\phi[/math] to be multiplicative)

>>15090018
If [math]\mathcal{A}[/math] is spanned by units like [math]M_n[/math], maybe?
Can't come up with anything better.

>>15090114
You know I thought this condition might be stupid when I posted it but it gets you the result for all [math]M_n(k)[/math] and triangular matrices when [math]k[/math] has characteristic other than two, non-degenerate Clifford algebras, all unital Banach algebras, octonions and friends, and probably some other unital algebras I'm forgetting about.

>>15090213
https://math.stackexchange.com/questions/889890/more-classes-of-rings-spanned-by-units
>A finite-dimensional algebra A over an infinite field F is spanned by units.
Also this btw (he's using algebra for unital algebra).

>>15090114
>>15090213
>>15090233
Fair point, looks like this (seemingly naive) criterion is very applicable. Thanks!

>>15085518
Very random board tourist question but I'm playing a single player game (runs are 2-5 hours), how do I do some kind of "MMR/ELO" thing where I play the game like 30 times with different sets of characters and somehow "rank" them? Even if it's not completely accurate since some characters may play better/worse with others. Also keep track of separate factors like playthrough speed, damage taken, and objectives fulfilled.

is it true that cardio exercise raises your IQ?

>In every finite group [math]G[/math], we have [math]a^{|G|} = e_G[/math] for every [math]a\in G[/math]
I'm confused. Isn't [math]\langle a\rangle =G[/math] an extra condition that needs to be stated for this to be true (as per Lagrange's theorem we'd get: [math]|G|=|\langle a\rangle|\cdot [G:\langle a\rangle] = o(a)\cdot [G:\langle a\rangle] \Rightarrow o(a)\;\big|\; |G| \Leftrightarrow a^{|G|} =e_G[/math])? Otherwise, every element of a finite group would generate it, no?

>>15090724
Not necessarily.
Simplest example of that is the Klein group, which has no generators, but for which [math]g^4=(g^2)^2=e^2=e[/math] for all g in the group.
Keep in mind that [math]a^{|G|}=e_{G}[/math] does not imply that this is the lowest power of a that's the identity.

>>15090743
*no single generators, I should say.

>>15085518
If I evacuate as much air from a container as possible, will the pressure exerted on the walls of it from the outside be at most 1atm, and will be safe to do so as long as the container can withstand 1atm of pressure?

>>15090743
>>15090745
Thank you. I had wrongly assumed that [math]\langle a\rangle[/math] existing as a subgroup of [math]G[/math] means it has to generate [math]G[/math]

>>15087396
>cure aging
Molecular biology, biochemistry, interdisiplinary biology with something like computer science (either PhD or PhD/MD level). Something needs to be figured out so we can use Yamanaka factors on the whole body to reverse age, gene edit an entire adult body which requires vectors getting around the immune system, or a way to restore neurons and synaptic circuits as they were before they were destroyed (so memories can be restored from dead neurons like in Nematode worms).
>Fix my mental illnesses
Neuroscience or Neuroscience with another disipline like engineering since neuroscience alone cannot solve all the problems. There is a need for engineers and people good with data to advance neuroscience. A lot is still unknown and medical imaging still isn't used clinically to diagnose mentall illness because mental illnesses are typically undetectable or we don't understand them.
>transfer or transform myself into a completely different body
Need better surgical techniques so if a body is grown without a brain you can do a brain transplant into it.

HAPPY NEW YEAR LADS AND LASSES

What's this symbol, circle with cross called? What does it mean..

Why is probability notation so garbage? Expectation is denoted as a function of a random variable when in reality, it is a function of the pdf.

>>15091210
happy new year remi
>>15091373
summation

>>15091767
[eqn]E[X] = \int_\Omega X dP[/eqn]
Not every random variable has a pdf. The pdf is the Radon-Nikodym derivative of the distribution of the random variable that is [math]P \circ X^{-1}[/math] with respect to the Lebesgue measure.

>>15091373
it's a multiplication between the two inputs

Is there a formal definition for a "forgetful" function or is it just an informal term for describing functions that "forget" an important aspect of their domain?

If two vector subspaces of a finitely dimensional vector space V have the same dimension, then the do NOT necessarily have the same complimentary vector subspace. Is this correct?

>>15086087
Probably the easiest way would be to get a trained dog to sniff it.

>>15092037
Meant for >>15086082

>>15092001
If you have two subspaces of a vector space [math]V[/math] with the same dimension, there's a third subspace which complements both of them. You can prove this in the finite dimensional case by inducting on the codimension, essentially.

>>15091855
It's a sum, not a product.

Let [math]V[/math] be a vector space over field F. Let [math]U_{i} \subseteq W_{i} \subseteq V[/math] for all [math]i \in I[/math]. Show that [math]\oplus_{i \in I}\, U_{i} \implies W_{i} = U_{i} \text{ for all } i \in I[/math].

Isn't this wrong, /sqt/. Couldn't I choose [math]W_{i} := V[\math] for all [math]i \in I[/math]? Even if all [math]\{W_{i}\}_{i \in I}[\math] are pairwise distinct, then this is wrong. Consider for example [math]\mathbb{R}^{4}[/math]. What am I missing?

>>15092087
But consider U1 := <(1, 0, 0), (0, 1, 0)> and U2 := <(0, 1, 0), (0, 0, 1)>. These are vector subspaces of R^3 with the same dimension 2, but their complimentary spaces are not the same.
If you detached their "0-component", then the wouldn't be a subspaces of R^3 anymore; since it's a necessary condition that they are subsets of R^3 to be its subspaces.

>>15092037
I don't think find a trained bomb sniffing dog is easy.

>>15085518
for what values of a and b does [math]\int_{0}^{1/2}\frac{1}{x^a|lnx|^b}[/math] converge?

>>15092137
Are you saying "complement" to mean "orthogonal complement"?
Both of those are complemented by <(1, 0, 1)>.

>>15092309
Nope, I was wrong. Thank you anon. Now I can solve this exercise.

>>15092265
[math]a<1[/math] or [math]a=1[/math] and [math]b>1[/math]

>>15085518
Guy from /tg/ doing some tabletop statistics spreadsheet math. I think I have this right, I just want somebody that actually knows to double check me.
I'm trying to figure out the average number of positive results over a number of instances.

So let's say you have a 6 sided die, and you roll it 5 times.

If you want to know the probability that ANY of them are 2 or less you'd do 1-(1-.33)^5= 0.8649

BUT If I wanted to know the average number of rolls of 2 or less over 5 rolls, I just multiply .66*5= 3.3, right?
A coin (50%) flipped 8 times gets an average of 4 heads, so I feel like this is right. But every time I think I have this stuff understood I end up having to learn another equation.

What's the best tablet you've come across for reading textbooks? I'm in medicine, so lots of images, tables, etc.

>>15092730
> lots of images, tables
The iPad because of the retina display. The Kindle is better for pure text but it sucks at other content and ofc the small screen.

>>15092714
>If you want to know the probability that ANY of them are 2 or less you'd do 1-(1-.33)^5= 0.8649
yep
>>15092714
>BUT If I wanted to know the average number of rolls of 2 or less over 5 rolls, I just multiply .66*5= 3.3, right?
should be .33*5 = 1.65, right?

>>15092746
FUCK.
Yeah .66 would be miss chance wouldn't it. I had the 1-.33 still in my head from the first equation.

But otherwise correct. okay good to know, thanks.

Let [math]A \subseteq \mathbb{F}[x][/math]. For all [math]n \in \mathbb{N}_{0}[/math] exists a polynominal [math]p_{n} \in A[/math] with degree n. IThen this set contains a basis of [math]\mathbb{F}[x][/math]. Is this correct?

>>15092811
Yes obviously. Just induct to show you can get each x^n .

>>15091853
No one asked anything about your tranny measure theory autism.

>>15092714
Let [math] \forall i \in \{ 1, 2, 3, 4, 5\}\; I_i = 1 [/math] iff the [math] i[/math]-th dice has 2 or less, and [math] 0[/math] otherwise. You want to find:
[eqn] \mathbb E \left[ \sum_{i=1}^5 I_i \right] =
\mathbb \sum_{i=1}^5 \mathbb E [I_i]
= 5 \left( \frac{2}{6} \right) [/eqn]
Since [math] \mathbb E[I_i][/math] is the probability of the [math] i[/math]-th dice showing 2 or less.

>>15092832
turns out it was not the notation, but anon that was retarded

>>15092714
33.33...% chance means out of 100 iterations, 33.33... would get 2 or less. In 500 iterations, that means 5*33.33... = 166.66... would be 2 or less.
so yes, just multiply the chance by the number of rolls.

finally made it to chapter five "linear maps and matrices". Can't wait to learn about this

>>15085518
Good Afternoon /Sci/entists!

>Project
I am working on text compression as part of Kurumi MaidCard. I started with LZW and modified it by removing integers and using Maid Space. Then it got more mutatations which made it smash down file size and resulting PNG image more at the cost of making the algorithm slower (Bible to Maid Address used to take 3 seconds. Now it takes 30.)

>Question
I am not sure how compressors are measured against eachother. I'm sure I can compress more than LZW, but that is about it. Is there some standard text for benchmarking tests or results that I can view somewhere?

I don't need to run any other compressors, I'm happy to trust whatever the report says. But I would like a copy of test data to try with mine.

This is the funnest thing I have worked on in a while. I will release it to CC0 when it completes. I will probably check it with Profiler again to see can I make it go faster too because Profiler is fun.

>tl;dr; Computational Maidposting has practical applications in file compression and I am exploring them.

Also if you know a book about making arithmetic with Successor Function, please tell me.

Thank you /sci/entists for reading my post.

I've found that [math]2023 = (2^1 + 0^1 + 2^1 + 3^1)^1 \times (2^2 + 0^2 + 2^2 + 3^2)^2[/math], and that 2023 is the smallest integer for which this property holds nontrivially (more precise statement here: >>15091941).
Can it be proved (or refuted) that there is no other larger integer that also has this property?

Is there a program I can use to generate a simple function that resembles pic related over the range 1 to 2?

Emphasis on the "simple" part

>>15093149
how about a simple graph plotter?
https://www.desmos.com/calculator?lang=en
with f(x) = 2.5x^2

>>15093163
thanks i'll try messing around with that, the graph needs to be a very low value (but not zero) less than 1.5 and rise steeply after 1.5 to 10

>>15093174
what about f(x) = (10/2^10)x^10?

>>15093189
perfect, thank you

>>15093148
I don't have pen and paper, but maybe try by refuting the statement for classes of numbers. For example the assertion is probably wrong for all numbers consisting of same digits.

>>15093148
I wrote up my own Python code to check. 2400 and 52215 are other examples.
I also forgot how much I hate Python because for some reason the code lost its shit if I let it try 1000, so I had to iterate around that

>>15093223
>2400 and 52215 are other examples.
Huh, guess I should have gone out of my way to make the calculations after all. Thanks for checking that for me.
>for some reason the code lost its shit if I let it try 1000
That's probably because you're trying to form a product like [math]1\times 1\times 1\times \ldots[/math], so if your test consists of dividing n by each factor until it reduces to [math]\leq 1[/math], then it'll never terminate. (The same would apply upon testing any other power of 10.)

>>15093248
That's the thing. I included a section specifically to skip the entire thing if it was a power of 10. It works for 10, 100, 10000, and so on, but not 1000 or 1000000. I don't get it.
Other examples: 615627 and 938600

>>15093250
1648656 is one more example.
my code isn't exactly optimised and took 15 minutes to search through all of the eight-digit integers, but didn't find anything in that range. I can't be bothered to write it competently, but I wonder if there are any more examples or if we've got a comprehensive list here

i want to prove that [math]\int_{1}^{\infty}e^{{-x}^2}dx[/math] converges.
is this a valid proof?

[math]e^{{x}^2} \geq x^2[/math] (do i even need to prove this or is it just obvious)
therefore [math]\frac{1}{x^2}\geq \frac{1}{e^{x^2}}[/math]
the integral from 1 to infinity of 1/x^2 converges. Therefore the starting integral must converge too.

>>15093278
Can confirm that your list is correct (up to 10^9). To salvage the original conjecture somewhat, 2023=7*17^2 is the only one for which the product is a prime factorization.
>I wonder if there are any more examples or if we've got a comprehensive list here
I thought to show that no examples can exist past a certain point, but this isn't as straightforward as it seems: the value of the product (for a fixed exponent k) doesn't really depend on n (say, n=2023) but only on the multiset of its digits {2,0,2,3}, and is invariant upon adding or removing '0' (that is: {2,2,3}, {2,2,3,0}, {2,2,3,0,0,0,0,0,0} ... will all yield the same product). So it seems like even if we fixed a multiset like {2,2,3} for testing, we would still have to keep on multiplying [math](2^i+2^i+3^i)^i[/math] for successive i, and checking if the digits of the result form a permutation of the multiset (up to removal of '0's). I don't know of any criteria for telling us when to stop, but then again this is quite far from my area of expertise.

>>15093385
I realised it's probably on OEIS, and indeed it is, as A257766. Complete with a very nice comment:
>Sequence is finite since it cannot contain numbers of 9 or more digits. Indeed a number of 9 digits is at least equal to 10^8, but the function computed here for a number of n digits is at most (9*n)*(9^2*n)^2, which for n=9 is 43046721 < 10^8. - Giovanni Resta, May 08 2015

>>15093395
Granted, I should mention that that sequence is specifically for the digital sum times the square of the sum of the squares of the digits, but it's still a start. Certainly, there are no other examples without moving up to the cubes, at least.

>>15093385
Tested up to 1 000 000 for powers up to 5 and bases up to 16.

I did not find any higher powers except 46656 in binary for cubes. For squares of bases other than 10 I found :

>3
144 ; 600
>4
32 ; 600 ; 2601 ; 3872 ; 4840
>5
400 ; 44217
>6
85697 ; 131061 ; 137781 ; 273263
>7
8 ; 3249 ; 3872 ; 9801 ; 39015 ; 78408 ; 133128 ; 449307
>8
189525 ; 216320
>9
243 ; 3087 ; 9801 ; 33813 ; 129600 ; 234099 ; 325703
>11
144 ; 338000 ; 457263 ; 510623 ; 968688
>12
338272
>13
11025 ; 418176 ; 525625 ; 748225
>15
277725 ; 787176
>16
32 ; 1024 ; 32768

None for binary or B14. It is interesting that the numbers repeat a bit.

Is it possible to prove LOTUS for continuous case with not necessarily monotonic functions, without using measure theory?

Is there a mathematical proof that shows that trans women are women?

pfp means profile picture. But I often see it's written like "PFP"(Profile (F??) Picture) and not "PfP"(Pro|f|ile Picture). Why is that?

What's the deal with James Gates' self correcting code thing?

>>15085518
given an interval of real number a<x<b, How do I define a function that maps (a,b) to a rational number in that interval?

>>15094453
Choose [math] m/n \in mathbb Q[/math] such that [math] 1/n < b - a, \quad m = \operatorname{ceil} (n a) [/math]. The above defined rational number is between the interval.

>>15093280
That's fine

>>15094246
You can use the inverse function theorem methinks

can someone give me an example of a function that might seem analytical but isnt

Did you guys have to memorize trig identities for tests?... Hope they have some identities as references, here's hoping...

>>15085518
for genetic sequence X, is there only one possible father/mother pair that can beget it?
or is there more than one unique way to get a genetic sequence via male/female reproduction?

>>15094691
it's way easier to just remember the exponential identities and manipulate those to get whatever identities you want in the moment, frankly
[math]sin(x)=\frac{e^{ix}-e^{-ix}}{2i}[/math]
[math]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/math]

>>15094691
frankly it's way easier to just remember the exponential identities and do whatever substitutions and algebra you have to with those to derive the other identities
[math]e^{i\theta}=\cos{x}+i\sin{x}[/math]
[math]\cos{x}=\frac{e^{ix}+e^{-ix}}{2}[/math]
[math]\sin{x}=\frac{e^{ix}-e^{-ix}}{2i}[/math]

>>15094691
[math]e^{ix}=\cos{x}+i\sin{x}[/math]
[math]\cos{x}=\frac{e^{ix}+e^{-ix}}{2}[/math]
[math]\sin{x}=\frac{e^{ix}-e^{-ix}}{2i}[/math]
these three tell you all of the basic sine/cosine identities you need, just using a little bit of algebra and substitution

>>15094782
why isn't the nth prime minus n-1th prime divided by nth prime squared, not equal to pi?

>>15094691
The angle sum identities can be derived from rotation matrices:
[eqn]
R(\theta) = \begin{pmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end {pmatrix} \\
R(a+b)=R(a)R(b) \\
\implies \begin{pmatrix}\cos (a+b) & -\sin (a+b) \\ \sin (a+b) & \cos (a+b) \end{pmatrix} \\
= \begin{pmatrix}\cos a & -\sin a \\ \sin a & \cos a \end{pmatrix}\begin{pmatrix}\cos b & -\sin b \\ \sin b & \cos b \end{pmatrix} \\
= \begin{pmatrix}\cos a \cos b - \sin a \sin b& -\cos a \sin - \sin a \cos b \\ \cos a \sin b + \sin a \cos b & \cos a \cos b - \sin a \sin b\end{pmatrix}
[/eqn]
Difference identities are the same with b=>-b. Multiple angle identities can be derived from the sum identities. Half-angle identities can be derived by solving the double-angle identity cos(2h)=2cos^2(h)-1=1-2sin^2(h) for sin(h) or cos(h). Tangent half-angle identity from sin/cos half-angle identities. The others are basically just the definitions of tan/cot/sec/csc and Pythagoras.

>>15094668
maybe you search for sth like this

this function is arbitrarily often differentiable at x = 0, but it isn't analytical at this point

do you guys have any tips for getting temporarily smarter for an exam? sometimes my brain goes into superman mode, i can think faster and can get a lot of shit done, but it happens randomly, most of the time i have bad brainfog

i know that there is no general rule, but when doing limits using taylor series how do i know when to stop expanding the function?
i asked my teacher and she said "when the nominator and the denominator are comparable" but im not entirely sure of what that means, and even so how do i know in advance when they're going to be comparable (she said "you'll have a feeling for it once you do the exercises", well im doing them but i dont have any feeling)

>>15095109
I heard Amphetamine does the trick

>>15085518
How to prove pi^n is irrational for all natural number n? Tried induction, stuck at n+1 case.

I don't know if this is the right board for medical questions but /fit/ seems like a poor alternative. I'm writing a story where a character with long hair has several pieces of shrapnel from an IED surgically removed from their skull at a modern hospital. Would the surgery prep involve shaving the area?

last time i read a math/physics book and solved some exercises was 10 years ago. is it over for me?
pls recommend some refresher books for me. i wanted to explore quantum mechanics not as a phd but as a "hobbyist". i dont plan on publishing any research paper. i just want the satisfaction of actually solving some exercises/prooving some theorems compared to just watching quantum mechanics documentaries in youtube tho some channels seems to have rigorous proof tho i cant understand them. is anyone here doing something similar?

>>15095222
yes, any head surgery requires clearing the area.

>>15095238
Thank you.

>>15095173
> not entirely sure of what that means
neither do I. depending on the limit you typically want to remove all x terms from either the numerator or the denominator.

Wherever I look up how to change from cartesian to polar, they just straight up use arctan, but that's incorrect right? This is what I do.

>>15095316
Why would you think it's incorrect? All you are doing is calculating a equivalent angle in the reverse rotation.

>>15085518
Zorich versus Amann & Escher

Is there a compact subspace of [math]\mathbb{R}^n[/math] that is contractible but not strongly deformation retractible to any of its points?

>>15095316
https://brilliant.org/wiki/convert-cartesian-coordinates-to-polar/

It causes problems when converting from cartesian to polar because the domain of arctan can only go from -pi/2 to pi/2, and doesn't cover a full -pi to pi.

The way I do it is always graphical, I ignore the signs of x and y, and calculate the angle between the x axis and the polar coordinate, then I'll add or take pi from there to get the angle.

The image and link seem to have a formula like yours though. Which doesn't need any graphical stuff.

On a side note, if you ever do any programming and want an arctan function with a domain of 2 pi, in C++ the function is called std::atan2(x, y), and it has a corresponding function in C too.

https://en.cppreference.com/w/cpp/numeric/math/atan2

Hope this helps, and sorry if I misunderstood something, or how things work here. I'm rather new to 4chan.

>>15085518
Kirchhoff told me that net current into and out of a system is always 0. This is fine when I have circuits like picrel left. But what about static charge/discharge? picrel right. Isn't current just flowing charges? What if there is only one charge moving? What about when I get zapped from static buildup? Was Kirchhoff wrong?

>>15096085
>Kirchhoff told me that net current into and out of a system is always 0.
simple answer is that both of kirchhoff's law are for lumped element models of circuits, i.e. your left drawing. i mean, think about it, if the voltage around a loop was actually zero, how would current ever flow?

>>15096085
Literally read wikipedia https://en.m.wikipedia.org/wiki/Kirchhoff's_circuit_laws

>>15096136
Current flows because some components provide voltage while others consume voltage kinda.

>>15096139
Thanks. Wiki says "The current law is dependent on the assumption that the net charge in any wire, junction or lumped component is constant." So basically the law is true whenever it's true...

>>15096156
>Current flows because some components provide voltage while others consume voltage kinda.
thats a fine way of thinking of it in a circuits 1 course but just know that physically what you just said is nonsense.

>>15096191
>5V battery gives provides voltage difference.
>5V motor uses provided voltage.
>Motor spins.
If the nonsense works then it isn't nonsense

>>15096201
the nonsense will eventually stop working. you gotta understand the limits of your models or else one day youre gonna have a masters in EE and be arguing with an MIT professor about why KVL always holds and youre gonna look like a fuckin moron.
https://www.youtube.com/watch?v=0TTEFF0D8SA
wow these comments make my blood boil to this very day, incredible

>>15096220
I have no intention of getting a masters. I fail to see what is wrong with the models I have proposed/use. They are what works. Unless you want to do a full on 3D EMF simulation it isn't going to get much better.

>>15096229
>I fail to see what is wrong with the models I have proposed/use.
yes, i know! and thats okay! but you came into this thread asking why KCL doesnt work for a single charge moving in a field! and i tried to explain to you that Kirchhoff's laws dont always hold! they are very specifically for lumped element models! and now youre asking me whats wrong with imagining that the elements of a circuit consume voltage! jesus christ!

>>15096231
>>15096231
>i tried to explain to you that Kirchhoff's laws dont always hold!
I already got that part >>15096156
The part I don't get is why it's wrong to go around a circuit and say that a battery adds voltage then the motor consumes it in order to utilize KVL. I know that they are actually providing/consuming energy that is transferred using voltage/current/fields

>>15096238
>why it's wrong to go around a circuit and say that a battery adds voltage then the motor consumes it in order to utilize KVL.
if it works for your simple DC motor circuit then thats fine, but there are circuits where it does not. an AC generator, for instance, does not follow KVL, and does not have batteries. an (ideal) antenna provides voltage but no current. current doesnt technically even flow *through* batteries, so KCL doesnt hold. capacitors dont work without violating KCL. inductors violate KVL. electrons dont push on each other. current doesnt actually flow inside of wires. electricity is really really hard and so we came up with a bunch of tricks to make it easier for ourselves. but its important to remember that theyre just tricks, and they dont work all the time.

>>15095751
Any opinions on Zorich books versus Amann & Escher?

>>15096267
I'm pretty certain a lot of this is wrong.
>an AC generator, for instance, does not follow KVL
Yes it does
>an (ideal) antenna provides voltage but no current
It does provide current, some signal to antenna setups can power a speaker off the signals they pick up
>current doesnt technically even flow *through* batteries, so KCL doesnt hold
There is current going in and current going. Which for circuit design is the same. But perhaps you are right on this
>capacitors dont work without violating KCL
Same case as batteries. There is current going in and current going out
>inductors violate KVL
How? They sometimes have voltage across and sometimes don't. This is not in conflict with KVL
>electrons dont push on each other
Yes they do. The same way magnets "push" on each other
>current doesnt actually flow inside of wires
People say it flows on the surface of conductors or in fields around it. I've not been convinced, but also don't care either way
>electricity is really really hard and so we came up with a bunch of tricks to make it easier for ourselves. but its important to remember that theyre just tricks, and they dont work all the time.
True.

>>15096299
>I'm pretty certain a lot of this is wrong.
well as long as youre certain
>Yes it does
if you agree that the only way to move an electron is via the electromagnetic field, and if you agree that electrons move in a circuit in an AC generator, then you cannot conclude that generators follow KVL. is it possible for a roller-coaster train to perpetually move through its circuit if the only force to propel it is gravity?
>It does provide current. some signal to antenna setups can power a speaker off the signals they pick up
emphasis on ideal. and you cant have it both ways, either it doesnt provide current or it violates KCL. or do you think its grabbing charge from the air?
>There is current going in and current going. Which for circuit design is the same. But perhaps you are right on this
you can charge/discharge one side of a capacitor without (dis)charging the other one. in a circuit diagram you would hand-wave this as a second capacitance to ground.
>How? They sometimes have voltage across and sometimes don't. This is not in conflict with KVL
see AC generator note above
>Yes they do. The same way magnets "push" on each other
if you fire two electrons at each other they will indeed bounce off one another, but thats not whats happening inside a wire. electricity isnt a tube of marbles where you push one in at one end and another pops out at the other end. the space between free electrons in a conductor is gargantuan compared to their size (well, "size").

>>15095980
Helpful answer, newfriend. I do the same. The other anon adds 2pi to make sure the angle is positive, but you can just as well leave it as negative.

>>15096267

>>15096393
why do you have this picture saved? go outside

>>15095173
It depends entirely what you're using the Taylor expansion for. E.g. sin(x)=x-x^3/3!+x^5/5!-..., so sin(x)-x=x^3/3!+x^5/5!-... and (sin(x)-x)/x^3=1/3!+x^2/5!-... gives a quadratic approximation. Essentially, the number of terms depends upon what you're subtracting or dividing; you need something left after any cancellation.

>>15095216
Lindemann-Weierstrass theorem.

>>15096085
The usual statement of Kirchhoff's laws is:
KCL: the net current into a node is zero
KVL: the net voltage around a loop is zero
This is an approximation which suffices for lumped-element circuits but ignores electrostatics and electromagnetism. The more accurate version is:
KCL: the net current into a node equals the rate of change of charge stored within the node
KVL: the net voltage around a loop equals the rate of change of magnetic flux contained by the loop

The more accurate version of KVL is essential to understanding electromagnetism, because the electric field created by a changing magnetic flux isn't a potential field so the concept of potential doesn't apply (i.e. you can't describe voltages relative to a common ground point).

>>15096136
Red herring. The simplified version of KVL works fine for circuits with a voltage source (e.g. Galvanic cell aka "battery"). The portion of the loop not containing a voltage source has voltage in the opposite direction to current flow => negative power. The voltage source has equal and opposite voltage (in the same direction as current flow) and the same current => positive power. Net voltage around the loop is zero => net zero power (production = consumption, conservation of energy).

>>15096482
>KVL: the net voltage around a loop equals the rate of change of magnetic flux contained by the loop
ah yes, i too often refer to faradays law as KVL for literally no reason.

>>15095980
Yes thank you anon. I derive it geometrically. I was actually trying to solve this, but no luck because I don't know how the Jacobian works for piecewise transformations. The author just assume arctan, which absolutely retarded because that would change the distribution of [math] \theta [/math]

Wtf does this logical equivalences with nothing on the left mean?

>>15096626
If there's no prerequisite, the conclusion is a tautology.

>>15095216
Pi is transcendental hence the result immediately follows.

How can I model a function cost for a grid?
I need to find a way to assign different costs to a batch of different coordinates (x, y z) with the following restrictions each:
- 1<=x<=42 ; step 1
- 1<=y<=2 ; step 1
- 1 <=z<= 40; step 1
And in ascendant order.
I'm trying to model the picking order for warehouse. So x would represent a hallway, y the height and z de column and just by locations closer to 1.

>>15096826
Here is an example image from the top

If I use the existential quantifier ∃x it can also mean that the thing applies to every element? Or is always has to be at least -1 than every element?

>>15096884
It always means that it applies to one or more elements. And the more can be any number, even all. For instance, is it true that there is a number x such 1+x = x+1? Yes it is, because 1 will do. And in favt every other nunber will also do. But all we need is one example.

>>15096970
Thank you.

>>15096415
same can be said for you tbqh

How have people like boogie2988 and nikocado avocado not had heart attacks yet?

>>15096884
>>15097019
You should also note that [math] \exists [/math] demands existence but [math] \forall [/math] necessarily doesn't. So the latter is not sufficient for the former, though it may seem so. The former requires a single example to prove; while the latter requires a single counterexample to disprove. For example:
[math] \exists x \in \mathbb R \quad x = x +1 \implies x =2 [/math]
is false, because no example of a real number exists such that the statement is true; but:
[math] \forall x \in \mathbb R \quad x = x +1 \implies x =2 [/math]
is true, because no counterexample exists such that the statement is false, i.e, no number exists such that [math] x = x + 1 \land x \neq 2 [/math]. Since there is no counterexample, we cannot disprove it, and hence it is vacuously true.

>>15096136
Isn't Rika's mouth a bit high?

>>15096716
>>15095216
then why don't matheticians know if pi^pi^pi^pi is irrational?

>>15097187
Because pi is irrational

>>15096716
[math]e^{\ln 2} = 2 [/math]

>>15097138
yea a bit. are you being cheeky after i commented on that one remi the other day?

>>15097358
[math]\ln{2}\not\in\mathbb{N}[/math]

>>15097358
... and ln 2 isn't a natural number, so that means nothing here.

>>15095216
If [math]a^n[/math] is a root of the polynomial [math]p(x) \in \mathbb{Z}[x][/math] then [math]a[/math] is a root of the polynomial [math]q(x) := p(x^n)[/math].

>>15095216
[math] \displaystyle
\pi ^ n = \frac{u}{v} \\
\pi = \left( \frac{u}{v} \right) ^\frac{1}{n}
[/math]
since [math] \left( \frac{u}{v} \right) ^\frac{1}{n} [/math] is obviously a root of the polynomial [math] x^n - \frac{u}{v} = 0 [/math], it is not transcendental, hence the assumption is false.

Is the most general unifier (MGU) in predicate logic unique?

>>15096716
>>15097380
>>15097383
this was a proof review problem in an analysis class, I'm not sure if it's allowed to use the fact that pi is transcendental.

>>15097612
You are not allowed to use math?

>>15097612
https://www.quora.com/How-do-I-prove-that-pi-2-is-irrational
youll have to generalize it yourself for n > 2. have fun!

>>15097044
i don't know anon, i'm not sure how anything applies to me here. I'm not the one that comes to an otherwise helpful general to project my mental image of trannies onto others just because the OP happens to have an anime griller in it. But maybe i am biased because i have been lucky enough not to meet any trannies irl... How fortunate i am to not live on the internet

>>15097877
>i have been lucky enough not to meet any trannies irl...
lmao you wouldnt last an hour in austin, youd be marching in the fourth reich the first time you walked into a restaurant.

>>15097631
They might only be allowed to use math they have been taught (in that class).

Where can I find the absorption coefficient of a material for *any* wavelength? What I can find is usually limited to something between the UV and far-IR. I want to know it for gamma rays and radio waves also. It doesn't have to be precise.

>>15097367
Obviously, yes.
>>15097612
Then google for a proof that pi is transcendental and present it to your professor.
>>15097890
Lmao.

>>15085518
Is it possible to make people stop saying
>Science says/shows X
When really a person uses science to show X
>Statistics proves X
When really a person uses statistics based on Y to get a probability of X
>Says the word *SCIENCE!!* at the end of their explanation as if it's some kind of magic spell
This has made me cringe more times than anything else

>>15098503
No.
SCIENCE!!

If I passed an official IRL Mensa test (with the highest result possible, 135=/<), speak three languages and like autistic rpgs like Pokemon or Fire Emblem do I have the potential to become a statistician? Is it a comfy job where you are a glorified code monkey paid a decent guaranteed salary to do mindless mechanical busywork from home, or is it stressful, agonising and cruel? What is easier, working for my national Bureau of Statistics, as an actuary, or a biostatistician? Thank you to whomever that answers

>>15097877
>i'm not sure how anything applies to me here
One weirdo has trans wojaks saved on his PC, you have drawings of young girls cuddling each other saved. Neither of you have to post inciting pictures, yet you do. I don't really care as you're helpful but you shouldn't call anyone out, nor is this on-topic.

>>15098912
[math]\geq 135[/math] and still too retarded to understand what belongs on /sqt/ and what on /scg/. None of the things you mentioned are related to your competency btw (nor are Pokémon or Fire Emblem "autistic", kek).

>>15085518
Hello anons, I'm working through a math textbook but I'm not sure about my answers. Can I post my solution to confirm whether it is correct as I work through a book? I'm working on problem 1a.
My solution:
Functional
Suppose [math] x_{1} = x_{2} \in X [/math], then [math] x_{1}\triangle_{X}y_{1} \implies y_{1} = x_{1} [/math] by definition of diagonal. The same argument can be apply to [math] x_{2} [/math] to obtain the following [math] y_{2} = x_{2} [/math].
Since [math] x_{1} = x_{2} \implies y_{1} = x_{1} = x_{2} = y_{2}[/math]. Thus, [math] \triangle_{X} [/math] is functional. Similar proof can be done for [math] \triangle_{Y} [/math].

Mutal Inverse Mapping
Suppose [math]R_{1}: X \to Y[/math] and [math]R_{2}: Y \to X[/math] such that [math] \triangle_{X} [/math] holds.
Meaning [math] \triangle_{X} = R_{2} \circ R_{1} = {(x,z}\in X^{2}| z = x} = e_{x}[/math] by definition.
Thus, [math] \triangle_{X} [/math] is mutally inverse mapping of X because [math] \triangle_{X} = R_{2} \circ R_{1} = e_{X}[/math].
We can apply the same argument for Y to conclude that the mutal inverse mapping of X and Y are [math]\triangle_{X}, \triangle_{Y} [/math].

-One question I have is, is second part is actually correct? Because I don't know the definition mutal inverse mapping on a set. The book only mention conditions for mutally inverse for two relations. So, I'm not entirely sure about that proof. Also, is the proof for function good enough? Thank you in advance.

Why do we use [math]F = \frac{d \mathbf{p} }{dt}[/math] instead of [math]F = \frac{\partial \mathbf{p} }{\partial t}[/math] when F is clearly a multivariable function?

>>15099305
>F
Sorry, meant [math]\mathbf {p}[/math] here.

>>15099305
Could be the total time derivative.
>>15098503
>When really a person uses science to show X
But that's not accurate either.
A person uses research based on the scientific method to posit or suggest that X.
>When really a person uses statistics based on Y to get a probability of X
That's not how p-values work either.

>>15099197
It's wrong. For starters the question asks to prove that [math]\mathcal{R}_1[/math] and [math]\mathcal{R}_2[/math] are functional rather than [math]\triangle_X[/math] and [math]\triangle_Y[/math] which are trivially functions even without that composition assumption.

>>15099305
> clearly a multivariable function
Is it? What variables do you think it depends on?

How do I go about finding the probability of getting a specific item from a gacha type system? There are different groups, each weighted by a percentage, but multiple items in each group.
ex. 45% chance of item from Group A, 35% from Group B, 20% from Group C; however each group has a different number of items that can be drawn. Assuming you can only receive 1 item, what's the set up to find the probability of receiving a specific item?

>>15099075
i dont like to do shit like this but i dont think the other guy is gonna bother fessing up despite him deciding to run interference for no reason;
thats not me. i didnt reply to the tranny poster, i never do.

>>15099743
https://en.wikipedia.org/wiki/Law_of_total_probability

What's the point of grading on a curve in university? In my country the average on most exams is always like 50/100. But there is no curve, it just means that about 10% of the people pass with a decent grade (American equivalent of at least B), the rest don't pass or pass with a shitty grade

Is it correct that [math]n! \leq n^{n/2}[/math]?
[math]\sqrt[n]{1 \cdot 2 ... \cdot n} ^2 \leq \sqrt[n]{n \cdot n ... \cdot n}^2 \leq 1^2 \leq n[/math]

>>15099871
The only cases where this is true (assuming n is intended to be natural) are n=1 and n=2.

>>15099871
I have no idea what the second term is supposed to be. Can you expand it a bit more?

>>15099881
Looking at n=4, you're right
I'm looking to bound [math]\frac{2\sqrt[n]{n!}}{n}[/math] below 1 (I know the limit is 1/e but I can't reach it), isn't there some simple n! upper bound like the one I posted?

>>15099899
can you please reread your original post for errors? the second line seems to be a non sequitur

>>15099914
Yes, it seems to be wrong. I don't remember what I meant

>>15099803
no i was going to leave it because he was right about this being off-topic
>>15099075
i see where the misunderstanding comes from, i am not the animeposter. I still think wojakposter deserves to be called out, at least the animeposter(s) answer questions while posting pictures. Other than that i am still deeply disgusted by what the picture implies and i struggle to believe that it's an accurate portrayal of anyone in this thread. But i'll ignore it in the future, not really worth it shitting up the thread any further

>>15088580
please do (if you're still here), i am curious

>>15099808
because if the class is big enough then you will have a more or less static distribution of the students' grades. You can just fit them to that distribution instead of failing an abnormally large portion one semester because the exam was very difficult. Obviously it is not perfect, but there isn't a perfect solution

>>15085518
So viruses are very small and some scientists think they're not alive because of how simple they are. And viruses work by hijacking living cells to reproduce.
Is there a word for a microbe that is as small and simple as a virus but reproduces without host cells? is such a thing possible?
I just threw out some sour cream that had been coughed on by someone sick with a virus and I was wondering if it was possible for the virus to take over the sour cream the way a bacteria would or if eating it would be not that bad
Also
Do viruses really really go away, 100%?

Does anyone know an ineqality which looks something like [math]n! \leq \frac{n^n+1}{e^n}[/math]?
I remember seeing it in a book that I don't have access to right now. It's been on my mind for a month at least.

Anyone uses TexMacs for math here? It seems like a nice alternative to painfully typing in latex

>look up Gibbs energy for a species
>it's one value
>try to derive it manually as enthalpy minus standard conditions temperature (298 K) by entropy
>it's not the same value
Explain.

>>15100204
[eqn]n! \leq \frac{n^{n+ \frac{1}{2}}}{e^{n-1}} [/eqn]

>>15100308
sank you

What makes an opioid more potent than another while binding to the same receptors? Is it just about bond strength or what's happening?

>>15099315
>Cow stands in field
>Cannon is packed and loaded
>Cannon is fired
>Cannon ball is recorded going Mach 0.25
>Cow is dead
>Posit cannonball hitting cow at Mach 0.25 kills cow
This clearly *shows* that's how you kill a cow

Are time crystals bullshit?

>>15099315
>That's not how p-values work either.
Our study finds that we are xx% certain that the Y has an average quality of X +/- Z

Disclaimer: I do not actually believe the earth is flat (or round for that matter) as I can't PROVE what shape the earth is. But what I can do is ask questions.

Ok, so here it is: Suppose some dude had a private jet with an infinite amount of fuel. Suppose he took of and quickly reached an altitude of 200 meters above the ground. Then he engaged autopilot and left the computer stabilize the plane at a vertical speed of exactly zero (meaning the plane should not be flying towards the ground or away from it). Then he left the autopilot on for like 10 hours and went to sleep. If the earth was a globe, when he woke up, he should see that the altitude of the plane was now orders of magnitude higher than 200 meters, even though the vertical speed had been zero all this time. (Why? Well, the plane was flying in a straight line, but since the earth is a globe the trajectory of any straight line starting at any given point on the globe, eventually has to leave the atmosphere and pierce out into space and beyond).

Obviously this does not sound like reality, intercontinental flights do not have to make constant vertical axis tilt adjusments just to keep a steady altitude.

Conclusion? You tell me.

>>15100977
to measure altitude, you measure the distance from your plane to the land directly underneath your plane, and you know which direction "underneath you" is in because gravity always points downward. on a spherical earth, the direction of gravity would begin to shift if you flew for long enough.
theoretically an airplane would have to make gradual adjustments if it wanted to stay at a constant altitude, if it produced enough thrust and if there was no lift, but then it would less of an airplane and more of a missile. real airplanes (and real autopilots) are designed to maintain a constant angle of attack, which depends on gravity (or more precisely, the direction of "down"), so these adjustments happen automatically and extremely slowly and subtly over many many hours. nonetheless, a gyroscope could measure these adjustments if it spun for long enough.

>>15100977
Gravity.

>>15101047
does the angle of attack ever coincides with the velocity vector (zero angle?) when a plane is not taking off or landing?

>>15101063
does an airplane ever move in the direction its pointing? yea, i think that does sometimes happen.

>>15101069
that's what i am saying. if the plane is moving along a straight line, the angle of attack must be zero. which doesn't depend on gravity, right?

>>15101100
no, angle of attack is angle to the horizon, so to speak; 0 degrees is parallel to the ground, a positive angle means youre gaining altitude (or at the very least pointing upwards), negative means downwards. if you flew for long enough, your angle would gradually begin to climb as gravity began to point slightly backwards and you go off into space. the autopilot, and the aerodynamics of the plane in general, will tilt the plane back downwards and maintain a steady altitude. but again, these adjustments are so subtle it would take special equipment and a several hour flight to notice them.

>>15101114
pitch attitude is angle between aircraft and horizon
angle of attack is sngle between wind velocity and aircraft/certain part of the aircraft
they are not always the same

>>15101132
thanks, i knew it was called something else but google failed me

>>15100113
Sour cream and yoghurt contain bacteria which the virus could potentially infect.

>>15101100
The angle of attack is the angle between the wing and the airflow. If the aircraft is in level flight, then the angle of attack is equal to the incidence angle (the angle between the wing and the plane's horizontal line). Early planes had a relatively high incidence angle so the angle of attack would be significant when the plane was flying level. As aerofoil design improved and airspeed increased, incidence angles decreased.

I'm retarded. I think when I was a kid, a combination of being indoors and not getting enough fresh air, not getting enough choline in my diet because I was a very picky eater, and getting really shitty sleep, may have resulted in me having a fucking shitty brain.

I'm 26, dropped out of high school from failing grades, I'm plagued by short term memory loss and brain fog, I'm easily distracted, commonly get migraines, so on.

I ate eggs today for the first time in a long time and felt like a fucking superhero compared to how shit my head is usually.

Are there any other foods that might be beneficial for me? Is it too late for me to see any significant long-term benefits from making changes of my diet and lifestyle now?

I'm afraid of dying from my brain just giving up, or more realistically, just spending the rest of my life stupid and incapable of paying attention to even the things I enjoy. I've tried ritalin and it didn't help me.

What is the complement in R^2 (R-Q)*Q? Is there another way to refer to it?

>>15101280
Is X_1 < X_2 independent of X_2 < X_3 is all X are mutually independent?

Is X_1 < X_2 independent of X_2 < X_3 is all X are mutually independent?

>>15085518
Are there any natural numbers m and n so that 3^m = 7^n?

>>15101443
no 3^m will never be divisible by 7 and 7^n will never be divisible by 3

>>15101280
For [math]A, B \subset X[/math], the complement of [math]A \times B[/math] in [math]X^2[/math] is [math](X \setminus A) \times X \cup X \times (X \setminus B)[/math]

Can this process be used to assign an ordinal number to any set?

Is this a a scam?-https://www.indiegogo.com/projects/imicro-q2p-an-800x-polarizing-fingertip-microscope--2#/

Almost no video of this company's microscope being used exists online apart from their own ads.

So the general consensus is that there's no "necessary" frequency to masturbation (on the longer-scale end): You can masturbate everywhere from once a day to once a decade. There's also the (unproven?) theory that regular masturbation helps prevent prostate cancer.

I haven't masturbated in about a week (not for any ideological reason, I just thought I should give myself a break) and my balls have a weird tangible "pressure" about them - Nothing painful, just a physical "attention" towards them. Is this my body's way of telling me to masturbate (if such an apparent "need" exists)? Is this a resurgence in testosterone production brought by decreased frequency in masturbation? What does the weird feeling in my nuts mean?

For any ordinal [math]\alpha[/math], its ordinal successor [math]S(\alpha)=\alpha\cup\{\alpha\}[/math] is never equal to it because of the axiom of foundation (by ensuring [math]\alpha\neq\{\alpha\}[/math]), correct?

>>15101790
yea, microscopes cannot physically be that small

What will happen if I ask a nonstupid question in /sqt/?

>>15101790
>>15101965
It's not a scam, it's just a macrolens.

>>15101803
you're a young man and you're just naturally horny. don't overthink it

>>15101976
macrolenses cannot physically be that small

How do I go by on creating my own supplement pills for personal use? I do not want to spend millions on up-marked prices anymore. Can you combine anything you'd like? What dosages can I fit in pill sizes? Where can I buy the ingredients for this endavour? Should I get my own lab or borrow from somewhere to create my batches? What methods do I use? Do I need any gear? Do I need any permissions? Are there any legal loopholes? Should I just hire someone to do it for me?
I have a few ingredients that I wish to combine into 1. These include, but are not limited to:
>Cholecalciferol (Vitamin D3) 75 µg/0,075 mg
>Magnesium L-Threonate or Malate 1000 mg
>Caffeine 200 mg
>L-Theanine 200 mg
>Creatine Monohydrate 5 g (Might exclude this due to amount)
I think that's it. Appreciate any (You).

>tfw i figure out on my own why if the sum of the digits of any number is 3 than it's divisible by 3 as well

>>15102047
how

does the spinning sense of a gyroscope matters?

is there a difference if i spin it clockwise or counterclockwise ?

>>15101471
Are there [math]m,n \in \mathbb{N}[/math] such that [math]3^n + 1 = 7^m[/math]?

>>15102055
it’ll precess it the opposite direction
>>15102051
im not gonna tex it out on my phone but the usual proof goes something like: write the number as d_0 x 10^0 + d_1 x 10^1 + … + d_n x 10^n where d_i are the digits. then you notice that each term is congruent to d_i mod 3 (10^i = 999… + 1), so the whole thing is congruent to d_0 + d_1 + d_2 + … + d_n mod 3.
you could also prove it using induction if youre cool.

>>15102069
>it’ll precess it the opposite direction
thanks

>>15102064
no. one side will always be even and the other will always be odd.

>>15102085
How did you know such a thing?

>>15102088
Odd times odd is odd.
Odd plus odd is even.

>>15102089
I verified it but I'm surprised you knew how to figure out the answer. It sounds like a specific thing to know how to figure out.

>>15102090
This is very, very basic number theory.
Am I being indoctrinated into a cult or something? Is that where this is going?

>>15102069
too complicated, wtf "mod" even is lol, speak in English bro

>>15102051
very simple bro

notice any number in the decimal system is composed of place values and digits that tell how many place values you have in each position. each place value is a power of 10 (for example, 123 means 1 * 10^2 + 2 * 10^1 + 3 * 10^0, this is because you compose a unit of higher value at a rate of 10 individual units, and this in turn is because you only have 0 to 9 digits to represent units).

if a number is divisible by 3 in the decimal system, that means each of the products of digit * respective power of 10 (place value in each position) will also all be divisible by 3, otherwise you're left with a non-integer remainder in the division.

the problem is, powers of 10 aren't divisible by 3, you will always be left with 1/3 (for example, 100/3 = 33 1/3, 10/3 = 3 1/3), so in any given division of a number n you have something like

a * 10^0 + b * 10^1 + c * 10^2 + ...

where a, b, c, etc. are natural numebrs called digits that go from 0 to 9

if you divide it by 3, you get

(a * 10^0 + b * 10^1 + c * 10^2 + ... ) / 3 = (a * 10^0) / 3 + (b * 10^1) / 3 + (c * 10^2) / 3 + ... =

= a * (1/3) + b * (3 + 1/3) + c * (33 + 1/3) + ... = a/3 + b/3 + 3b + c/3 + 33c + ... =

= 1/3 * (a + b + c + ... ) + 3b + 33c + ...

As you can see, this result of the division of the number by 3 will only be a natural number, and thus the number will be divisible by 3, if and only if the sum of the digits i.e. (a + b + c + ... ) is a multiple of 3 too

>>15102093
My cult is that I wanted to know your process in solving the math problem. I'd heard of odd times odd being odd etc., but remembering that in order to answer are there those m, n sounded more specific of a thing to know how to be able to figure out. I could see it was right after you had suggested it because I can see 3^x and 7^x cycle certain odd numbers.

>>15102069
>you could also prove it using induction if youre cool.
I still want to prove it using little boxes for each unit I just don't know how.

>>15102105
On second thought, I don't think I had heard of that rule.

>>15102105
>>15102107
ah. It's not specifying that m and n can be any natural numbers to give you the impression that there are infinitely many values to pick from (well, there are, but...), but to limit the values you can pick from. If they were just arbitrary real numbers it would be absolutely trivial.
In general modular arithmetic is the very first thing you want to jump into with this sort of question, although it might take a couple of tries to find the number you need to disprove it (assuming it exists, at least).

red pill me on actuary
Why is a math field dominated by women?

>>15102085
Hm. What about [math]3^n + 2 = 7^m[/math]?

>>15102127
Take both sides mod 3 and you get [math]0-1\equiv1^{m}[/math].

>>15102127
Still none. Take both sides mod 3.

>>15101973
we will refer you to /sqt/ - smart questions thread

>>15102135
Anon I don't think it's that simple

>>15102148
Any power of 3 is congruent to 0 mod 3, trivially.
7 is congruent to 1 mod 3, so any power of 7 will also be 1 mod 3.
And 2 mod 3 is congruent to 2, or -1, whichever notation you prefer. In either case it has to be congruent to some power of 1 mod 3... but that's just 1 mod 3.
So we end up with [math]-1\equiv1\pmod{3}[/math], which is false. Hence there are no solutions.

>>15102155
Yep sorry meant to say you were right

>>15102155
>congruent to 0 mod 3,
what does congruent mean in division? congruent in geometry means of the same size and shape

>>15102160
Congruence in the context of modular arithmetic and abstract algebra means that they're not necessarily equal, but they behave identically with respect to a given operation.
In this case, 0 and 3 are indistinguishable when considered with addition and multiplication mod 3. In general, working mod n, any numbers that differ by a multiple of n are congruent to each other.

>>15102160
It means they have the same residue (remainder). If a≡c and b≡d then a+b≡c+d, a-b≡c-d and ab≡cd. IOW, modular arithmetic only "cares about" the residue; two numbers with the same residue may as well be the same number.

Congruence is an equivalence relation: ∀a,b,c: a≡a (reflexivity), a≡b <=> b≡a (symmetry), a≡b∧b≡c => a≡c (transitivity). If two elements belong to the same congruence class, you can replace one with the other in any expression without changing the congruence class to which the result belongs.

Congruence of geometric shapes means that they're the same ignoring rotation and translation. Geometric construction is invariant under rotation and translation (moving or rotating the paper doesn't change the validity of the proof).

What's up with the structure of Xenon hexafluoride? We were supposed to draw it's structure according to VSEPR on an exam. Since the free atom has 8 valence electrons, and in the molecule a valence of 6, it should have one free electron pair and therefore a pentagonal pyramidal structure like in pic rel.
I just checked it's real structure, and apparently it's octahedral. Where did the electron pair go?

>>15101904
Yes.

>>15102135
The logical extension of this question is whether there exists a number [math]k \in \mathbb{N}[/math] such that there exists an infinite amount of pairs [math]m,n \in \mathbb{N}[/math] that [math]3^m + k = 7^n[/math]?
Obviously the case is trivial for a finite amount.

>>15102286
>>15102135
>>15101471
m = n = 0

>>15102286
Wanna see a cooler extension?
[eqn]a^\{\mathbb{N}}+b^{\mathbb{N}}\cap c^{\mathbb{N}}[/eqn]
Where the power is as the power for all the elements in the set

>>15102286
[eqn]a^{\mathbb{N}}+b^{\mathbb{N}}\cap c^{\mathbb{N}}[/eqn]

Faggot latex jannies

>>15102286
My immediate assumption is that it does not, but I don't immediately know how to go about proving it; about all I can say is that this is a specific case of Pillai's conjecture.
If such a k exists, we know from previous examples that it has to be even and it has to be congruent to 1 mod 3, so it's going to be k=4+6x for some x.

>>15087591
dunno why but this is making me laugh

>>15098912
If you are above 110 iq, just grind anything and you'll have a decent shot at becoming good at it.

>>15098912
i value more and more people with bravery enough to try to be entreperneurs despite their low IQ than pathetic high IQ cattle like you who only seeks safety and comfort

>>15102286
Based on the arguments presented in this thread, k has to be
1. even
2. k mod 3 = 1
does there even exist a k such that there are 2 pairs m,n for which this is the case? the trivial case to find is a single pair, e.g. 4 because 3^1 + 4 = 7^1
this is trivial to find for any m,n because you simply need to find the difference
however so far I'm not sure whether there are many or just one

>>15102565
4 (n,m=1), 40 (n,m=2), 46 (n=2,m=1)... there's a value for every possible pair of m and n.
The question of whether or not some value appears for infinitely many strikes me as one where the answer is firmly "no", but I'm not immediately sure how to rigorously prove it.

>>15102580
>there's a value for every possible pair of m and n
yes, I said it was trivial to find

>>15102565
I reduced this to a multi-variable polynomial equation and it looks like it has only one solution.

What's the term for how so much 'energy' is lost per level of predator in nature? Like how it takes (These numbers are obviously not accurate, just to make it clear.) say 10000 calories of grass for a mouse to eat, but a mouse only provides like 1000 calories of meat for a cat to eat in exchange for that, and then the cat only provides like 100 calories of meat from that for the coyote that eats it? I know there's a term for it, but it's slipping my mind and I'm having trouble googling it.

>>15102565
There are even more restrictions at play than what's being considered here.
For example, since equality also has to hold mod 7, k and m are restricted by each other. Since the powers of 3 mod 7 are {3, 2, -1, -3, -2, 1}, repeat, for k=1 to 6 mod 7 (it cannot be 7), our values of m (mod 6) are forced to be 3, 5, 4, 1, 2, and 6, respectively (the converse is also true).
A little more math (that, full transparency, I can't be assed to figure out right now) will also net you restrictions on n as well.
>>15102619
Ecological efficiency?

>>15102626
>Ecological efficiency?
Maybe, but I don't think that's the word I'm looking for. Some kind of 'pyramid' or 'chain' kind of word. Or, it's for a story so if you have a suggestion for a term like that even if it's not the exact scientific term, that's fine too.

>>15092735
Ended up buying a 9th gen iPad. Cleared off everything that doesn't have to do with reading textbooks, but that's what I wanted. First up, 'The Biology of Cancer, 2nd Edition'

>>15102631
>>15102626
>>15102619
'Trophic level' was the term I was looking for if anyone wants closure. Someone on another board helped me.

>>15102223
>The structure of XeF6 required several years to establish
>VSEPR theory predicts that due to the presence of six fluoride ligands and one lone pair of electrons, the structure lacks perfect octahedral symmetry
>indeed electron diffraction combined with high-level calculations indicate that the compound's point group is C3v (trigonal, longitudinally asymmetric).
>It is a fluxional molecule. [Octahedral] is only insignificantly higher, indicating that the minimum on the energy surface is very shallow.

>>15102036
look up what a pill press is and whether or not it's considered drug-manufacturing paraphanelia (i.e. a permanenent suspension of your fourth amendment rights) in your state or country

Also the chinese or japanese used to wrap herbs in a packet of thin rice paper then swallow it whole, so maybe just buy a bunch of those at your local chink herbalist. "Oblate wafer film" I think they're called

>>15102777
if you don't mind can you give a mini review? i'm also contemplating getting one for textbooks
specifically wondering about
>does the screen size feel big enough for a textbook?
>how is the battery life when reading?
>does it hurt your eyes if you read for long time periods?
>is it easy to page back and forth to reference things?
>can you read in sunlight/outside?
>can you take notes on the textbook or in some other way while reading?
>does it support some sort of pen?
>anything you particularly like/dislike?

opinion on pic related?
it's one of the most recommened books for beginners to QM.
i tried reading it but on the first page it already has the wave function.
i admit that im a retard but isnt it too early to introduce wave function?
also please recommend an alternative.

>>15103519
Not him but I have an 2013 iPad air which is much worse. It is very slow, has LCD display, no pen, but I still use it for reading. It is almost as big as a paperback textbook, and since you can crop margins in a PDF editor, theoretically you could get a bigger typesize. Also you can get a bigger model. The largest pro is bigger than a hardcover. You can make notes inside its book apps using apple pencil (not supported in mine), and can switch back and forth between two hyperlinked pages. So like if a referenced theorem is hyperlinked you can jump to that page and also return back with a single button press. Still it's not as comfortable as a real book. It does not cause eyestrain. No you cannot read it in sunlight. I think it has only one real advantage over a textbook aside from price, and that is highlighting any sentence and being able to look it up with a press of a button. I think it's better to just get a textbook printed and sewn.

>>15103519
I just received it yesterday anon, so after a few days I will come back to answer your questions, seeing as with the new semester being only days away, I have to begin reading at least a few chapters a day.

>>15103519
not the anon but i also bought an ipad tho mine is an ipad mini. i really like it. it's perfect for reading and taking notes. the size it just right and very portable.

>does the screen size feel big enough for a textbook?
size is perfect for me tho im only mostly reading text and some diagrams
>how is the battery life when reading?
my ipad lasts for almost a week tho i only read indoors so the brightness is way low
>does it hurt your eyes if you read for long time periods?
not really
>is it easy to page back and forth to reference things?
sure but that depends on the app
>can you read in sunlight/outside?
haven't tried it yet
>can you take notes on the textbook or in some other way while reading?
yes
>does it support some sort of pen?
yes but it's a separate purchase
>anything you particularly like/dislike?
the glass screen is a fingerprint magnet

>>15085518
What is the symbol for capita? Google doesn't know.

8 liters of water per day can be written as
>8 L/d

But how the fuck do I write the equivalent for 8 liters of water per day per person?

>>15103519
I'm also thinking of getting an ipad 9th gen.
Can't find anything cheaper, so if any anons know any better options please let me know.

there're like $550aud everywhere I can see for just the base model, and then $200aud to ugrade 64gb to 256gb.
Is the upgrade in space worth it??

>>15103647
>8 liters of water per day per person
Like that.

>>15085518
Show there's a subset of irrational numbers that is countable?

>>15103661
{pi}

Please help, I'm losing my mind.
At work I happened across a quadratic equation. I entered it onto symbolab in some form of 0 = ax2 + bx + c (input algebraically ie. no values), which returned the solution for x. HOWEVER, when I enter the different values of a, b, and c the formula never ends up being 0 ???? I'm losing my mind here. Shouldn't I be able to input any values of a, b, and c and the formula would always = 0?

>>15103775
nvm, I just realised that having different values of a,b and c would actually give different solutions for x LMFAO.

>>15103647
8L/day/person

>>15103628
>>15103619
>>15103618
thx anons, still a bit hesitant to spend that much, but i'll probably buy one soon

>>15103661
Do you mean countably infinite? Then [math] \pi + \mathbb N [/math]

>>15103661
the algebraic numbers minus the rational ones

>>15099586
Either mass and velocity, or mass, acceleration and time.