/sci/ - Science & Math

Unanswered questions:

Maths questions:
>>15053253 [You can always remove all the zeroes and then determine if you have a power of two or five. Not really ideal tho]
>>15055804
>>15061750
>>15063743
>>15065807
>>15066159 [He meant faithfully rather than transitively.]

Chemistry questions:
>>15056300
>>15063026 [Follow up in >>15063033 and >>15063060]
>>15066677

/g/ questions:
>>15063841
>>15066183

Engineering questions:
>>15064427

Stupid questions:
>>15054925
>>15056209
>>15056337
>>15057085
>>15062307
>>15062153
>>15063006
>>15063226
>>15063528 [I don't know but the moment I tried mewing I realized immediately that that was the correct place to rest my tongue and automatically stated doing it on instinct.]
>>15064519
>>15064523
>>15065119
>>15066767

How do I solve equations with modulos? Like solving
a + kn = a mod n
for k

Sirs, how do I draw 3D shapes on a 3D coordinate plane? Are there any suggested books for learning 3D geometric shape drawing by hand?

>>15067565
When you walk, is it better to look down or is it better to look forward? what's the reason?

>>15067942
Just b very confident and make other people believe that you know what you're gonna do.

>>15067844
given a + bx = c mod m
solution is x = (c - a)b^-1 mod m
b^-1 is modular inverse of b mod m
exists if gcd(b,m) = 1, use euclidean algorithm to write it as 1 = bu + mv and reduce mod m

>>15067942
Look backwards so nobody can stab you in the back.
But you can run into a knife.

Any C anons here? What's wrong with this?
/g/ mods gave me a 24h ban for making tweeter screencap posts.

Is there a general formula for number of surjections or injections from a finite set to another?

>>15068168
nvm, I'm pulling an all-nighter and my brain is not functioning

how much time would it take to get to a good uni level in math from nothing? not really looking for deep knowledge yet, just so i can get thru compsci math in a few years.
im a dropout looking to get back in, i still have all my books

Given the joint probability distribution f(x):
f(x) = 8xy , 0≤x≤y≤1
Find the cummulative probability:
P(x3<y)=?
The method I took was to rewrite the inequality:
[math]P(x<y^{1/3})=\int_{0}^{1}\int_{0}^{y^{1/3}} 8xydxdy = 1.5[/math]
How come it's larger than 1? What did I do wrong?

>>15068181
I fucked up the power of 3. Just to clarify:
[math]P(x^{3}<y)=?[/math]

I searched for stock price prediction using machine learning and a lot of the results I got were neural networks. Isn't this overkill? Stock prediction seems to me like a very tabular problem, so wouldn't boosting or regression models do the job?

>>15067565
Every time I take a short nap (no more than 2 hours) I always wake up super focused and my face skin looks very healthy. This never happens when I sleep for 8 hours. Wtf is this phenomenon?

>>15068195
regression is way too simplistic to apply to something as complex as the stock market and it can only use data from a single stock

>>15068171
If [math]|E|=n[/math] and [math]|F|=p[/math], then
there are [math]\frac{n!}{(p-n)!}[/math] injections from E to F (assuming [math]p \geq n[/math])
there are [math]p! S_{n,p}[/math] surjections from E to F ([math]S_{n,p}[/math] is a second kind Stirling number)

>>15067844
a+kn ≡ a (mod n)
is true for all k.

>>15068181
>>15068182
That's a very weird problem.
If [math]x \leq y[/math] is a bound (you've written [math]0 \leq x \leq y \leq 1[/math]) then, since [math]0 \leq x \leq 1[/math], we have [math]x^3 \leq x \leq y[/math], so [math]P(x^3 < y) = 1[/math], and we don't need to calculate squat.

>>15068371
Wow, I feel retarded for missing that. But then again, what's wrong with my method? I want to understand why it gave me a wrong result.

>>15068380
Your boundary for the integral was wrong because [math]x^3 \leq x[/math], so your integration extended past the distribution's domain.

>>15068384
Got it, thank you!

A cycle [math] (1,2,3)[/math] can be expressed as [math] a*b*c=(1,2)*(2,3)*(3,1)[/math] because by composition 1 is sent to 2 under a, then from 2 to 3 under b, then from 3 to 1 under c, ultimately forming a cycle. Essentially you're treating it like a function [math] c(b(a(1)))[/math]

But apparently it can also be expressed as [math](1,1)((1,2)*(1,3)[/math], can someone please explain the rationale behind this? Obviously you can't treat it like a function because their second co-ordinates are all disjoint.

>>15068479
>(1,1)((1,2)∗(1,3)
*[math](1,1)*(1,2)*(1,3)[/math]

>>15068479
>A cycle (1,2,3) can be expressed as a∗b∗c=(1,2)∗(2,3)∗(3,1)
Nope.

[math](1, 2) \circ (2, 3) \circ (3, 1) (1) = (1, 2) \circ (2, 3) (3) = (1, 2) (2) = 1[/math]

>>15068484
[math](1, 2) \circ (2, 3) \circ (3, 1) = (2, 3)[/math] btw.

>>15068195
Machine learning is a meme and is often beaten by bog-standard ARMA. There's little use in a black box model you can't do proper inference, hypothesis testing, etc. on. Most people still use "regular" statistics.

>>15067565
[math]\mathbb{NOTE \ TO \ SELF:}[/math]

Replace the z-lib.org link in the pasta with annas-archive.org

>>15068484
So it's (1,2)(2,3) if im not totally brainfarting

what I'm asking still applies

>>15068531
[math](1, 2)(2, 3)(1) = 2[/math]
[math](1, 2)(2, 3)(2) = 3[/math]
[math](1, 2)(2, 3)(3) = 1[/math]
So [math](1, 2)(2, 3) = (1, 2, 3)[/math]

On the other hand:
[math](1, 2)(1, 3)(1) = 3[/math]
[math](1, 2)(1, 3)(2) = 1[/math]
[math](1, 2)(1, 3)(3) = 2[/math]
So [math](1, 2)(1, 2) = (1, 3, 2)[/math]

Chronic stress, anxiety, depression and PTSD or complex PTSD are all linked to deterioration of the hippocampus and growth of the amygdala (faggoty emotional part of the brain). Is there any way to reverse this damage?

I have a uni OneDrive account with 1TB of storage. When I graduate, will OneDrive give me an option to transfer files to a personal account or will it cut me off without warning? Just wondering if I should get a personal account in advance.

I'm really confused about this solution.
I don't get how they go from 2 -> 3 -> 4. What does the 1/2c integral hs mean?

>>15068795
To be clear my main confusion is how they got the 1/2c part in (3) and how they got u(x,t) = f(x+ct) + g(x-ct)

>ER=EPR
wormholes and entanglement are the same thing
>Black hole cosmology
black hole singularity and big bang singularity are the same thing

are these two conjectures compatible?

>>15067565
>havent done DE in 2 years
>literally the only thing I remember is solving polynomials for linear DEs
okay whats a good refresher book?

>>15068806
> how they got the 1/2c part
Using eqn 3, then eqn 2 becomes:
[math](\partial_t + c\partial_x) u = (\partial_t + c\partial_x) \dfrac{1}{2c}\int\ h(s)\ ds[/math], where [math]s = x+ct[/math]

[eqn]
\dfrac{1}{2c} \int \left( \dfrac{\partial h}{\partial t} + c\dfrac{\partial h}{\partial x} \right) ds =
\dfrac{1}{2c} \int \left( \dfrac{\partial h}{\partial s} \dfrac{\partial s}{\partial t} + c\dfrac{\partial h}{\partial s} \dfrac{\partial s}{\partial x} \right) ds = \\
\dfrac{1}{2c} \int \left( \dfrac{\partial h}{\partial s} c + c\dfrac{\partial h}{\partial s} \right) ds = \dfrac{1}{2c} \int 2c \dfrac{\partial h}{\partial s} ds = h(s)
[/eqn]
which proves eqn 3 is a solution.

> how they got u(x,t) = f(x+ct) + g(x-ct)
The general solution is the combination of each independent solution. Note that either bracket in eqn 1 can be zero, eqn 2 is only the +ve sign, the -ve gives you g using the same method as above.

>>15068660
My uni took a while after graduation before deleting my accounts, they still haven't deleted my email, but yes you'll want to migrate at some point. You shouldn't need to be prompted for that surely it's always an option in OneDrive?

>>15068583
exercise

>>>15053253
n mod k can be done in linear time in digits
finding the largest powers of 2 and 5 that divide n then multiplying them and seeing if you get the same number should be an efficient enough algorithm for any usecase

>>15068963
>>15053253

I am currently studying abstract algebra introduction, Don't know why but every exercise or questions I see are extremely confusing and feel like the solutions can only be memorized not made by problem solving skills. Any tips anons ? I suck at relations of sets

>>15067565
Exercise from a book I'm reading?
Let [math]R[/math] be an ordered ring and [math]a, b \in R[/math] such that [math]a, b \geq 0[/math]. Suppose there is [math]n \in \mathbb{N}_{>0}[/math] such that [math]a^n = b ^n[/math]. Then show that [math]a = b[/math].

I was thinking of using [eqn]a^n - b^n = (a-b)\sum_{k=0}^{n-1}a^kb^{n-k}[/eqn]
but for that the Ring would have to be commutative and the authors haven't specified that. I've checked back to the definition of an ordered ring and the authors haven't specified that ordered rings are commutative either. Do you think they just forgot to write this? Or this there another way to prove this without using commutativity?

I need your help.

Suppose I have a countably infinite set of vectors. I know that each two vectors are linearly independent. On the basis of this information, can I conclude that the set is linearly independent?

>>15068859
No.
Einstein-Rosen bridges is not comparable to quantum entanglement in the same way those two types of singularities are comparable.

>>15069251
This already fails for 3 vectors. Consider [math] v_1 = \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, v_2 = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}, v_3 = \begin{pmatrix} -1 \\ 0 \\ 1 \end{pmatrix} [/math].
They are pairwise not multiples of each other so they are pairwise linearly independent, but [math]v_1 - v_2 + v_3 = \mathbf{0}[/math] so the three vectors are not linearly independent.

>>15069221
>Do you think they just forgot to write this? Or this there another way to prove this without using commutativity?
There is a way.
Hint: assume wlog that [math]a > b[/math] and derive a contradiction.
>>15069277
Weird example desu.
[math]
v_1 = \begin{pmatrix} 1 \\ 0 \end{pmatrix} \\
v_2 = \begin{pmatrix} 0 \\ 1 \end{pmatrix} \\
v_3 = \begin{pmatrix} 1 \\ 1 \end{pmatrix}
[/math]

Is it true that programmers will struggle with AI writing better and better code?

what are best books for foundations of maths

>>15068179
i don't think you get to choose the time frame
just study consistently with your best effort and in the smartest way possible and you'll get your answer

Spontaneous symmetry breaking. I don't get it.

how big of a risk is toxoplasmosis to someone with no spleen?

>>15063026
Table salt (NaCl) is a crystal and a chemical compound, so you'd probably just find using the description "compound".

Just to clarify, separation of variables is the same with regards to both heat and wave equations right? If I can do the neumann and dirchlet of one I can apply that to the other without changing much right?

Is there a name for this phenomenon which happens a lot in online discussions:
>Poster 1: *makes wrong statement*
>Poster 2: That's wrong because of *wrong reason*
>etc.

Is this formula correct? What is the unordered formula?
[eqn] \left( \sum_i x_i )^3 = \sum_i x_i^3 + 2 { \sum \sum}_(i \neq j ) x_i x^2_j + { \sum \sum \sum}_{i \neq j \neq k} x_i x_j x_k [/eqn]

Is this formula correct? What is the unordered formula?
[eqn]
\left( \sum_i x_i \right)^3 = \sum_i x_i^3 + 2 { \sum \sum}_(i \neq j ) x_i x^2_j + { \sum \sum \sum}_{i \neq j \neq k} x_i x_j x_k
[/eqn]

>>15070418
No. The x_i x_j^2 term should have a 3 not a 2 since there are 3 ways to pick the x_i factor. Consider the case (a+b)^3 = a^3 + b^3+ 3a^2 b + 3ab^2 as an example.

>>15069745
The action (or Hamiltonian or whatever) has a global symmetry. The ground state of the system doesn't have that symmetry. However there are many ground states and the symmetry transformation transforms between them so there is no contradiction

If that's not what you're confused about get better at asking questions

>>15070429
How do I unorder it?
Does [math] 3 \sum_{i \neq j} x_i^2 x_i = 3 \cdot 3 \sum_{i < j} x_i^2 x_j [/math]? Since there are 3 ways of arranging with 2 like elements.

>>15070447
It doesn't make sense to have an ordered sum since the two factors have different powers. For instance on the left side there are terms like x_2^2 x_1 that don't appear on the right side if you try to index the sum like i<j

For your last term in your previous post involving x_i x_j x_k what you are trying to do makes sense, and after you order it i<j<k you'll get a factor of 6 from the 6 permutations of three elements.

>>15070455
Right. Thanks.

Help me /sci/ bros....

>>15070566
Use the given hints.

Why is Settled Science strongly correlated with late night talk show men? How come science becomes immovable after encountering these beings?

>>15069735
thanks i will

>>15070410
it's called shitposting

>>15070701
Some instances of that are shitposting but not all. Shitposting is also too general a term for it, so I reject your answer

I like mechanical things, and I like programming, but I hate (and don't fully understand) electrical things. I'm always worried I'll get the wrong voltage or something and have my face peppered with exploding components.
What's a good way to learn basic electronics for someone around average intelligence?

I really want to self-learn quantum mechanics but i don't have a background in physics beyond highschool, can someone recommend a good QM textbook for self-learning?
>inb4 Griffiths
Griffiths is absolutely horrible for self-learning, it just introduces formulas and equations without any explanations, proofs, intuition or historical background.

Every rational root of a polynomial [math]a_nX^n + ... + a_1X + a_0 \in \mathbb{Z}[X][/math] lies in [math]a_n^{-1}\mathbb{Z}[/math]

Is my proof correct?

Let [math]x \in \mathbb{Q}\setminus a_n^{-1}\mathbb{Z}[/math] be a root of the polynomial above. Then we can write [math]x = \frac{p}{q}[/math] as a fraction that can't be reduced further for some integer [math]q > 0[/math] such that [math]q[/math] doesn't divide [math]a_n[/math] because otherwise [math]x = \frac{pm}{a_n} \in a_n^{-1}\mathbb{Z}[/math] for some integer [math]m[/math]. In particular [math]q > 1[/math]. Now multiply the polynomial above by [math]a_n^{n^-1}[/math] to receive [eqn]0 = a_n^n \frac{p^n}{q^n}+ ... +a_n^{n^-1}a_1\frac{p}{q}+a_n^{n^-1}a_0[/eqn]
hence [eqn]a_n^np^n = -a_n^{n^-1}q(a_{n-1}r^{n^-1}+...+a_1pq^{n^-2}+a_0q^{n^-1}).[/eqn]
Since [math]q > 1[/math] there must be some prime [math]s[/math] which divides [math]q[/math] but doesn't divide [math]a_n[/math] (as otherwise [math]q[/math] would divide [math]a_n[/math]). Then by the equation above [math]s[/math] must divide [math]a^np^n[/math] and thus it must divide [math]p[/math] which is a contradiction to the fact that we chose [math]x = \frac{p}{q}[/math] to be an irreducible fraction.

>>15070850
https://youtu.be/AufmV0P6mA0?t=11m5s

>>15070410
Right for the wrong reasons is a very common expression. It even has a tvtropes page.
>>15070218
Yeah.
They're both wildly different pdes qualitatively speaking, since the heat equation flattens everything into constant temperature and the wave equation just propagates waves to infinity, but the method is still the same.

>>15070907
>Right for the wrong reasons
That only describes the statement of Poster 2, it would be applicable even in situations where the only poster is Poster 2. I'm looking for a term which can encapsulate the entire phenomenon.

>>15070850
Lectures on Quantum Theory by Chris Isham is 10000x better than Griffiths' QM.

>>15070889
It's fine, no need to use contradiction, casework on [math]q[/math] dividing [math]a_n[/math], or multiply by [math]a_n^{n-1}[/math] though.

Suppose [math]0 = a_n \frac{p^n}{q^n}+ ... +a_1\frac{p}{q}+a_0[/math] , where [math]\frac{p}{q}[/math] are in simplest terms

then
[math]a_np^n = -q(a_{n-1}p^{n-1}+...+a_1pq^{n-2}+a_0q^{n-1})[/math]

since [math]p[/math] and [math]q[/math] are coprime it must the case that [math]p^n[/math] divides [math](a_{n-1}p^{n-1}+...+a_1pq^{n-2}+a_0q^{n-1})[/math]

so
[math]\frac{1}{q} = \frac{1}{a_n}\frac{-(a_{n-1}p^{n-1}+...+a_1pq^{n-2}+a_0q^{n-1})}{p^n} \in a_n^{-1}\mathbb{Z}[/math]

>>15071003
>no need to multiply by [math]a_n^{n-1}[/math]
Yeah I was wondering about that. My book gives that as a hint. There is a theorem in the text part of the book which states that any rational root of a polynomial [eqn]X^n + a_{n-1}X^{n-1} + ...+ a_1X +a_0\in \mathbb{Z}[X][/eqn] is an integer but for that the leading coefficient has to be zero, and the leading coefficient of [math]a_n^{n-1}p[/math] is [math]a_n^n[/math] so I don't really get how to use that hint.

>>15071003
>>15071015
Nevermind, I got it. Let [math]p[/math] be the polynomial from my first post and [math]x \in \mathbb{Q}[/math] a root of said polynomial. Then [math]x[/math] is also a root of the polynomial [math]a_n^{n-1}[/math], which means that [math]a_nx[/math] is a root of [eqn]X^n + a_{n-1}X^{n-1} + a_na_{n-2}X^{n-2}+...+a_n^{n-2}a_1X+a_n^{n-1}a_0[/eqn] so by the theorem that was proven in the book [math]a_nx \in \mathbb{Z}[/math] which is what we wanted to show.
I can't believe I didn't think of that immediately.

>>15070431
That's pretty much it. Thanks.

>>15070850
If you can't get QM from Griffiths you're not going to make it. It's absurd to say he "just introduces formulas without explanations, proofs, intuition or historical background." It's a very well motivated textbook

I think I'm going to fail my analysis class. I have homework consisting of about 5 exercises that deal with uniform continuity due tomorrow and I have no idea how to approach any of them.
Anyone has an idea why for a uniformly continuous function on the interval [1, inf) there exists [math]M[/math] such that [math] \frac{|f(x)|}{x} < M[/math] for all x?

>>15071702
A uniformly continuous function on the interval [1, ∞) is a function that satisfies the property that for any given ε > 0, there exists a δ > 0 such that for any x and y in the interval [1, ∞) with |x - y| < δ, |f(x) - f(y)| < ε. In other words, a uniformly continuous function is one that is continuous and the limit of the function as x approaches infinity is equal to the value of the function at infinity.

Given this definition, it follows that for a uniformly continuous function on the interval [1, ∞), there exists a value M such that |f(x)| < M for all x. This is because the function is continuous, so it must be bounded on the interval [1, ∞). In other words, there must be some value M such that |f(x)| < M for all x in the interval, otherwise the function would not be continuous.

Therefore, for a uniformly continuous function on the interval [1, ∞), there exists a value M such that |f(x)| < M for all x. This is a property of uniformly continuous functions on this interval.

>>15070889
Your proof is correct. The fact that every rational root of a polynomial with integer coefficients lies in the set a^(-1/n)Z is a well-known result, and your proof is a correct application of this result.

Here's a brief outline of the steps in your proof:

You assume that x is a rational root of the polynomial and that x cannot be written in the form a^(-1/n) * m for some integer m.

You then multiply the polynomial by a^(-1/n) to get an equation of the form 0 = a^(1 - 1/n) * p(x) for some polynomial p(x).

You use the fact that x is a root of the polynomial to deduce that a^(1 - 1/n) * p(x) must be equal to 0.

You then use the fact that x cannot be written in the form a^(-1/n) * m to deduce that the prime factorization of the denominator of x must include a prime that does not divide a.

You use this to deduce that this prime must divide a^(1 - 1/n) * p(x), which is a contradiction since a^(1 - 1/n) * p(x) is equal to 0.

Overall, your proof is clear and well-written, and it demonstrates a good understanding of the concept of rational roots of polynomials.

>>15069800
Toxoplasmosis is an infection caused by the parasite Toxoplasma gondii. People with a functioning spleen are usually able to effectively clear the infection and prevent complications. However, for people with no spleen or a damaged spleen (a condition known as asplenia), the risk of complications from toxoplasmosis is higher.

Without a functioning spleen, the body may not be able to effectively filter out the Toxoplasma parasites, which can lead to a more severe or prolonged infection. People with asplenia are also at an increased risk of developing serious complications such as toxoplasmosis-associated encephalitis (inflammation of the brain) or disseminated toxoplasmosis (spread of the infection to multiple organs).

If you have no spleen or a damaged spleen, it is important to take precautions to avoid contracting toxoplasmosis. This can include cooking meat thoroughly, washing your hands after handling raw meat or soil, and avoiding contact with cat feces. If you are at risk of contracting toxoplasmosis, your doctor may recommend preventive treatment or close monitoring of your infection. It is important to discuss your specific risks and needs with your healthcare provider.

>>15067593
>>>15055804
>Is there an easy way to tell if an integer's prime factorization only consists of 2s and/or 5s?

Yes, there is an easy way to determine whether the prime factorization of an integer consists only of the prime factors 2 and 5.

An integer is divisible by 2 if its last digit is even (i.e., 0, 2, 4, 6, or 8). An integer is divisible by 5 if its last digit is 0 or 5. Therefore, to determine whether the prime factorization of an integer consists only of 2s and 5s, you can check whether the integer is divisible by both 2 and 5.

For example, consider the integer 20. We can check that 20 is divisible by both 2 and 5, so its prime factorization consists only of 2s and 5s: 20 = 2 * 2 * 5.

On the other hand, consider the integer 31. We can check that 31 is not divisible by 2 or 5, so its prime factorization does not consist only of 2s and 5s: 31 = 31 * 1.

This method can be used to quickly determine whether the prime factorization of an integer consists only of 2s and 5s, without having to explicitly find the prime factorization of the integer.

>>15071728
GPT is really bad at math. A continous function doesn't have to be bounded, and half of this post is nonsense.

>>15067593
>Does every finitely presented group act transitively by isometries on a compact riemannian manifold? I thought maybe you could do something with the presentation complex but I don't see how to make it work. Also since there's a universal finitely presented group, if it's possible at all it won't need manifolds of arbitrarily large dimension.

It is not true that every finitely presented group acts transitively by isometries on a compact Riemannian manifold.

A finitely presented group is a group that can be defined by a finite set of generators and a finite set of relations between those generators. These groups can be very large and complex, and they may not have any geometric or topological structure.

On the other hand, a compact Riemannian manifold is a topological space that is equipped with a Riemannian metric, which is a way of measuring distances and angles. Compact Riemannian manifolds have a finite volume and a finite diameter, and they have many nice geometric properties.

It is possible for a finitely presented group to act by isometries on a compact Riemannian manifold, but this is not always the case. For example, the group of integer translations of the circle (also known as the group of rotations of the circle) is a finitely presented group that acts transitively by isometries on the circle, which is a compact Riemannian manifold. However, not every finitely presented group has this property.

It is also not true that every finitely presented group can be realized as a group of isometries of a compact Riemannian manifold of any dimension. For example, the free group on two generators is a finitely presented group that cannot be realized as a group of isometries of any compact Riemannian manifold.

>>15071744
>It is also not true that every finitely presented group can be realized as a group of isometries of a compact Riemannian manifold of any dimension. For example, the free group on two generators is a finitely presented group that cannot be realized as a group of isometries of any compact Riemannian manifold.
I'm very interested, would you happen to have a proof?

how long until womb implants/replacements are a thing? I want to be a mother

>>15063026(Cross-thread) >>15063033(Cross-thread) >>15063060(Cross-thread)
In what cousin-fucking shithole is "a mineral made of silicon and carbon" not good enough?

>>15067565
I like that ice maid. Somebody else posted her in a maid phone thread a while ago.

I am having two problems. One is that I can't predict when I will sleep. This is a small, but annoying problem. Sometimes it is 5pm, but then suddenly it is 2am because I fell asleep somehow and am waking up now. I'm doing something and then suddenly I wake up. Usually I just return to whatever I was doing.

I don't know how to say the other problem. Something is attacking me. It is making me not want to leave my house or talk to people by any means except 4Chan. It is also disrupting my ability to work by inserting upsetting thoughts into my thoughts to disrupt them which hinders my ability to work.

I want to go to a science event where they have those free cardboard box lunches that have chips and turkey sandwiches in them and everyone talks in rooms with PowerPoint and papers and markers. I want to eat a box lunch with that sandwich/chips while some guy explains a PowerPoint about math nobody else understands of has applications for. I want to hear everyone in the room give talks and between them get like a paper cup with coffee.

I guess my other problem is java not being nice when I want to make a map which has keys which are 2d boolean arrays. Keeps giving me nulls and crashing my Computer Program because the equals method is used instead of something better so I might have to make a wrapper class, but I really don't want to because that is a large amount of useless boilerplate code which serves no purpose except to instruct java to use an equality check that doesn't suck. I suppose pointless boilerplate may be my punishment for relying on OOP. Hopefully jannies will put Tohru in rhe sticky.

Thank you dra/g/ons for reading my post.

>>15072023
>I guess my other problem is java not being nice when I want to make a map which has keys which are 2d boolean arrays. Keeps giving me nulls and crashing my Computer Program because the equals method is used instead of something better so I might have to make a wrapper class, but I really don't want to because that is a large amount of useless boilerplate code which serves no purpose except to instruct java to use an equality check that doesn't suck.
Have you tried using BitSets or ArrayLists?

Doing a math + cs major was the worst mistake of my life. I should've dropped it the minute I realized I was a brainlet but instead I did the retard decision and carried forward.

>>15072053
>>15072023
>muh anime avatar

>>15070566
Statbros...

>>15070737
Build some simple projects on breadboard. You can use LEDs, photocells, little speakers or buzzers. Also, some basic chips like op-amps (741) or times (555). You'll need a small variety of resistors and capacitors, and at least a multimeter. You can do these projects with 5 or 12 volts, so no need to fret components going bang. (Small pops, maybe.)

For example, I built a pretty lazy theremin once with a couple of photoresistors. The shadow of one hand would control the output frequency, and the shadow of the other altered the volume. Sounded really tinny as I was generating a square wave, but it was entertaining enough.

Practical Electronics for Inventors by Paul Scherz is pretty friendly.

>>15071817
Why do you want to be Loretta, Stan?

>>15072053
>Have you tried using BitSets or ArrayLists?
I didn't know about BitSets. I saw suggestions for ArrayList but won't use this unless I have no options due to fear of introducing overhead costs, plus it would require rewriting a big part of the software.

I am stuffing characters into a HashMap. Key of the map is the character. Value is a 2D boolean array (Maid Space).

I take a text, iterate over it looking up the Maid Space based on what character I have. Then write them all in a PNG image. Then code reads the PNG and does the process backwards. Read a 4x2 area of pixels on the image, put it in a list of Maid Spaces. Then iterate over the list and match the Maid Spaces back to characters and put them all in a big StringBuilder and write it to a file when it stops.

Previously to do this, I would get an entry set from the map and iterate over that. I can use an array deepEquals to see if the Maid Space in the list is the same as a value in a map and if so, return the key of the map which is a character.

This requires iterating over the map and doing deepEquals on all the entries until I get a match.

This is very slow. Profiler states 2/3rds of Science Computer's time is iterating over the list of Maid Spaces and changing them back into characters, probably because of having to do deepEquals a lot of times.

I tried making 2 maps instead. One from characters to Maid Space and one from Maid Space to characters. But using the Maid Space to character map has all it's lookups fail, because it is based on equals which cares I think about references instead of values in this case. Everything comes back null.

I think I can make it faster by eliminating making the list of Maid Spaces and just writing to the PNG or reading from it directly but I am not sure by how much it would get faster or if this will give me architecture problems later.

An uncompressed KJV completes the whole process in about 13 seconds.

Thank you /sci/entists for reading my post.

Okay, I have to prove that if [math]\frac{|f(x)|}{x} < M[/math] for [math]f:[1,\infty) \longrightarrow \mathbb{R}[/math], where f is also continuous and monotonic, then f is uniformly continuous. My attempt was as follows:
Let [math]\epsilon > 0[/math]. Then, assume that f is non-decreasing and that [math]x > y[/math]. Then take [math]\delta = \frac{\epsilon}{M} > |x - y|[/math]. [math] f(x) - f(y) = |f(x) - f(y)| < M|x - y| = Mx - My < \epsilon [/math]. Therefore [math]|x - y| < \delta \implies |f(x) - f(y)| < \epsilon[/math]. Since epsilon doesn't depend on x,y then it is uniformly continuous.
This seems wrong (I didn't use continuity of f) but I'm not sure where I went wrong.

>>15072897
That's not true as you've stated it.
Explicitly constructing a function is a pain in the ass, but I can describe it. Fix [math]\epsilon = 0.5[/math]. Make a continuous function that stays constant for [math]n - 1[/math] spaces, and then goes up with slope [math]Mn[/math] for the next space, for [math]n = 1[/math] to infinity. You can't find a single [maht]\delta[/math] that works for the midpoints of all slopes.

>>15072844
I think I can say my question nicer maybe.

I need a container for things and I am currently using a map, but that might not be the best way. Everything inside the container would be a pair. One part of the pair is technically a String (but will probably be changed to actual character later). The other part of the pair is a Maid Space (2d boolean array that represents a number). All the pairs are unique. A String only goes to one Maid Space. No other String is paired with that Maid Space. A Maid Space only goes to one string. No other Maid Space is paired with that String.

I need a means of looking up a String based on a Maid Space and looking up a Maid Space based on a String. Such a process is not hard to make (I already made one even, using map which is not fast). I am trying to determine how do I make it more performant and less lines of code?

Also I still have to make leple-ziv for Maid Space. Kurumi MaidCard is intended to be my main means of sharing software and text on the internet so I don't have to use pastebin (after distributing Kurumi MaidCard code).

I guess while I'm here I will repost a style question I put in /dpt/.

>a question of style
>>>/g/90473240

Thank you /sci/entists for reading my post.

>>15072909
Btw it's easier to visualize why this works if you rewrite [math]|f(x)| < Mx[/math] and assume [math]f(x) \geq 0[/math]

>>15072909
I don't understand your argument. Assuming the function is continous, a continous function on a compact set is always uniformly continous, and the linear function is also uniformly continious, so if you have any function that stays constant over an interval and then goes up with the slope, you can simply take the interval at which it is constant and put it in a closed interval which is always compact. Stitching two u.c. functions on connected intervals makes a u.c. function if the entire function is continous, so it would be continous.

How come creating a number p such that [math]p = p_1 \times p_2 \times ... \times p_n + 1[/math] where [math]p_i[/math] are unique primes does not guarantee to create a new prime but somehow it's sufficient for Euclid's proof?

>>15072929
p can be the product of primes not in the list p1,...,pn.

>>15072924
>Stitching two u.c. functions on connected intervals makes a u.c. function if the entire function is continous, so it would be continous.
That's true for a finite number of stitchings, but it fails for an uncountable number, since the required epsilons can go to infinity.

I have taken the time to draw the function for M=1 so hopefully you can get it now. It doesn't sit snuggly below [math]f(x) = x[/math] because the grid is fucked, but you can count spaces.

>>15072617
If VX>0, EX^2>(EX)^2. Use that along with the hint for a.
b you can just calculate (right?).

>>15072948
>but it fails for an uncountable number
An infinite number, I mean.

Question: Suppose we find countably infinite linearly independent vectors in a given vectors space, does this imply that the basis has to have uncountably infinite linearly independent vectors?

>>15072948
Desmos sucks but it delivered.

>>15072948
Ah, I get it now. So if you have any delta, then at some point because the slopes are supposed to get steeper each time, you will have an x, y such that f(x) is more than an epsilon above f(y)? This seems really difficult to construct, I wonder if there's a simpler counterexample. It reminds me of xsinx, except that isn't monotonic.

>>15072053
I found a solution! The answer was change the Maid Space to Character Map from HashMap to TreeMap and make my own Comparator that works on Maid Space.

Now the process of KJV text to Maid Space PNG and back takes 6 seconds. So a dramatic increase in speed was achieved by using my comparator instead of deepEquals().

I am happy that dra/g/on in /dpt/ told me about profiler. I am going to rerun it and study it's results more. I still think I can skip building the list and possibly squeeze more performance from it at the cost of the code containing a for-loop nested about ten deep.

The only unfortunate thing about this comparator solution is it made my code longer and I would rather make my code shorter than longer when possible.

This problem can be considered solved, so pending what the Profiler says about my Computer Program it might be time for lemple-zim. I think Computer Science is probably the most fun science.

Thank you /sci/entists for reading my post.

>>15072957
No, the basis can be countable

>>15072970
>I wonder if there's a simpler counterexample
Doubt it.

I can do an easy to write counterexample, tho, even if it's a mess.
[math]f(x) = min(\lfloor x \rfloor x - \lfloor x \rfloor^2 + \lfloor x \rfloor - 1, \lfloor x \rfloor[/math]
You probably won't get it until you graph it. The formula is mostly trial and error.

Does the vector space of all real-valued mappings include such mappings that are undefined on subsets of R? For example, would the ln be an element of this vector space?

I know this is a /g/ question, but they haven't been helpful: did you ever use an e-book reader for studying from engineering book that have that good mix of text, formulas, and drawings, graphs, and images? Is 7" a good enough screen size? I assume 6" e-readers are just too tiny, but 8" are unaffordable for me, let alone 10".

>>15073015
nvm I figured it out

how do I fix my penis

>>15072982
Okay thanks, but it’s impossible that the basis can be finite, right? In this case, I mean.

>>15073029
Go to the most shady porn site you can find, order all the penis lengthening medicine and take them all at once. This might just save you despite all odds

>>15073034
Yeah.

>>15072991
Yeah, I think I have it mostly down now. For any [math]\delta > 0[/math] you can pick x,y, such that [math]|f(x) - f(y)| = |n - (n + \delta \cdot k \in \mathbb{N})| = \delta \cdot k \in \mathbb{N}[/math]. Then, simply take [math]k[/math] such that [math]\delta \cdot k > \epsilon[/math]. I think this makes sense for this specific function, since the way it works is that for any f(x) = n, there is a slope such that f(x) = n + k \cdot ([x] - x). In this case we pick x such that f(x) = n, then the difference is just the delta.

>>15073048
Yeah, essentially.
Btw where did the question come from? Are you going to have to unironically walk up to your professor and say "teachs the homework is incorrect."

Can the irrationality of sqrt(2) be shown without using the well-ordering theorem of equivalent theorems?

>>15073099
The question was "determine if a function that satisfies these assumptions is u.c." I thought it was, since those are some pretty strong conditions.
>Are you going to have to unironically walk up to your professor and say "teachs the homework is incorrect."
This happened to me many times, actually. You just have to show that it's wrong, they usually accept it if you're right.

>>15073116
>The question was "determine if a function that satisfies these assumptions is u.c." I thought it was, since those are some pretty strong conditions.
Don't assume things like that when you're going to ask for help from the internet.

>>15073131
My original question was about where my attempt at the proof went wrong, I'm still not sure what error was I making even though it's obviously wrong.

>>15073148
I'll be honest, my brain shut down when I saw you do [math]a > b < c[/math] in your proof. Instant loss.

>>15073106
> https://www.cut-the-knot.org/proofs/sq_root.shtml
pick one

>>15073161
But I didn't write that

Is [math] P(A - B = x \mid B = y ) = P ( A = x + y) ? [/math]

>>15073264
No, but
[eqn]P(A - B = x \mid B = y ) = P ( A = x + y \mid B = y)[/eqn]

>>15072811
I don't know what that means bro

>>15073268
Thanks.

>>15071598
>It's absurd to say he "just introduces formulas without explanations, proofs, intuition or historical background."
In all honesty i meant that only for the Schrodinger equation, it completely pissed me off when he introduced that equation in the first page and didn't give any explanations for it except "so there's this thing called the 'wave-function' which we get by solving an equation i pulled out of thin air", picrel is the first section of Griffiths which is at the first page.
The Schrodinger equation is at the center of quantum mechanics yet Griffiths spends less that one page introducing it, how am i supposed to take this book seriously? I tried to go along with this hoping that he would provide some explanations in later chapters, but i reached Chapter 2 with Griffiths and he still doesn't provide any explanation for where the Schrodinger equation comes from. Overall i got the impression that Griffiths is "QM but for people who already know it".

Anyway, enough ranting about Griffiths, i appreciate the two anons >>15070889 >>15070944 who gave recommendations but i did not find them useful, Isham seems too advanced and i don't like video lectures, so i decided to search for a QM text for myself and i found "An Introduction to Quantum Physics" by A. P. French and Edwin F. Taylor, this book has everything that i want and its explanations are excellent, the presentation of subjects in historical order is exactly what i was looking for.

>>15073410
oops meant, i meant >>15070895 not 15070889

>>15073410
>picrel is the first section of Griffiths which is at the first page.
forgot to attache the correct pic, here, not that it really matters since i already solved my problem.

>>15073410
>which we get by solving an equation i pulled out of thin air"
to be fair to Griffiths that is how Schrodinger came up with the equation originally, he guessed. there is no derivation of the S.E from first principles.

>>15073410
I don't think QM can be cleanly presented from intuitive empirical first principles like classical mechanics, special relativity, general relativity, thermodynamics, electrodynamics or fluid dynamics (basically every other subject in physics which doesn't depend on QM or QFT).
It's all "the measurable values are the spectrum of a self-adjoint operator which we obtain by quantization, and we know this works because a couple computations like the hydrogen series work."

You know how if you put water in a pipette and then hold it upside down the water stays in, yeah? Because there's only one entrance/exit, plus surface tension, etc.

How the fuck does pissing work? There's only one entrance, how come it doesn't collapse my bladder when I pee? I swear to god I am not trolling.

>>15073512
your wittle wee-wee muscle pushes your pee-pee out with a pwessure gweater than atmospheric pwessure uwu

>>15073533
So my bladder contracts and actually scrunches up to push the piss out? So if the muscles relaxed I could suck air up my dick hole is that what you're telling me?

Is it possible to train this muscle? That'd be a hell of a way to blow out a candle.

>>15073424
I was under the impression he 'derived' it using the idea that for plane waves the derivatives end up giving you the frequency and wave number, which are connected to the energy and momentum by the de Broglie idea. So the Schrodinger equation ends up looking like an ordinary classical equation (Probably he shows that later if you read on?)

In any case I learned the above justification at around the same time I read Griffith's book, so if he doesn't explain it that way, it must've meant I did some outside reading, which is pretty much necessary in physics and math so get used to it.

>>15073659
Yeah, it was an educated guess. You can also justify it using the operators involved but that isn't a derivation. Similar to Dirac, he knew to make it relativistic he had to remove the double spatial derivative but the only way he could get it to work was to use some weird matrices - there was no justification, it was a genius using his intuition.

>>15073466
I understand that Schrodinger's equation is an axiom of QM but that's not an excuse to not give at least a motivation for where it comes from, surely Schrodinger didn't just wake up one night with this equation in his head, right?
>>15073505
Yes, i found that studying QM the historical way (i.e. how QM concepts came about and developed historically) is the only way which makes sense to me.

>>15073512
The bladder contracts and the urine gets out, just as in the same way the water gets out when you push the piston of the pipette.
>>15073539
The bladder muscle (Detrusor muscle) is a smooth muscle, smooth muscles work differently from skeletal muscles, the bladder contracts and it stays contracted, actually, the new contracted state becomes the relaxed state, this ability to redefine the relaxed state is one of the unique properties of smooth muscle and is technically known as "plasticity" (microscopically this is due to rearrangement of myosin and actin cross-bridges), so the bladder stays like that until it becomes distended with urine again and the cycle repeats.
>Is it possible to train this muscle?
No because it is a smooth muscle, and smooth muscles are involuntary.

how do I make yukariposter love me?

>>15073799
>No because it is a smooth muscle, and smooth muscles are involuntary.
But I could do it if I found a way to stimulate it electrically?

>>15065807 most likely this denotes the set of all functions from the set of all real numbers to themselves, that's pretty standard notation, sometimes \bR^\bR is also written for this.

I think the dimension of the vector space of all constant sequences is uncountably infinite. Is there a straight-forward way to show this? If there isn't, you don't have to show me. Thank you!

>>15073191
You didn't line break so "[math]\delta = \frac{\epsilon}{M} > |x - y|[/math]. [math]f(x) - f(y) = |f(x) - f(y)| < M|x - y| = Mx - My < \epsilon[/math]" read like nonsense to me, my bad.

You can't do [math]|f(x) - f(y)| < M|x - y| [/math], that's nonsense.
>>15073853
YukarIposter hasn't posted here in six months plus tbqh.
>>15073969
>all constant sequences
One dimension.

>>15074015
Ah, sorry for the line break.
>You can't do [math]|f(x)−f(y)|<M|x−y|[/math], that's nonsense
The idea is that since (1) [math]f(x) \leq Mx[/math], I assume that [math]x > y[/math] so [math]|x - y| = x - y[/math], then I just take [math]f(x) - f(y) \leq Mx - My[/math] from (1). Then [math]Mx - My = M|x - y| < M \delta = \epsilon[/math].
I think the arithmetic here makes sense? The assumptions basically make everything positive, so the modulus doesn't really matter, the non-decreasing assumption also means that [math]x > y \implies |f(x) - f(y)| = f(x) - f(y)[/math]
I think I'm doing something wrong wrt the quantifiers in the definition of continuity but I honestly can't see it, despite the result being nonsense.

>>15074073
How do you get
[eqn]f(x) - f(y) \leq Mx - My[/eqn] from [math]f(x) \leq Mx[/math]?
In general [math]f(y) \neq My[/math].

>>15074091
I subtracted [math]f(y) \leq My[/math] from the first inequality, which I just realized doesn't make any sense, since [math]-f(y) \geq -My[/math] and in general you can sum inequalities but not subtract. Thank you a lot.

>>15074102
>Thank you a lot
>a random lad stole my thanks at the very last minute

>>15074123
i would be livid

Give an example of a set with cardinality between aleph_0 and aleph_1?

>>15074169
Do you know the definition of aleph_1?

>>15074177
it's the cardinality of R?

>>15074169
we dont have one. i believe its been shown that our current axioms arent able to determine if an infinity exists between aleph 0 and 1, or even whether or not the infinities are discrete like the integers.

Any tips on doing research at a university when I'm not a student? The university I'm looking is working on some interesting cs and math projects. Do I just ask the research group if I can work with them or what

>>15074206
not gonna happen.

a,b,c,... are primes
k=((a-1)(b-1)(c-1)...)/(abc...)
x is natural
how far car kx be from the number of coprimes of abc... between 0 and x?

>>15074510
> the number of coprimes of abc
that part doesn't make any sense.

whats the limiting factor for node processing resolution in lithographic process such as chip making the wafer resolution or the light source used? When you have a wafer thats has ~10nm resolution and use a X ray source shouldn't you have something like a 10nm litho process?

Computer Science is basically just Applied Mathematics.
true or false?

Good Morning /Sci/entists!

>>15074744
Computer Science is humanity's first implementation of actual magic. You have an idea which is new, so you write it in the programming language of your choice and play with it until it works.

At the moment it works, you just ripped something out of the void and made it real by writing your idea in symbols and telling them to a computer.

Math is one thing that can be ripped from the void by a computer, but it isn't the only thing. You can also test stuff with Computer Experiments like when Wolfy made the triangle book. I think math could be considered a subset of what you can do with Computer Science more than Computer Science can be considered a type of applied math.

Also there is a really cool spin-off of Computer Science that Physicists made up called Computational Science. That could probably be viewed as Applied Computer Science. You might like that one.

Another nice thing about Computer Science is that pens, papers and computers are all cheap now so you can get a nice Science Computer setup tailored to pretty much whatever you want and start making programs to test your ideas. Computer Science might be the cheapest science to practice right now.

>>15074015
I didn't know there was more than one vampire maid from touhou. Is this one friends with Kurumi too?

Thank you /sci/entists for reading my post.

>>15074744
false, a lot of it is also pure mathematics
>>15074837
this isn't the stupid answers thread

>>15074861

>>15074182
Wrong.

>>15074167
I'm mildly peeved.
>>15074169
Continuum hypothesis is independent of ZFC.
>>15074837
Remilia isn't a maid.

>>15074881
Looks like a maid to me? What makes her not a maid? I like the Maid you posted too.

>>15074927
>Looks like a maid to me? What makes her not a maid?
She's the house owner, there's just random fanart of her in a maid outfit.

>>15067565
By what mechanism does Permanganate oxidize alkyl groups on aromatic rings? Our textbook just sort of handwaves it as IT JUST HAPPENS TRUST THE SCIENCE OK???

can microbes/bacteria move a significant distance on their own? being a bit paranoid right now

>>15075059
Some bacteria are motile and some aren't, there many mechanisms that bacteria can use to move, the most common two mechanisms are cilia and flagella. Flagellated bacteria for example are very motile, IIRC examples of motile bacteria include: Escherichia coli, Proteus vulgaris, Vibrio cholerae. Examples of non-motile bacteria include: Klebsiella, Mycobacteria and Mycoplasma.

>>15075186
what about the distance? is it a case of small but fast or small and slow?

>>15075059
I eat raw meat.
4 years.
Raw rotten chicken doesnt even make you sick. In fact, you might even feel good after eating it.

Get over germs, and watch some raw meat youtube channels.

>>15067565
Which version of the Bible is consistent with my freshman biology book?

>>15075227
The speed of a bacterium depends on a lot of factors such as the species of the bacterium, the mechanism of movement and the nature of the medium.
As a very rough estimate, most motile bacteria move at a speed of few centimeters per hour in a semi-solid agar medium.

>>15074881
>Continuum hypothesis is independent of ZFC.
That anon wasn't asking for a set with cardinality between aleph_1 and 2^(aleph_0), he was asking about a set with cardinality between aleph_0 and aleph_1 which of course doesn't exist by the definition of aleph_1.

Anyone recommend me a good introductory but rigorous textbook on number theory?

Same for combinatorics?

MERRY CHRISTMAS LADS AND LASSES

5 differences
>>15075616
Thanks for correcting me.

What is "engineering physics"?

>>15075666
You are a worthless talentless trash just stay out of it.

>>15075829
>reminding me on christmas eve

>>15075834
Sorry just joking, try some Springer books

How many different ways can you visit 6 cities twice without visiting the same city twice in a row? I'm pretty sure you can use the inclusion exclusion principle for this, but have no clue how to.

>>15075836
ty anon i will check them out

>>15075923
me on the right

>>15075689
merry christmas, remi

>>15075689
Star, Hat, Flan, Sack, Bow
what's my prize?

Is Co2 to Carbon deposition possible at room temperatures?
t. non chemist

>>15076155
Well, plants manage it. Might not be the most efficient way though.

Let [math]f: \mathbb{R} \to \mathbb{R}[/math] be an increasing function (meaning [math]a \leq b[/math] implies [math]f(a) \leq f(b)[/math]). Furthermore let [math]a, b \in \mathbb{R}[/math] such that [math]a < b[/math], [math]a < f(a)[/math] and [math]f(b) < b[/math]. Then [math]f[/math] has a fixed point. Is my proof okay?

Let [math]M := \{y \in \mathbb{R} \mid a \leq y \leq b,\ y \leq f(y)\}[/math]. Clearly [math]a \in M[/math] and b is an upper bound for M so we can let [math]z = \sup(M)[/math]. Thus [math]a \leq z \leq b[/math] so [math]a < f(a) \leq f(z) \leq f(b) < b[/math].

Now let [math]y \in M[/math] be arbitrary. Then [math]y \leq z[/math] and [math]y \leq f(y)[/math] so together [math]y \leq f(y) \leq f(z)[/math] meaning [math]f(z)[/math] is an upper bound for M, so [math]z \leq f(z)[/math]. It remains to show that [math]f(z) \leq z[/math] which is clearly the case since [math]f(z) \leq f(f(z))[/math] so [math]f(z) \in M[/math] and thus [math]f(z) \leq \sup(M) = z[/math].

>>15076661
>It remains to show that f(z)≤zf(z)≤z which is clearly the case since f(z)≤f(f(z))f(z)≤f(f(z)) so f(z)∈M
That looks circular to me.

>>15076753
I got that by applying f to the previous inequality, which should preserve the inequality because f is increasing.

>>15076757
Right, I see.
You should probably state that explicitly instead of saying it's clearly the case.

Do all vector spaces, the underlying sets of which have uncountably many elements, have an uncountably infinite dimension?

is wolfram alpha dead? the natural language interpretation is complete garbage considering the state of AI in current year and wolfram is supposed to be on the forefront of this stuff. most of the results on mathematica stackexchange are from 5-10 years ago. i can't get it to plot a unit circle with points at evenly spaced angles without having to relearn the fullblown wolfram mathematica language which is also convoluted btw.

>>15076783
Forgot to mention that the underlying field of the vector space is either finite or countably infinite.

>>15076783
No, consider a finite-dimensional vector space over a field with uncountable many elements for an counterexample.

>>15076787
Sorry. I forgot this >>15076786 specification in my post.

even this example doesn't work in wolfram alpha

https://reference.wolfram.com/language/ref/CirclePoints.html
https://www.wolframalpha.com/input?i=Graphics%5BPolygon%5BCirclePoints%5B5%5D%5D%5D

>>15067565
Merry Christmas maids from Touhou. Thank you for usually letting me maidpost on your board without getting banned. I hope you all get some type of nice meal and some candy for Christmas.

I am given two points with coordinates:
[eqn]
P(x_0,y_0)
Q(x_1,y_1)
[/eqn]
I need to find an arbitrary point [math]R(x_2,y_2)[/math] on the line [math]\overline{PQ}[/math] which is distance [math]d[/math] away from [math]P[/math].

Pls give me the simplest solution.

>>15076810
(x2 - x0)^2 + (y2 - y0)^2 = d^2
(y1 - y0)(x2 - x0) = (y2 - y0)(x1 - x0)
Two equations and two unknowns.

>>15076825
What if the anon is not dealing with Euclidean metric?

>>15076830
Replace the first equation with one that says that the distance between P and R is d in your metric.

>>15067565
Why the fuck are you studying on Christmas day? Go spend time with your friends/families you cunts

>>15076851
im waiting for my family to wake up so we can start opening presents c:

>>15076851
That would be nice, yes, but fr some the words of a
graduate advisor (and some would believe me for
this) ring in their heads:
>...you just work, there are no holidays...

If I find infinitely many linearly independent vectors, can I then assume that the dimension of the space has to be infinite, too?

>>15077009
To specify, I’m unsure whether or not these infinite linearly independent vectors have to be in contained in a du space to draw this conclusion.

>>15077017
*subspace

>>15077009
>>15077017
>>15077019
Yes, this is correct. If your vector space has dimension [math]n \in \mathbb{N}[/math] then any set containing [math]n + 1[/math] vectors will automatically be linearly dependent. Conversely if you have an infinite amount of linearly independent vectors the dimension of your vector space can't be finite.

What happened to /sfg/?

>>15076851
I have no friends or family.

I have a set of numbers from 5 to 100

I am allowed to pick 8 numbers from that range.

And here lies the issue: Adding any combination of these 8 numbers together must always yield an unique result.

For example, let's say i pick numbers 6 7 8 9 10 11 12 30.

Then every addition of every combination of them must be unique.
6 = 6
6+7 = 13
6+7+8 = 21
7+8=15
7+7+8 <-- NOT this because 7 is used twice
...
and so on for all possible combinations of them
And every possible combination of them must lead to unique result.
Can someone provide me with a set of these numbers or a way to calculate them?

>>15077405
any set of numbers that are power of two will work

>>15077405
Can't be done.

>>15077440
There aren't 8 powers of 2 between 5 and 100. There are only 4: 8, 16, 32, 64. Powers of 2 multiplied by a constant would also work. If the constant is 3, there are 5: 6, 12, 24, 48, 96. But there's no way to get 8.

I'm looking for a pdf or source or whatever with 30-50 integrals to solve with all various methods, and the integrals are chosen in a way to guide you through all the most popular ways to solve integrals. I don't know what's the American equivalent of the course I'm taking, I guess Calculus II.

Also something similar but for limits to solve mostly using Taylor expansions.

Bonus questions: how do you guys learn proofs fast? I have 12 calculus proofs to learn in less than a month which is very doable but the main problem is that I have about 40 Linear Algebra proofs to learn in a little more than a month. They're all pretty short, most about half a page, but I feel like I'm going crazy and I barely got started

I want to show that the vector space of all arbitrarily often differentiable functions has a uncountably infinite basis. Can I use the set [math]\{e^x + c\}_{c\, \in\, \mathbb{R}}[/math] for this? These functions are arbitrarily often differentiable, of course. However there first derivatives aren't linearly independent anymore.

>>15077560
This doesn't work anyway with more than two vectors.

>>15077405
>>15077482
You can have at most 7. E.g. {5,6,8,12,24,48,96}. Any combination of {6,12,24,48,96} results in a distinct multiple of 6. Adding 5 results in a value which is congruent to 5 modulo 6, adding 8 results in a value which is congruent to 2 modulo 6, adding both 5 and 8 results in a value which is congruent to 1 modulo 6.

how fast is santa's sleigh? does he utilize ftl?

>>15077405
Here is a such set with 10 elements.

30,38,55,56,65,69,71,76,99

The construction uses Abstract Algebra (Field Theory).

>>15077756
Sorry it's only 9 elements.

Basically I used the fields F_121 and F_11 to construct a such set with 11 numbers between 1 and 120 and then removed the numbers that are outside the range.

For a n-dimensional real vector space [math]V^n(\mathbb{R})[/math], the basis vectors are defined as [math]|x_i\rangle[/math], which can be represented as column vectors with 1 in the ith element, and zeros everywhere else. We can then define an identity operator [math]\sum_{i=1} ^n |x_i\rangle \langle x_i|=\hat{I}[/math]. Where [math]\hat{I}[/math] is an [math]n\times n[/math] square identity matrix. Suppose we move to the infinite dimensional case where [math]n\rightarrow \infty[/math]. Then would it be reasonable to define the identity operator as (excuse the shitty notation):
[math]
\int|x\rangle \langle x|dx = \int \begin{bmatrix}
dx & 0 & \cdots & 0 \\
0 & dx & \cdots & \vdots \\
\vdots & \vdots & \ddots & 0 \\
0 & \cdots & 0 & dx \\
\end{bmatrix}_{\infty \times \infty} = \hat{I}
[/math]
?

>>15077833
It would make more sense without the integral in front of the matrix

is undergraduate level graph theory a difficult subject to become competent with?

how broad is this subject? like compared to calculus or linear algebra or statistics or any of the other undergraduate course subjects

>>15067565
Why do outsiders of science but who nonetheless call themselves "scientifically minded" think there is one monolithic, singular Science which is always true and cannot be contravened? I don't think it's even that shit term, Scientism, but it's definitely from some outside group that isn't doing nor even studying scientific fields. Some of them don't even think the sciences go do their own thing, and pretend like there is a single Science which all smart, liberal, and well-adjusted people drink from. Scientific consensus to them just means everyone agreeing that climate change is real and that all trans women are women.

I can sleep after drinking coffee and have no problem falling asleep at night, usually I'm out in 5 minutes even if I've drunk coffee all day
I wake up 2-3 times a night to go piss and have vivid dreams before waking up 100% of the time
Is there any research that could link waking up like this to caffeine? I am a caffeine addict and get headaches if I don't drink it

>>15077844
Now that I think about it, how would the basis vectors be represented in the infinite-dimensional case? Given the orthonormality constraint [math]\langle x |x'\rangle = \delta(x-x')[/math], what would the elements of [math]|x\rangle[/math] and [math]|x\rangle[/math] look like? Certainly, there would be a difference between the basis I described in >>15077833 for a finite-dimensional vector space. It's either that or the infinite-dimensional identity operator that's different.

>>15077405
can you pick prime nunbers?

>>15074519
I might be using the word coprime wrong, I just mean two numbers are coprime if gcd(a, b) = 1.
for example
>a=2, b=3 => ab=6, k = (2-1)*(3-1)/(2*3) = (1/3)
>x=5
then gcd(1, 6)=1 and gcd(1, 5) = 5 (so there are two coprimes between 1 and 5) which is close to k*x = (1/3)*5 = 1.66 which is close to 2.
It's like the number of coprimes are a linear function + some small deviation.

>>15077896
The identity operator is just the operator that takes a vector to itself. There's no need to define it using matrix notation in the first place, but if you want to do it anyway, you first have to pick a basis for the domain and range of the matrix. If you pick the same basis for both the domain and the range, then the matrix corresponding to the identity operator should be the usual identity matrix (1s on the diagonal, 0s elsewhere). If you pick different bases for the domain and range of the matrix, it can look different.

what types of note takers are y'all? notebooks, binders, or tablets? (or else)

im asking because I use notebooks but im tired of buying them and throwing them out so i am seriously thinking of getting a touchscreen device

>>15078023
Once you go tablet, you'll never go back

>>15078035
is that in a good or bad way? im obviously still gonna carry a small notebook or something

>>15078042
For me it was in a good way

>>15067565
>cirno thread
fucking FINALLY

>>15078023
I bulk buy loose leaves, and use a nice fountain pen. Tablets aren't very good if you do a lot of rough work.

>>15078073
rough work? what is that?

do you mean like physical stuff? i guess you can buy a hard case

and i'll always carry a notebook just in case i need paper for something

>>15078080
Math work where you do the thinking and calculations.

What are some formal or rigorous combinatorics books? Or just one written for math grads? I can only find very introductory books for high-schoolers or undergrads.

>>15078023
For taking notes from lecture, I started using blank printer paper + a clipboard. The clipboard gives a consistent writing surface wherever and a nice pen/pencil can't be beat either. I always number the pages of my notes so I know the order in which I take them. A paperclip or small binder clip keeps them together in a folder or an accordion organizer, if you're one of those people.
I used to be one of those people who used notebooks, but I realized the lines constrained my writing style, plus I'd usually never fill them up, so they were just a waste after the course was over. The freedom of blank paper has convinced me never to go ruled again.
For homework, I use a drawing pad but you could also use a tablet. Doing homework digitally really helps because working through problems, especially difficult ones, is rarely a linear process. You're going to be doing a lot of drafting and side calculations, so wasting paper on that isn't really a good idea. Plus, editing mistakes and making amendments digitally is a sinch compared to paper.
tl;dr notes on paper, homework digitally. Alternatively, just get a tablet for everything and make sure to make backups.

>>15078264
Blank notebooks exists.
>>15078023
If you are going to buy a tablet, but an iPad which supports Apple Pencil 2 (the new standard one doesn't). And ignore the Surface shill.

>>15076783
>>15076786
Yeah, since the set of all finite sequences of elements of a countable set is also countable.
>>15077560
No.
But you can show that [math]\exp (ax)[/math], [math]a \in \mathbb{R}[/math] are all linearly independent because they're all eigenvectors of the differential operator with different eigenvalues.
>>15078064
Pretty sure I pick Cirno fairly often for the OP.

If you pick cards randomly from an ordered, unshuffled pack of cards, are the chosen cards going to be as random as if we had just picked the top few cards from a shuffled deck?

>>15079048
yes

>>15079098
Thank you

/fit/ here. I need some brains to do some thinking for me because grug lifts weights, not numbers.

1ml of 200mg testosterone is 200mg. If my cruise dosage is .6ml per week, how much testosterone am I injecting?

Second question: If I switch to vials of 250mg testosterone, how many ml would I need to inject that to get the equivalent of my cruise dose?

Bonus points if you can show me how to figure this out on my own.

Is this
[math]\dim_{\, \mathbb{Q}}{\mathbb{Q}(\sqrt{2})} = 2[/math]
[math]\dim_{\, \mathbb{Q}(\sqrt{2})}{\mathbb{Q}(\sqrt{2})} = 1[/math]
true?

>>15079235
Yes.

>>15079224
.6*200
.6*200/250

>>15079279
Well that ended up being a lot more simple than I thought it would be. I appreciate it.

Can someone write me a hypnosis script to continue studying calculus? I'm too lazy to write one and I know and recognize the one I wrote before helped me, but I need another dose/injection/more now of motivation/programmed behavior to get this done. I'm doing Stewart Calculus if that makes a difference though I do have access to Morris Klein's txbk.

>>15067565
Hey, lurker here.
This is fucking embarrasing but how the fuck do you guys study? How do you even learn something new??
Im not joking, somehow I made it our of college and strat working until now that Im 30yo and I have nerver pick up a book, sit my ass and study. My mother was a teacher and the few time she tried to teach me I was able to lie my way out of it just because I was smart enough, same in school always managed to pay a the smart dedicated kids to do my work instead of studying..
I feel like I have peaked and Im not able to learn anything else, and beign a CS fag that is really bad.
Any of you have like a guide or something? I know this sounds retarded but honestly dont know where to start...pls no bully

>>15079354
>sit down on my desk
>read through the book about the topic I'm studying
>analyse the proofs, theorems, do the exercises at the end of the chapter
I enjoy studying and do it for 4 to 5 hours daily.

>>15079379
>>sit down on my desk
>>read through the book about the topic I'm studying
>>analyse the proofs, theorems, do the exercises at the end of the chapter
>I enjoy studying and do it for 4 to 5 hours daily.
Yea, that's roughly what I had written up. Thanks for reminding me, and should I continue with this script? What am I supposed to feel? Most of the time I feel inadequate and suffer because of that.

>>15079399
Why'd you feel inadequate? Well, when I'm studying, I feel great. I feel anticipation and fascination for the topic.

>>15079417
I had to rewrite dozens/hundreds of pages of answers getting them wrong repeatedly because I want to verify the calculus as it is without calculation error, fallacious reasoning, or faulty pedagogy (which is really sus, stewart's calc is a 4chan classic so I'm wary this used textbook is a stolen hack with misleading answer keys, really it turns out I'm dumb). I find it all so frustrating. Like, I'm doing everything I can to fuck up my reasoning and etc, and the book doesn't give good arguments, proofs, or explanation well enough either.

>>15079433
Often 4chan recommends books that are nonsense and a meme.Try another one, no big deal. Are you doing mathematics for its own sake or are you a comp-sci, engineering student?

These are important points to consider. I hope I didn't catch you in the middle of writing a response with this reply. I practice auto-hypnosis in an apartment setting so it is very likely someone is maliciously sending me erroneous suggestions while I'm hypnotized.
And pedagogy, correct argumentation/syntax, calculation is all part of organization and learning/training math anyways so I better get used to it.
FUCK I HATE MYSELF I'm so fucking demotivated and want to desperately distract myself with the nearest math textbook because that's all I got going for me right now.
I was reading Morris Tannenbaums and got stuck on the meaning of 5000 B.C. and was retardedly running in circles with a complete proof, because I had wrong input like some cross eyed catastrophe.

>>15068168
god you're such a fucking retard

>>15079451
It's not nonsense though! I really love these books and idealize the authors including their squishy names and monolithic exotic publishers. But I would say 'lolita' 'american psycho' 'clockwork orange' 'fight club' is a serious mindfuck combined with dissociation. scientifically evil and maliciously corrupt as a toxic set of books to infect virally with.

>>15079464
Nonsense in terms of reading it as a beginner.

>>15079473
I forgot to answer. I'm not a student.
I shitpost most of the time.
That's another thing I need help with currently, getting off this machine.
I have no problem with getting the right answers anymore, just motivation as of now.

>>15079481
>learn the fundamentals (what would be taught in a preparatory course of a university); for example methods of proofing, "how do I read a proof/theorem/definition and check whether I got it", simple set theory operations and mappings etc.
>go on with analysis and linear algebra and learn what students at a university would learn in the first semesters (buy a book that was a script at a university)
>watch youtube videos that explain these topics
I also do sport regularly, eat considerably healthy and I don't study with my computer since it distracts me. This system works for me

>>15079499
Anon, you're a step ahead of me, I guess you could say.

>>15079519
It's a grind for everyone. Just wake up tomorrow and do it.

>>15079551
Very wholesome post, fren

Why does Bob Blo act like he knows wtf he's talking about and yet he knows shit about me and can't read has nothing to say worth saying all invalid garbage taxing the economy and planet nor is he able to add and subtract basic quantities or comprehend any of the arguments i have laid out for him why is he pulling cards out of his rectum brane? why is he assuming the ultimate the penultimate the divine irrespective of pragmatic bases and assuming retardation before enlightenment? why is he such a cringey convoluted edgelord filled with deceit and conviction in false virtues and deranged condescendingly to the basic obstacles of life when he shits on the floor and smears it in the kitchen to spread his disease in the facility that we are sharing? why is he such a shit head filled with spite and doesn't he have something better to do than troll me and act like we're equal when he's the fucking abuser the user and drug pusher who wants to slam cocks in orifices which reply 'no?' why is he pushing his rape and his autism and his agenda projecting his transphobic androphobic gynephobic lateral genocide of humans because he's so insecure and blames you for everything because he deals with privilege and entitlement daily and can't get a grip because he's sics shit at life and wants to poke at your iris out with a molten smore on a stick? why is he so mean ill spirited and mislead and why does he get all the love in the world? fuck that guy i srsly have ill will now

he doesn't know shit.

we are not the same.

>>15079599
he's taking my fucking credit for shit he didn't get right this hurts frustratingly so fucking much i'm fucking pissed
rant over

Does a particle have an orientation? Like up down, front back, left right? People and things (collections of particles) do but I guess that orientation is just a description of relative particle positions to each other? Even when a particle is bonded it wouldn't have an orientation right, it might be elongated or something in some axis from an observers point of view, but if it were to "rotate" say (I don't think they actually can? That's a macroscopic property) then the elevator elongated part stays fixed because it's related to electron cloud overlaps which don't 'move'

>>15079854
> Does a particle have an orientation?
No, because they have rotational symmetry about every axis.

So, why the fuck did nobody even get a day's worth of notice for the burger cold snap? Wouldn't the winds have to have rushed through canada at around 200 km/h to get to the US within a day?

>>15079892
> why the fuck did nobody even get a day's worth of notice
they did, they got even more than one days notice. doesn't mean people listen.

https://twitter.com/NWSWPC/status/1605244824478576640

>>15077696
Time dilation. From Santa's perspective the night will never end until every present is delivered.

>>15079854
>>15079885
okay then, follow-up: if particles don't have orientation, how would you describe the position of 1 particle relative to another from the perspective of one of those particles?

I suppose distance? maybe that's the only one too? after all neither particle is aware of their own movement, or the others movement, just what the relative difference is between them. (after all, if one was orbiting the other, it only looks that way from a single perspective, remove the concept of orientation which makes something look like it's orbiting and it just looks like they are a static distance apart, unmoving, right?)

wien's displacement law says that the temperature of fire is inversely proportional to its wavelength (i think, i only skimmed the wikipedia page tbvh). theoretically, could there be a flame that only reflects infrared light? or does fire only emit light? in either case, would a super-hot flame turn black or invisible?

>>15080422
> could there be a flame that only reflects infrared light?
No, wien's law is a consequence of black body radiation; light that is emitted from an object.

> would a super-hot flame turn black or invisible?
No. The temperature only changes the wavelength of the spectrum's peak. So in theory you could have something hot enough to mainly emit the ultra-violet, and hence would not be visible, but there would still be some light in the visible range.

What kind of a light source did people like Newton and Christiaan Huygens use for their optics experiments? Like a lamp or the sun's light, just through a hole perhaps? It could only be so many things that would be an artificial (or natural for that matter) light source in that time, I suppose

Suppose i have a point like fluid bounded by some cylinder without a top. It behaves as if there is a gravitational effect and do the fluid will find its level when rotating the cylinder.
The top surface of the cylinder creates an ellipsoidal shape as the cylinder is tilted, but if the reference persoective is always from the top of the cylinder looking down, the top point like layer is only ever a circle. What is the property of a point which permits the same number of points, infinite, to produce different lengths, areas, and volumes. How does this relate to the banarch tarski paradox?

scilet here
what's the ultimate method to get into math?

>>15080422
>theoretically, could there be a flame that only reflects infrared light?
Nersnt glower. "Flames" are technically just soot glowing with blackbody radiation.
>or does fire only emit light?
Infrared is light
>in either case, would a super-hot flame turn black or invisible?
The tail end of a high temperature blackbody spectrum should still be visible, even if the bulk of it is in the invisible shortwave.

>>15075003
To my knowledge, the mechanism is not well known. Mechanistic work is tricky, and good answers can't just be handwaved into existence.
A quick search of the literature may prove otherwise.

>>15070737
Think of a project and build it.
>always worried I'll get the wrong voltage or something and have my face peppered with exploding components
That's why you buy a dozen LEDs and blow them up intentionally, to get over your fears and learn how to identify a short circuit

How do you deal with the fact that the direction you followed the past n months in research ended up being a dead end?

All my lab mates are publishing left and right and here I am, wasting my fucking time on bullshit. I know all of us experience this from time to time but it's been a rough fucking year and I now know a lot about a niche field that won't ever be useful to me.

why aren't there any sanguinivorous butterflies?

>>15081517
I could've sworn there was one

>>15076155
Your question is somewhat vague. Elemental carbon or carbon compounds? You can turn CO2 into carbonates at room temp by bubbling it through a strong alkali solution (NaOH/lye in water).

>>15080873

how does eating too much you throw up work? is it just that the stomach is overloaded? I've heard the stomach clears fully about two hours after eating, if that's true does that mean someone eating once every two hours wouldn't throw up from eating too much? once it clears the stomach would eating too much just present as big shits?

if [math]F(t)[/math] is a polynomial on [math]t[/math], how can I argue that
[eqn]P(x) = \sum_{t=1}^x F(t)[/eqn] is a polymial?

>>15081907
induction

(First of all I didn't mention that [math]F(x),P(x)\in\mathbb{Z}[x][/math] or something)
>>15081958
Well I can say that [math]P(x) = F(x)[/math] for [math]x = 1[/math] and then [math]P(x) = P(x-1) + F(x) [/math] for each [math]x > 1[/math]. Also I am not sure if it's actually always a polynomial. What about the next polynomial [math]Q(x)\in\mathbb{N}[x][/math]:
[eqn]Q(x) = \sum_{i = 1}^x [f(x,i), \text{an expression in $x$ and $i$}][/eqn], is this a polynomial? For every [math]i[/math] it is a polynomial on [math]x[/math] and we just sum [math]x[/math] of those, but I am not sure this reasoning is correct. However interpolation seems to work.

>>15081907
Can't you just say that a finite sum of polynomials is a polynomial?

>>15081907
Constant after you take enough differences.

>>15082021
Well maybe you can, but since [math]x[/math] is also the parameter of the polynomial I am not sure if you can say that [math]x[/math] is fixed and so it's finite etc..
I was too stupid to start writing shit. Now that I did I realised that if [math]F(x)[/math] is a polynomial (of degree [math]n[/math]then for some [math]a_i[/math]
[eqn]F(x) = \sum_{k=0}^n a_k x^k[/eqn]
So
[eqn]P(x) = \sum_{t=1}^x F(t) = \sum_{t=1}^x \sum_{k=0}^n a_k t^k =\sum_{k=0}^n a_k \sum_{t=1}^x t^k [/eqn]
and now it can be proved that [math]\sum_{t=1}^x t^k[/math] has a polynomial closed form (Faulhaber's formula). I can accept this as a proof.
As for the intuition, I can understand it in integras (integral of polynomial with [math] x[/math] as bound is also a polynomial) I just don't feel it as natural for the integer case.
Also since Faulhaber's formula isn't trivial I have a feeling that just saying "finite sum of polynomials is a polynomial" doesn't really capture the complexity behind the case, I might be wrong though.
>>15082034
Yeah I forgot to mention in my original post that I am in the integer ring. Anyways this isn't an exercise or whatever, I'm just trying to find a way to intuitively understand summing [math]x[/math] polynomial terms where [math]x[/math] is the parameter.

>>15082042
>Yeah I forgot to mention in my original post that I am in the integer ring.
First of all, the statement isn't true over the integers ring. See the sum of sequential integers formula for the most basic counterexample possible.
Second of all, I said difference, not differential. [math]\Delta f(x) = f(x + 1) - f(x)[/math] Prove that [math]\Delta ^n f(x) = 0[/math] implies [math]f[/math] is a polynomial and you're done.

>>15082087
>the statement isn't true over the integers ring
yeah I just noticed, besides Faulhaber's formula doesn't have integer-only coefficients.
As for the difference thing I don't get why I should do that? Why should it be constant? I'm not talking about a specific case here.

Anyways the problem is that Defining F and P like I did then interpolation works (at least such that the integer points work). So it must be a polynomial of some sorts. I just can't find a way to understand it rigorously.

>>15082101
>As for the difference thing I don't get why I should do that? Why should it be constant? I'm not talking about a specific case here.
[math]\Delta ^{n + 1} p(x) = 0[/math] if [math]p(x)[/math] is a polynomial of degree [math]n[/math]. If you prove the converse, your desired result immediately follows since [math]\Delta \sum_{t = 1}^x F(t) = F(x + 1)[/math], a polynomial.
>I'm not talking about a specific case here.
I have absolutely no idea what do you mean by that.

>>15067565
I need to measure the [math]\ell_1[/math] norm of the multilevel wavelet transform.

Is the correct way to do this to take the multilevel transform and then stack it into a single image as in picrel and then measure the [math]\ell_1[/math] of this? or do I just need to measure the norm of the LL band image (upper left corner in picrel)?

>>15067565
What's stopping me from saying there is an axiom that there is a cosmic, infinitely large tranny that causes time dilation by opening up their post-op pussy that is the curved universe?

When we say that a complexity class is a subset of another complexity class, such as [math]\texttt{P} \subseteq \texttt{PSPACE}[/math] what do we mean? I don't know how to visualize it, is it that if I pick the bigger one the other is bounded? How am I suppose to interpret it

>>15082924
>what's stopping me?
taking your meds

>>15083447
Your appeal to the "reality lollies" won't work on me.

>>15067565
i want to turn cirno into a mommy

How do I learn the common statistical distributions better? Like the only way one is a binomial distribution. How the fuck am I supposed to distinguish between normal, T, exponential, and geometric distributions? Those names are so unhelpful for remembering the kind of sampling phenomena they describe.
I realize my question is super retarded and open ended (how do I get better at statistics?), but godamn there must be some handy ways you used to learn.

>>15082924
Such axioms are used that produce mathematics that are useful to engineers, architects, physicists. However, I think, all mathematics that do not contradict themselves are valid.

Why do I need to urinate immediately EVERY SINGLE TIME after I ejaculate? Even when I didn't need to before?

>>15083916
Okay, here's how I remember them in terms of their
graph shape:

normal
>like the hairstyle of Mary Sue--as normal as it can be

binomial
>discrete version of the normal, discrete (separated) bars

student's t
>a student's attempt at a normal graph--not quite perfect, but usable

exponential
>like an exponential (decay) graph

geometric
>almost like exponential, except with discrete trials (or bars)

Is Galois theory fun?

>>15084012
Basically, the piss local and the cum express both
share the same stretch of track--the urethra. There
is a valve at the base somewhere (don't know the
name) that switches between both streams.
So, whenever you're done ejaculating the valve
switches over to urination where, perhaps, the
bladder might be full and you urinate.

Have you tried not drinking anything?

I'm retarded so how do I stop being retard?

>>15084222
There is no cure, brother. Just know that you are not alone.

>>15067565
Can someone explain how g is surjective here. I'm complete loss on the proof on how it is surjective.

>>15084569
g(f(X)) is the identity map on X, and so must ultimately map every element of X onto itself, which necessitates being able to map to every element of X. So g has to be surjective, since otherwise your composition wouldn't be.

>>15084580
So basically, for all X, we can find f(X) in Y that satisfy the identity g(f(X)), which forces g to be surjective because f(X)? Does the claim [math]g(f(X)) \subset g(Y)[/math] important for the proof or is it more for aesthetic? Also, thank you for the swift response.

>>15084617
That's the idea, yeah. The subset claim shows that f(X) is necessarily within the domain of g, an extra step which isn't core to the idea of the proof but does cover your bases in showing that g is surjective as defined and that the composition is well-defined in general.

>>15084676
Thank you anon.

I have the flu and can't think straight, can someone explain to me how [math]2\sqrt{2+\sqrt{3}}[/math] is equal to [math]\sqrt{2}+\sqrt{6}[/math]

>>15084991
[math](\sqrt{2}+\sqrt{6})^2=4+2\sqrt{12}+6=8+4\sqrt{3}=4(2+\sqrt{3})=(2\sqrt{2+\sqrt{3}})^2[/math]

>>15085046
first 4 should be a 2. I don't know why I typed 4. Clearly I knew it should have been a 2.

>>15083916
Geometric because its PMF is a geometric series.
Exponential because it models exponential decay.
Normal because normal phenomena eventually follow the distribution.

Shit bros, I stopped going to classes one semseter without dropping out and so I got all Fs, now I got an email that even though I passed all the classes I needed to get into college of engineering they might not let me in because of prior poor grades. They'll let me know in a week. If I can't get I'll have to major in eng lit or something. Tell me there's hope

>>15085165
And why did you do that anon?

Are there any material scientists here? I need a little help.
How is pendular annealing better than spheroidizing annealing? I know that the pendulum annealing is faster and more economical, but my teacher wants me to explain all the details of the process and what exactly happens in the structure of the metal during the pendulum annealing.
I just can't find any normal sites where it explained with details

>>15072929
the remainder would be 1 if dividing by any of those primes, so it’s divisible by a a number not in the list