/sci/ - Science & Math

am I retarded? how is B not greater

>>14776278
fuck nevermind I had a brainfart, for some reason I was thinking 4 + y was even

https://youtu.be/XRr1kaXKBsU?t=779
Why does the light remain in a straight line to an external observer?

>>14776276
I have recently (about 2 months ago) discovered that touhou is a thing, now it is apparently everywhere here, has this board (or this thread at least) been always posting touhou pics or am i experiencing the frequency illusion?

>>14776314
At least three years now. You can see in the catalog.


I might have been unnecessarily harsh with the questions this time.

Unanswered questions:

Maths questions:
>>14763648 [Quaternions are kind of a meme subject tbqhwyf]
>>14766484 [Not my area, but algebra, lie algebras, vertex operator algebras and you can go at it, I think.]
>>14773961

Biology questions:
>>14772188

Stupid questions:
>>14761910
>>14761949
>>14762357
>>14763249
>>14763359
>>14764157
>>14764624
>>14764661
>>14766089
>>14767300 [Because the domain is bidimensional and you represent either the real or complex part of the image with colors. Or you have a 3d graph and the colors are the missing axis.]
>>14768116
>>14768594
>>14769956

>>14776319
>You can see in the catalog.
The archives, that is.

>>14776276
Suppose I am considering jumping from a building, but I don't know what floor I am on. I weigh 100 kg and when I jump from this building I land on a cylinder 4" in diameter and a meter long and it impales me, but not through me. I travel on the cylinder for 40 ms before hitting the ground and I rebound back up 0.5 m in 160 ms and finally come to rest another 160 ms later, 0.2 m off of the ground.
What height did I jump from?
If this system was viewed as the hydrodynamic system absorbing an impulse, what is the τ(tao) or ζ dampening terms?

>>14776314
>I have recently (about 2 months ago) discovered that touhou is a thing
you should read higurashi!
>has this board (or this thread at least) been always posting touhou pics
honestly i think only like half the /sqt/ are 2hus. i remember a while back, wemi stopped posting for a month because he got tricked into think hot water freezes faster than cold water.
>>14776319
this >>14764157 is not a stupid question. the last two threads didnt have it. its on the verge of becoming lost media.

>>14776346
>this >>14764157 is not a stupid question. the last two threads didnt have it. its on the verge of becoming lost media.

Consider the following:
>open either warosu.org or eientei.xyz
>click on /sci/
>type scg into the search bar
>scroll down
>it's there

test
>>14763648

>>14776368
>warosu started achieving /sci/ again
>search works again
wow

>>14776319
might as well try to answer as many as possible
>>14763648
never studied quaternions specifically, but knowing abstract algebra, the wikipedia page looks pretty elementary
>>14766484
First spend a year learning abstract algebra. Find a textbook and watch these.
https://www.youtube.com/watch?v=O4plQ5ppg9c&list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_
https://www.youtube.com/watch?v=qFBDbpjtjcM&list=PLAvgI3H-gclZ-DYOVyyTkJBUXZ_R1JEZP
>>14773961
It better not make any difference since R is symmetric. Left and right multiplication makes a difference, but the two alternate worlds are isomorphic.
>>14761949
Opposite of a sigmoid curve
>>14762357
not much, apparently
>>14764661
not sure, but no one is going to pay to work. Plus europe is socialist so it can't be worse.
>>14767300
shallow answer, but to represent additional data such as additional dimensions or rate of divergence
>>14768594
looks like a tensor. Don't EVER believe a physicist or scientist explaining tensors. They are suspended multiplication. Don't forget it.

>>14776391
>he hasn't taken the eienteipill
Bruh moment.
I'm the one hosting it. You can trust your good friend remiliafag not to log your IP, can't you?

>>14776346
Honestly i never consumed any anime or anime-related media, i never liked anime in general until i discovered 2hu, it's mostly the music that got me into 2hu
I feel slightly sad that i discovered 2hu only now because i feel too old to enjoy looking at pics of anime girls
>higurashi
Is that a 2hu manga? if not then i'm probably not reading it

>>14776447
Wouldn't it be nice if Revy could quit her 4chan addiction after this
https://youtu.be/fKkOmXNyWUc

>>14776436
>I'm the one hosting it.
pretty ballsy to disclose that here. youre gonna end up like that one namefag on /sp/.
but thanks for the heads up, ill make sure to boot up a VPN before looking at it.
>>14776447
>Is that a 2hu manga?
its a sound novel from 2003.
>>14776457
we have enough avatarfags here.

>>14776474
KEK they're all me

I have not yet taken any college/professional level chemistry courses. How do I read this?

>>14776474
>pretty ballsy to disclose that here. youre gonna end up like that one namefag on /sp/.
How so? People post personal websites in /g/ all the time and it's fine. Also at least 80% of the personal info I post is misdirection.

>>14776486
https://en.wikipedia.org/wiki/Skeletal_formula
>>14776487
i was alluding to the fact that you may or may not have a stalker, a la that one namefag on /sp/.
i dont think ive ever seen you post any personal info, except i think you mentioned one time youre italian or something.

But I've identified the problem with /sci/ and 4chan.

A teacher once said teaching is fun, but you never get to progress yourself because its the same stuff over and over again.

>>14776518
i once TA'd for a professor that said "they dont pay me to teach, i'd teach for free, they pay me to grade"

Let [math](a_n)[/math] be a sequence with [math]a_n \geq 1[/math] for all [math]n[/math] such that [math]\lim_{n \to \infty} \left( a_n + \frac{1}{a_n} \right)[/math] exists.
Prove that [math]\lim_{n \to \infty} a_n[/math] exists.

Is there any way to do this only using the definition of the limit?

(I know that you can solve this by using differential calculus to prove that the function [math]f:[1,\infty) \to [2,\infty)[/math] with [math]f(x) = x + \frac{1}{x}[/math] is a homeomorphism but there should be a more elementary method.)

>>14776584
?

f is a continuous bijection hence its inverse is too. an+1/an =bn -> b by hypothesis.

Since continuity implies sequential continuity f inverse (bn) converges to f inverse b.

lately I've been drinking myself to into oblivion and I'm getting noticeably more and more stupid is this reversible?

>>14776638
I hope you die of liver failure for unironically seeing any value at all in onions faggot garbage like in the image you posted.

>>14776655
It's like the freddy kruger effect haha

>>14776276
Why do people say psychology is a "soft" science, or even shouldn't be included in the sciences?

>>14777150
Reproducibility crisis

>>14776319
None of the previous thread's unanswered questions have been answered either, in case someone here has some time to kill

>>14776276
Scientifically speaking, why do Wildberger, 0.999=1, Mandlbaur, vaccine threads, etc. always get so many replies on /sci? Is this board really that stupid?

>>14777390
Wildberger is beyong your understanding. He is dangerously and esoterically genius that's why you blend him with the stupids. You are just retarded.

>>14777390

>>14777390
Mandlbaur threads get so many (You)s because the guy replies to every single post individually, even if it is just a stupid fucking shitpost or insult. He also has severe Alzheimer's, which is why he often replies to the same post twice (or posts not even related to him). As for these other types of threads, they just have their own resident schizos, from what I know.

What are the long term effects of inflammation from a long term wound like pressure sores? Those things can last for years won't the extra inflammation fuck up the heart?

>>14777390
>Is this board really that stupid?
Yes.

>>14777405
It is well known that long term inflammation is one of the main causes of cancer
For example, smoking causes chronic inflammation of the lungs which is associated with lung cancer, while drinking causes chronic inflammation of the liver which is associated with liver cancer.
The mechanism is believed to be as follows:
In an inflamed area cells die and divide and die and divide again. If this cycle of death and division lasts for a very long time (years or decades) then it is possible that some cells can aquire mutations that makes them precancerous (the more cells divide the more likely they're to mutate) these precancerous cells may aquire more mutations that make them cencerous.
If you're interested in the process of carcinogenesis (which i oversimplified above) i suggest reading the 'Hallmarks of Cancer' by Hanahan and Weinberg
>won't the extra inflammation fuck up the heart?
I'm not sure what you mean by this, if the inflammation is localized in the skin such as in pressure sores for instance then i don't see how it can affect the heart unless you're losing blood or fluids from the wound.

>>14776276
If 0.999...=1 then 0.111...=0

What is wrong with this?

>>14777751
Everything after the word 'then'

>>14777603
>t is well known that long term inflammation is one of the main causes of cancer
Do frequently damaged and then repaired/replaced tissues have shorter telomeres compared to the rest of the body?

>>14777751
0.000…=0

>>14777757
Depends on the type of tissue, stem cells can regenerate their telomeres, while differentiated cells can't
Take the skin for example, the skin is generated when basal cells at the lowest layer of the epidermis divide, when such a cell divides each of the resulting two cells has 1/2 chance of either becoming a mature skin cell or continuing as a stem cell so as to maintain a stem cell population. The same is true for intestinal epithelium which, just like the skin, is regenerated every week or so.
However if you consider liver cells, then these cells aren't stem cells, there are no liver stem cells, instead when the liver is damaged the cells simply divide to repair the tissue so they have shorter telomeres (if you have chronic liver damage), liver cells have a remarkable ability to divide compared to other differentiated cells, it is sometimes said that the liver can regenerate half of itself if it is damaged to that extent, however i'm slightly doubtful of that.
TLDR; tissues that repair themselves by dividing have shorter telomeres (examples: liver, smooth muscle tissue) while tissues that repair themselves by having stem cells that replace them don't (examples: skin, intestinal epithelium, blood cells)

>>14777751
>0.111
1 - .9... = .0...1

>>14777757
>>14777795
To make it more clear i made the list below, this is not a complete list, it's just to give you a general idea:
>cells that can divide and regenerate their telomeres (all of them are stem cells):
Basal cells (in skin, intestinal epithelium and other epithelial tissues)
Hematopoietic stem cells
Any other kind of stem cells
Cancer cells
>cells that can divide but can't regenerate their telomeres:
Hepatocytes (liver cells)
Lymphocytes
Smooth muscle cells
Fibroblasts
Endothelial cells
>cells that can't divide:
Neurons
Heart muscle cells
Skeletal muscle cells
RBCs (Obviously since they don't have nucleus)

>>14777834(me)
>all of them are stem cells
Except the cancer cells

Anyone know of a good book on "practical cryptanalysis"?
Maybe that's not the right way to call it, but I'd like something where I might start feeling a bit confident in analysing cryptography protocols.. even with stuff like building and using rainbow tables and actually attacking the protocols (demand on mathematical skill may be high in the book).

>>14777218
Don't other sciences have the same issue?

>>14777884
Practical analysis isn't about cracking the protocol but disseminating shit policies and procedures which allow you to have backdoors inherited into some implementation. There used to be a screencap on this as intel agencies have been doing this for a long time. How many hacks were directly the result of discovering some feature wasn't type checking some variable.

>>14778255
OK, that sounds like something a book can't cover, one must just acquire some experience.
But I have to say that having some base skill is still important imo. I have some "theoretical" knowledge of cryptography and also some knowledge of comp. networks, but I know I'm still missing a lot that a good book could patch.
Exempli gratia: I know the A5/1 protocol that is still in use is weak as hell, but I just wouldn't be able to actually put together HW and SW to sniff and decode text messages of people around.

Ok i must be very stupid to get stuck on this one
>Exercise 2.2.7. Show that X and Y are independent if and only if for all x, y, P(X ≤ x, Y ≤ y) = P(X ≤ x) P(Y ≤ y).
It's very easy to show that if X and Y are independent then P(X ≤ x, Y ≤ y) = P(X ≤ x) P(Y ≤ y) must hold but how do i prove the converse?

Context: The definition of independence here is that X and Y are independent if for all x, y∈R if the events {X=x} and {Y=y} are independent, the book then proves this definition is equivalent to P(X∈A, Y∈B) = P(X∈A) P(Y∈B) for all sets A, B⊂R

>>14778448
How many x in R have P(X=x) nonzero?

>>14778511
It's not specified but from the context i guess that number is countable becuase the book introduces continuous and discrete probabilities seperately and i'm still in the discrete pobability chapter, though i feel the proof shouldn't depend on how many non zero probabilities are there.

>taking the gre tomorrow
>got 80% of practice questions wrong
scientifically speaking, should I just kill myself?

>>14778535
The proof for the uncountable case is non-trivial. You need Dynkin's theorem. You may be able to get away with the countably infinite case with an infinite sequence of unions, intersections, and complements which equals an arbitrary countable set.

>>14778535
You should give up on it until you learn Dynkin's Theorem. But knowing statistics professors you probably won't be taught it.

>>14778557
ok then how do prove it for the countable case?

>>14778583
do i*

>>14778575
luckily i don't have to deal with statistics professors because i'm self studying probability theory

>>14778583
>>14778594
Sec, trying to figure out the countable case

>>14778448
By the assumption the sigma algebra generated by the events {X ≤ x} is independent from the sigma algebra generated by the sets {Y ≤ y}.
{X=x} is an element of the sigma algebra generated by the events {X ≤ x} since
[eqn]\{ X=x \} = \{X \leq x\} \cap \left( \bigcap_{n=1}^\infty \left \{ X \leq x - \frac{1}{n} \right \} ^c \right)
[/eqn]
and {Y=y} is an element of the sigma algebra generated by the events {Y ≤ y} since
[eqn]\{ Y=y \} = \{Y \leq y\} \cap \left( \bigcap_{n=1}^\infty \left \{ Y \leq y - \frac{1}{n} \right \} ^c \right) [/eqn]
So the events {X=x} and {Y=y} are independant.

>X and Y are independent if for all x, y∈R if the events {X=x} and {Y=y} are independent, the book then proves this definition is equivalent to P(X∈A, Y∈B) = P(X∈A) P(Y∈B) for all sets A, B⊂R
This definitely doesn't hold for random variables in general. The sigma algebra generated by the single element subsets of R only includes the subsets of R that are either countable or whose complement is countable.

>>14778594
>>14778583
[math] P(X \in (a,b]) P(Y \in (a,b]) = P((X,Y) \in (a,b]^2) = P((X,Y) \in \{(p_i,p_j)\}) = \sum_{i,j} P((X,Y) = (p_i,p_j)) [/math]
using countable additivity. Take [math] a \rightarrow b [/math] and use nested intersection property to get [math] P(X = b) P(Y = b) = P(X=b,y=b)[/math]
Your textbook showed this was enough.

>>14778671
>TeX

>>14778624
If an element is generated by independent events how can one show it implies it is independent without fancy theorems?
>>14778671
Think you need to modify this to use two different (a,b]'s. Missed that your textbook had it for different points.

>>14778624
Uhhhh i have to prove this without sigma algebras because the book i'm reading doesn't introduce measure theory, i specifically chose this book because i don't know much measure theory and i wanted something rigorous (see attached pdf)

>>14778721
I have a PhD and understand measure theory and even I have a question >>14778695 kek.
Unfortunately you NEED sigma algebras for probability. Statistics professors give little emphasis to the underlying axioms of their discipline.

>>14778721
Anyway hopefully this >>14778671 works. Spend an evening to read this sometime. https://almostsuremath.com/2019/10/06/the-monotone-class-theorem/
You'll understand measure theory better than many statisticians if you do.

>>14778727
>Unfortunately you NEED sigma algebras for probability
I know, i just want to learn the basics of probability first, then learn measure theory to improve it.
As the book's preface put it:
>As a result of my approach, it will become clear where the limits of this approach are, and this in fact forms the perfect motivation to study measure theory and probability theory based on measure theory later in the study. Indeed, by the end of the book, the student should be dying to learn more about measure theory.

>>14778736
I don't understand how >>14778671 works when a=infinity

>>14778743
Probability is not a precursor to measure theory. Measure theory is the precursor to probability. Its like studying topology without knowing what an open set is.
>a = infinity
FUCK not again. I wrote out the whole thing and then going to copy 4chan closed it and lost it. This fucking happens all the time.

Fix your fucking latex window 4chan.

Turn P(a < X \leq b)P(c < Y \leq d) into subtracted intervals and multiply out.

>>14778743
>>14778779
Sure you can study the applications of topology without knowing what an open set is, but any "proof" is not a proof at all.

>>14778779
If you mean like this[eqn]P(a<X\leq b)P(c<Y\leq d)=P(a<X\leq b, c<Y\leq d)=\sum_{a<i\leq b,\atop c<j\leq d}P(X=i, Y=j)[/eqn] I can see how this works when i take a to b but how does the assumption imply the first step when [math]a\neq\infty[/math]?

>>14778779
If you mean like this[eqn]P(a<X\leq b)P(c<Y\leq d)=P(a<X\leq b, c<Y\leq d)=\sum_{a<i\leq b,\ c<j\leq d}P(X=i, Y=j)[/eqn]I can see how this works when i take a to b and c to d but how does the assumption imply the first step when [math]a,c\neq\infty[/math]?

>>14778842
[math] P(a< X \leq b) = P(X \leq b) - P(X \leq a) [/math]
Multiply two of these out and recollect.

>>14778854
Oooh i see now, thank you very much

reposting

>>14779100
>3.
By g-inverse you mean any generalized inverse or a specific one?
Assuming you mean the former, you can ansatz
[math]
\begin{pmatrix}
\lambda & \lambda & \lambda & 0 & 0 \\
\lambda & \lambda & \lambda & 0 & 0 \\
\lambda & \lambda & \lambda & 0 & 0 \\
0 & 0 & 0 & \theta & \theta \\
0 & 0 & 0 & \theta & \theta
\end{pmatrix}
[/math]

and then apply the definition to find the correct [math]\lambda[/math] and [math]\theta[/math]
>4
Elaborate on what is meant by g-inverse. Generalized inverses can be funny and this isn't necessarily true.

>>14779155
A generalized inverse of a matrix A is any matrix G such that AGA = A.

>>14779171
Set
[math]
A = \begin{pmatrix}
1 & 0 \\
0 & 0
\end{pmatrix}
[/math]

Consider that with
[math]
B = \begin{pmatrix}
1 && 0 \\
0 && \lambda
\end{pmatrix}
[/math]
you always have [math]ABA = A[/math], meaning [math]B[/math] is always a generalized inverse.
But [math]B[/math]'s eigenvalues are [math]1[/math] and [math]\lambda[/math].

>inb4 maybe the question was phrased incorrectly?
I'd usually assume not so because I think the statement is true word for word for the Moore-Penrose inverse. But whatever.

How important is GPA really in grad school (PHD) admissions? My gpa isn't too terrible (3.1 major, 3.6 overall) and I come from a pretty good college (Top 25 or so for EECS), so do you guys think I should spend more time doing research/internships/projects, or should I step aside from that for a bit to try and get my major gpa higher?

>>14779474
you shouldnt let your GPA get too low, but actual experience looks far better on an application (or even better, you get your advisor to recommend you).

another repost

I read a really good two sided essay a while back that started out with the author kissing the metric systems ass and how it was perfect in every way. But then he cleverly switched off into scientific precision in the field and error rates. the thing I remember about the thing was this, sure you can freeze and boil water with the thermometer and get two lines. but with 0 to 100 you're basically done with your precision. But with Fahrenheit, you fold a piece of paper 5x and you get a usable field calibrator with 32 increments where error is a simple constant so any experimental error can be removed in lab data. there was also a line about how most temp work hates celcius b/c of divide by zero and Fahrenheit doesn't have that problem. and by the end of the essay he's made a very strong case for the validity experimental development cycle of parts of the standards.
If anyone has this essay I'd appreciate it. I've searched every index and gone through my old bookmarks. Because I'm fighting an autist on reducing error rates.

>>14779201
哇这么可爱
https://www.youtube.com/watch?v=wPCOPC9P8fY

tl;dr reconciling different notions of conditional entropy

Let [math]\mathcal{P}, \mathcal{Q}[/math] be finite partitions of a probability space [math](X, \mathcal{B}, \mu)[/math] and let [math]\mathcal{G} \subset \mathcal{B}[/math] be a sub-sigma algebra. The information content of [math]\mathcal{P}[/math] given [math]\mathcal{Q}[/math] is defined by [math]I (\mathcal{P} \mid \mathcal{Q}) = \sum_Q \sum_P \log \frac{1}{\mu(P \mid Q)} 1_P 1_Q[/math], and the information content of [math]\mathcal{P}[/math] given [math]\mathcal{G}[/math] is defined by [math]I (\mathcal{P} \mid \mathcal{G}) = \sum_P \log \frac{1}{\mu(P \mid \mathcal{G})} 1_P[/math] (where [math]\mu(P \mid \mathcal{G}) = E_\mu (1_P \mid \mathcal{G})[/math], i.e. conditional expectation).

Does [math]\int I (\mathcal{P} \mid \mathcal{Q}) d \mu = \int I (\mathcal{P} \mid \sigma(\mathcal{Q})) d \mu[/math] ?

>>14779640
>celcius b/c of divide by zero
Why would you ever divide by an absolute temperature that's not in kelvin? Dividing by temperature only makes sense if it's a difference or if the origin is absolute zero.

Pls anons
>>14743347

>>14779973
r = 2pircn/V
P(k collisions in time t)=(rt)^k e^(-rt)/k!

Where can I learn about tensors?
And please, don't recommend me Eigenchris. I like in general the level of depth he goes in, but his videos are riddled with errors, many of which he didn't even catch and put in updates, and he either omits important things (he never once even mentioned you can find the new dual basis of a linear transform in the row space of the inverse of that transform) or does things in non-intuitive ways (he avoids matrices and uses summations instead, and uses the fugly Einsteins notation).
I studied his videos, but now that I'm over with them I need something to heal me from the damage he has done.
I would also appreciate if it weren't another youtube material.

>sitting in chair
:>phone vibrates in pocket
>go to get phone out of pocket
>not there
>look around
>see phone on table
>vibration in pocket stops

HOW

>>14780167
>important things (he never once even mentioned you can find the new dual basis of a linear transform in the row space of the inverse of that transform
I have no idea how that is important.
>does things in non-intuitive ways (he avoids matrices and uses summations instead, and uses the fugly Einsteins notation).
Everyone uses it. Physicists don't usually explain that there's good geometric reason to contract indices appearing above and below, and mathematicians sometimes ruin the whole thing by using low indices for everything, but it's a pretty slick, convenient notation when used correctly.

The most autistic material I know of about the algebraic aspects of tensors is Greub's books. For differential geometry, I'd tell you to go with Lee's Smooth Manifolds.

So I'm a retard trying to learn some Statistics.

I'm watching a video with examples of working out confidence intervals. The example I'm confused with is "Estimating proportion of Women in a city"

The standard deviation is unknown so using standard error as an approximation. But the formula he gives for working out standard error uses the standard deviation, and just plugs in "0.50" out of nowhere.

I cant for the life of me figure out what is going on here.

>>14780177

https://en.wikipedia.org/wiki/Phantom_vibration_syndrome

>>14780257
I'm not reading all that shit. You're saying ghosts did this?

>>14776276
Is there a word for subtracting something from the total for "inverting" the value? i.e,
>1 - 0.25 = 0.75
>100-10=90
Or is this too trivial to warrant its own word?

>>14780382
Complement?

>>14780392
Looked it up, and looks like this is the word I'm looking for. Thanks, anon.

Suppose there are four possible events whose probabilities A(x,y), B(x,y), C(x,y) and D(x,y) depend on the two variables x and y. Is there a general term for the solution of A(x,y) = B(x,y) etc.? I'm pretty sure I've known it, but I just can't remember it

>>14776276
I'm getting filtered by AC circuit analysis. Can someone solve this question? It'd be much appreciated.

------------------------------------------

Assume we have an AC circuit with U_RMS = 10V and the following in series: a resistor with R = 20 Ohm resistance and an inductor with L = 4 * 10^(-3)H and lasty a capacitor with C = 100 * 10^(-6) F.

Calculate the current through all components and the voltage drop over all components. Give the phase shift between current and voltage.

------------------------------------------

The solution we've been given solves this using reactances, but I'm lost as to why.

>>14780634
I forgot, the frequency f = 10^3 Hz.

>>14780634
Z_R = 20
Z_L = 2πfLj = 2π×10^3×4×10^-3×j = 8πj ~= 25.13j
Z_C = -j/2πfC = -j / (2π×10^3×100×10^-6) = -5j/π ~= -1.59j
Z = Z_R+Z_L+Z_C = 20+25.13j-1.59j = 20+23.54j
I = V/Z = 10/(20+23.54j) = 0.210-0.247j
|I|=0.324
arg(I) = -0.867 = -49.6°

>>14780761
Ok, I get the same values. But one thing I'm wondering is why you chose to calculate |I|? Same with pic related, why do they directly work with the reactance (X_L and X_C) instead of your approach using complex numbers.

Maybe I'm getting confused over retarded things, idk.

>>14780845
X = |Z|, i.e. reactance is the magnitude of the impedance, ignoring phase.
Z_L = j X_L
Z_C = -j X_C

Z_L+Z_C = j(X_L - X_C)

|Z| = √(Re(Z)^2+Im(Z)^2)
Re(Z) = X_R, Im(Z) = X_L-X_C
|Z| = √(X_R^2+(X_L-X_C)^2)

As for why, probably because it avoids having to calculate 1/Z explicitly when you only need |1/Z| and arg(1/Z).

|1/Z| = 1/|Z|
arg(1/Z) = -arg(Z)

1/(a+bj) = (a-bj)/((a-bj)(a+bj)) = (a-bj)/(a^2+b^2)
1/Z = Z*/|Z|^2

Why do we have 1 dick and 2 balls, instead of 2 dicks and 1 ball

>>14780382
subtraction??

>>14781122
why would we ever need two dicks?

>>14781122
1 ball would not be sufficient to provide enough sperms for both dicks to be fertile

>>14781130
threesome

>>14776276
do you guys have any advice for managing time in school?

despite me doing well in school, i still feel as though im not properly using my time efficiently

>>14781125
Well, I meant subtraction for the specific purpose of getting a complement in a range. For example, subtracting anything between 1 and 0 from 1:
1 - 0.0 = 1.0
1 - 0.1 = 0.9
1 - 0.2 = 0.8
1 - 0.3 = 0.7
1 - 0.4 = 0.6
1 - 0.5 = 0.5
1 - 0.6 = 0.4
1 - 0.7 = 0.3
1 - 0.8 = 0.2
1 - 0.9 = 0.1
1 - 1.0 = 0.0

>>14776276
Any recommendation for beginner probability and stat books? I'm looking for books to bounce to machine learning. Also, I took a basic course on probability that finished on moment and distribution. I hope that narrow down what I should look at. Thanks a bunch.

People who joined a mentorship scheme(can be mentor or mentee) , what was your experience and how useful was it? (asking for career perspective)

Let [math]X[/math] be some finite set and [math]Y \subset X[/math]. Show that [math]Y[/math] is finite.

How's my proof by induction over [math]|X| =: n[/math]?

If [math]n = 0[/math] then [math]X = Y = \emptyset[/math] so Y is finite by Definition.
Now suppose [math]X = \{x_1, ..., x_{n+1}\}[/math] and [math]Y \subset X[/math]. If [math]x_{n+1} \notin Y[/math] then [math]Y[/math] is finite by induction hypothesis. If [math]x_{n+1} \in Y[/math] consider [math]Y\setminus\{x_{n+1}\} =: Z[/math] which is finite by induction hypothesis. If [math]Z[/math] is empty then [math]Y = \{x_{n+1}\}[/math] so it is finite. If [math]Z \neq \emptyset[/math] then there exists [math]m \in \mathbb{N}\setminus\{0\}[/math] and a bijection [math]f: \{1, ..., m\} \rightarrow Z[/math]. Then define [math]g: \{1, ..., m+1\} \rightarrow Y, g(j) = \begin{cases}
x_{n+1} & \text{if } j = m+1\\
f(j) & \text{if } 1 \leq j \leq m
\end{cases}[/math] which is clearly a bijection. Thus [math]Y[/math] is finite.

How do I enroll Cirno's Perfect Math Class?

>>14783412
Be a retard(doesn't seem like you have a need to do that though).

How do I stop myself from using the Solution manual :(

>>14782477
Blitzstein for Probability. Casella & Berger for Math focused Statistics. I don't know anything about Machine learning, but this is what I liked. I have heard Rice's book is data focused, but I haven't read it.

>>14783323
It's fine.
You shouldn't use [math]\subset[/math] for non-strict inequality, in my opinion, but whatever.
You can simplify the proof's writing by assuming wlog that [math]X = \{ 1, 2, \ldots, n\}[/math].

>>14781295
Maybe read Cal Newports "how to become a straight A student". It has a whole entire plan in it that helps you plan your day more efficienctly

Any books that make you better at solving problems / more creative? I heard Einstein even had an education that thought him that

>>14783579
>You shouldn't use [math]\subset[/math] for non-strict inequality
I wholeheartedly agree, but that's what you get when this is the standard symbol that comes up when you type \subset. That's why most books use it like that, too, probably.

>>14783641
>that's what you get when this is the standard symbol that comes up when you type \subset.
[math]\subseteq[/math] is \subseteq, and this is consistent with \geq and \leq and probably other stuff I'm not remembering.

How can an expression like [math]\{ x | P(x) \}[/math] be converted into formal logic? What is the "such as" of propositional logic?

newfriend here, what fields of analysis are especially important for theoretical physics?

is it retarded to read many math books at a time? I continuously review my notes and stuff but I wonder if it were smarter to just focus on a few at a time.

>>14783714
Functional Analysis is very important for QM.

The principle of induction is [math](E\subset \mathbb{N})\land (1\in E) \land ((n\in E)\Rightarrow ((n+1)\in E))\Rightarrow E=\mathbb{N}[/math].
If I wanted to show, with induction, that, for instance, the sum of real numbers [math]x_1 + ... + x_n [/math] is independent of order and where you insert parenthesis, what would [math]E[/math] be in this case and how would I prove the individual statements so [math]E=\mathbb{N}[/math] is true?

>>14783911
Read this

>>14783911
E is the set of natural numbers for which this statement is true.

Absolute fucking retard here, how do I solve for [math]x[/math] in [math]y=\arccos\left(\frac{2x}{\sqrt{x^2+1}}\right)[/math]?

I got [math]-\frac{4}{\cos^2 y}\pm\sqrt{\frac{16}{\cos^2 y}-1}[/math] but apparently that's wrong and idfk anymore

>>14784257
>Apply cos
>Square equation
>Multiply with (x^2+1)
>Subtract 4 x^2
>Divide by (cos^2(y) - 4)
>Take squareroot

>>14779845
Did u get this? Entropy ew

So the differentiability theorem states that if all partial derivatives exist and are continuous in a neighbourhood around a point, then the function is differentiable at that point.
So consider:
[math]
\begin{equation*}
f(x,y)=\begin{cases}
1 \quad &\text{if} \, x \le 0 \lor y \le 0 \\
0 \quad &\text{if} \, x > 0 \land y > 0\\
\end{cases}
\end{equation*}
[/math]
Now, my question is, what is the correct way to approach finding the partials of this function? Since doing it piecewise (assuming I did it correctly) gives the answer that it is zero everywhere, and therefore continuous, and therefore the derivative exists at the origin. Yet there is clearly a discontinuity of f especially if one approaches from the diagonal.

>>14784257
[eqn]y=\arccos\left(\frac{2x}{\sqrt{x^2+1}}\right) \\
\cos(y)=\frac{2x}{\sqrt{x^2+1}} \\
\cos^2(y)=\frac{4x^2}{x^2+1} \\
\cos^2(y)x^2+\cos^2(y) =4x^2 \\
\cos^2(y)x^2-4x^2 = -\cos^2(y) \\
x^2 \left[\cos^2(y)-4\right] = -\cos^2(y) \\
x^2 = \frac{-\cos^2(y)}{\cos^2(y)-4}=\frac{\cos^2(y)}{4-\cos^2(y)} \\
x = \frac{\cos(y)}{\sqrt{4-\cos^2(y)}}[/eqn]

>>14784257
[eqn]y=\arccos\left(\frac{2x}{\sqrt{x^2+1}}\right) \\ \cos(y)=\frac{2x}{\sqrt{x^2+1}} \\ \cos^2(y)=\frac{4x^2}{x^2+1} \\ \cos^2(y)x^2+\cos^2(y) =4x^2 \\ \cos^2(y)x^2-4x^2 = -\cos^2(y) \\ x^2 \left[\cos^2(y)-4\right] = -\cos^2(y) \\ x^2 = \frac{-\cos^2(y)}{\cos^2(y)-4}=\frac{\cos^2(y)}{4-\cos^2(y)} \\ x = \frac{\cos(y)}{\sqrt{4-\cos^2(y)}}[/eqn]

>>14784555
Trying for the last time before i give up
[eqn]y=\arccos\left(\frac{2x}{\sqrt{x^2+1}}\right)\\\cos(y)=\frac{2x}{\sqrt{x^2+1}}\\\cos^2(y)=\frac{4x^2}{x^2+1}\\\cos^2(y)x^2+\cos^2(y)=4x^2\\\cos^2(y)x^2-4x^2 =-\cos^2(y)\\x^2\left[\cos^2(y)-4\right]=-\cos^2(y)\\x^2=\frac{-\cos^2(y)}{\cos^2(y)-4}=\frac{\cos^2(y)}{4-\cos^2(y)}\\x=\frac{\cos(y)}{\sqrt{4-\cos^2(y)}}[/eqn]

>>14783501
Thank you anon.

>>14783694
Since when does propositional logic have sets? In predicate logic, if you have sets then it's part of the predicate language. But if you're defining sets through predicates then the set part is probably redundant. E.g. if S={x|P(x)}, then x∈S is just P(x).

Am I going to jail for quoting so many copyrighted books during my time in school? This guy thinks so and went to Oxford.

>>14785182
He seems to be ranting about no citations and all that shit, which seems irrelevant to the question asked. So I'd say no.

apparently, I can't do elementary fractional calculations now. How does this happen? Shouldn't it be (ad - bc) / bd

>>14785639
>Shouldn't it be (ad - bc) / bd
yes, they clearly forgot the minus sign in the third stem

>>14785654
step*

>>14785654
Thank you, anon.

>>14776276
Eliminating dt between eqns 1 and 2
Eq1 v = ds/dt
Eq2 a = dv/dt
Yields
[eqn]\frac{dv}{dt}\times\frac{ds}{ds}=\frac{ds}{dt}\times\frac{dv}{ds}=v\frac{dv}{ds}=a[/eqn]

What?

>>14785665
what are you even trying to do?

>>14785691
I get v by taking the limit of position over an infinitesimally small time interval = ds/dt
I get a by taking the limit of velocity over an infinitesimally small time interval = dv/dt

Substituting 1 into 2 i get the second derivative of position over time, a = d2s/dt2

Book says eliminate dt between one and two and i get the a = v dv/ds. I don't know how this was allowed to happen

>>14785665
>>14785701
dv/dt * ds/ds

What did they mean by this?

>>14785182
Imagine you watch a youtube video which in the beginning includes a notice "No part of this video may be reproduced in other youtube videos or twitch streams."
Would you suddenly assume that cr1tikal can no longer react to it on stream?
Obviously not, because youtubers know jack shit about copyright law, book authors are largely on the same level and book editors purposefully exaggerate their legal power.

>>14785701
>dv/dt * ds/ds
that's just the same thing as dv/dt which is just the definition of acceleration
what is your book trying to prove?

>>14785763
>>14785665

The ds/ds is being substituted as (1/1) allowing it to be written dvds/dtds, changing the order allows it to be written dvds/dsdt, thus it's identical to say dv/ds * ds/dt.
We can then substitude v = ds/dt leaving us with
a = v * ds/dt

>>14785182
thats like those signs on the back of dump trucks that say "not responsible for cracked windshields". just because you say something doesnt make it legally enforceable. quote books all you want.

How can I show that [math] x + 1/x[/math] is increase after [math] x=1/x[/math] without using the faggotry that is calculus?

>>14786009
The derivative of [math]f(x) = x + \frac{1}{x}[/math] is [math]f'(x) = 1 - \frac{1}{x^2}[/math] which is strictly positive for [math]x>1[/math].
So for all [math]y>x[/math] we have
[eqn]f(y) = f(x) + \underbrace{\int_x^y f'(t) dt}_{>0} > f(x)[/eqn]

>>14786009
Define [math]f(x) = x + 1/x[/math].
Compute [math]f(x + \Delta) - f(x) = \Delta - \dfrac{\Delta}{(x + \Delta)x}[/math]
Whenever [math]x \geq 1[/math] and [math]\Delta > 0[/math] you have [math]x(x + \Delta) > 1[/math] hence [math]\dfrac{\Delta}{(x + 1)x} < \Delta[/math] concluding the proof.

Test:
[math]55555555555555555555555555555555555555555555[/math]

>>14786092
Thanks, my heterosexual friend.

>>14786053
You just outed yourself as a faggot, I hope you know that.

what are some books that explain induction more rigorously or introduce other types of induction? I've heard some guy here talk about "[math]\epsilon_0[/math]-induction" and that piqued my interest.

>>14776414
>Don't EVER believe a physicist or scientist explaining tensors
partly agree, although theoretical physicists think of them as multilinear functions or sections of some tensor bundle, which is an ok def

>>14786214
Induction is an axiom or is derived from an equivalent axiom. It's already rigorous. I think you are talking about induction for real numbers, which while is a neat extension, I have not seen it used anywhere.

>>14784509
you’re missing the ‘neighborhood’ part. Although your two partial derivatives exist along the horizontal and vertical axes (respectively), the ‘neighborhood’ is supposed to be 2-dimensional, meaning (in effect) that it your horizontal line should be able to move up a bit and still work, and your vertical should be able to move to the right a bit and still work. but you designed em so that they dont, which explains it

>>14785182
>confessing to crimes on 4chan
Heh. Enjoy the visit from scotland yard, information thief.

>>14786214
You should look up ‘transfinite induction’ and ‘well-founded induction’.

[math]\varepsilon_0[/math] induction is transfinite induction up to the ordinal called [math]\varepsilon_0[/math]. It’s special partly because this is the extra axiom required to carry out based Gentzen’s proof of consistency of arithmetic

are there always infinitely many proofs for something?

For every [math]e>0[/math], there exist two rational numbers [math]s, s'[/math], such that [math]e>s-s'[/math]. Given two real numbers [math]\alpha[/math] and [math]\beta[/math], [math]s'\geq \alpha \geq s[/math] and [math]s'\geq \beta \geq s[/math] show that [math]\alpha = \beta[/math]. Why is this true?

>>14786306
There is something wrong about this statement consider
[eqn] e = 5 \\
s' = 4 \\
s = 1\\
\alpha = 2 \\
\beta = 3
[/eqn]
Then clearly
[eqn]e > s - s' \\
s' \geq \alpha \geq s \\
s' \geq \beta \geq s[/eqn]
Yet [math]\alpha \neq \beta[/math].

>>14786341
I'll just try translating the proof the book (unfortunately untranslated) gave which I didn't fully understand (hence why I asked). It's a proof by contradiction.
For [math]\alpha, \beta[/math] with [math]\alpha>\beta[/math], there exist two rational numbers [math]r', r[/math] with [math]r'>r[/math], such that [math]\alpha > r' > r > \beta[/math]. Therefore, for two arbitrary numbers [math]s', s[/math] that lie between [math]\alpha[/math] and [math]\beta[/math], [math]s' > r' > r > s[/math] holds, which implies [math]s'-s>r'-r>0[/math], such that the difference [math]s'-s[/math], contrary to the assumption of the lemma, cannot be less than, for instance, [math]e=r'-r[/math], thus proving the lemma.

>>14786251
Thank you. I had considered this but was still unsure if I was truly understanding it. Looking at it, say I go epsilon away from (0,0) at the pi/4 and pi3/4 angles, then run them horizontally at the y axis, using the definition of the partial, the limit DNE which is perfect. Thanks again.

I am working on an ODE for stuff. It looks like this :
[math] y' = A + By [/math], with [math] A [/math] and [math] B [/math] some constants.

My goal is to exhibit its stiffness, which I do by comparing several explicit schemes against schemes that are "stiff resilient". Is there a more rigorous way to show my ODE is stiff? The only ressources I've seen about it so far study the Jacobian/Eigenvalues, which only makes sense to me when it comes to a system of ODE, and not a single ODE like I am working on.

>>14786593
to be more precise, I solve my ode with several numerical schemes. pic rel shows the normalized error compared to the analytical solution of my ODE. As we can see, the explicit schemes all sperg out really quickly once the transient phase is over. This seems typical of a stiff ODE to me, but I would like to show it in a better manner other than "look at this photograph"

Why does a bike want to fall outwards when turning?

What is 1 joule equivocal to? I know work can be used to measure a bunch of different things but is there a baseline version? Say, the one thats 1 newton per metre?

>>14786614
If only there was a site where you could search for such basic questions ...

https://en.wikipedia.org/wiki/Joule#Practical_examples

>>14786389
Unreadable.
Is the original in a romance language or german? I can sort myself out with those.

>>14786697
yes 4chan /sqt/ qtddtot/ is a great spot to ask basic questions

>>14786923
The original is in Russian, but I found a German translation and now realize I made a few big mistakes translating it, my apologies:

Den Beweis werden wir indirekt führen. Es sei etwa [math]\alpha > \beta[/math]. Nach Lemma 1 (see below) lassen sich zwischen [math]\alpha[/math] und [math]\beta[/math] zwei rationale Zahlen [math]r[/math] und [math]r'>r[/math] einfügen, so daß [math]\alpha > r' > r > \beta[/math] ist. Daher gelten für zwei beliebige Zahlen [math]s[/math] und [math]s'[/math], zwischen welchen [math]\alpha[/math] und [math]\beta[/math] liegen, offensichtlich die Ungleichungen
[math]s' > r' > r > s[/math],
woraus [math]s'-s>r'-r>0[/math] folgt, so daß die Differenz [math]s'-s[/math] entgegen der Voraussetzung des Lemmas nicht kleiner gemacht werden kann als beispielsweise die Zahl [math]e=r'-r[/math]. Dieser Widerspruch beweist die Richtigkeit des Lemmas.

And Lemma 1:

Zu zwei beliebig gegebenen Zahlen [math]\alpha[/math] und [math]\beta[/math] mit [math]\alpha > \beta[/math] läßt sich eine rationale Zahl [math]r[/math] finden, die zwischen ihnen liegt, für die also [math]\alpha > r > \beta[/math] gilt (folglich gibt es sogar eine unendliche Menge solcher rationaler Zahlen [math]r[/math]).

>>14776276
Dont know if this is the right place for this but what the hell,

ive always been fascinated by theoretical physics and mathematics, got my physics degree and then a MsC with a thesis on supersymetric QFT (SW duality), which i also did in my uni. (The MsC program was poor tho, did not offer any classes on more recent subjects (strings, CFT, anything more mathematically sophisticated than simple group theory, etc)). Now wanting to continue for a PhD, but havent been as caught up in research as a post grad from other places, is there any hope of finding something in this field in Europe event if i know nobody? (Any suggestions on interesting/fruitful topics for searching would be welcome) Or should i abandon the theoretical redpill altogether and go into something more applied like condense stuff?

>>14787045
I think the original statement is that, if [math]\alpha[/math] and [math]\beta[/math] are two given real numbers, and for any rational [math]e > 0[/math] there exist rational [math]s', s[/math] such that [math]s' \geq \alpha \geq \beta \geq s[/math] and [math]s' - s < e[/math], then [math]\alpha = \beta[/math].

So intuitively speaking, the result is true because the distance between [math]\alpha[/math] and [math]\beta[/math] needs to be smaller than the distance between [math]s' - s[/math], which can be arbitrarily small, a contradiction.
The proof proceeds by assuming [math]\alpha \neq \beta[/math] and fixing [math]r', r[/math] distinct rationals between [math]\beta[/math]. The distance between these two needs to be smaller than the distance between [math]\alpha[/math] and [math]\beta[/math], which can be made arbitrarily small by the previous argument.

>>14787221
>which can be arbitrarily small, a contradiction.
I don't know why I finished the sentence with "a contradiction", ignore that part.

>>14786607
Any single ODE is also a system of ODE:s, but the Jacobian is 1x1 (just the regular derivative).

>>14786593
>Is there a more rigorous way to show my ODE is stiff?
There isn't even a rigorous definition of stiffness, so no.

>>14787247
The main use of eigenvalues in determining stiffness is for the stiffness ratio, which is the ratio of the magnitudes of the largest and smallest eigenvalues. Which isn't applicable for a single variable.

>>14786092
clunny <3<3<3

what exactly is a gas giant planet? does this mean jupiter doesn't actually have any solid bit to it like earth does? or is most of it just atmosphere that we count towards its radius? if it does have solid bit, how big is that compared to earth?
why don't we count our atmosphere to artificially inflate earths radius?

>>14787450
It's a planet where most of the mass is "gases" (mainly hydrogen and helium). Although due to pressure, most of the mass is above the critical point where there's no distinction between gas and liquid.

why are homeomorphism not just continuous bijections?

>>14787822
Because the inverse function of a continuous functions doesn't have to be continuous.

>>14787822
They are if the domain is compact and the range compact.

Counterexample: let f:X -> X be the identity function where the range has the trivial topology and the X a non-trivial topology

>>14787916
*range hausdorff
R isn't compact, but this can be gotten around by considering expanding closed intervals or one point compactification extensions

How do I prove that, if I have two Dedekind cuts [math]A\vert A'[/math] and [math]B\vert B'[/math], that [math]A=B[/math] necessarily implies [math]A'=B'[/math]?

>>14784509
Use a more complicated function if you want more interesting results?

>>14788095
hint 1: notice that A' is the complement of A, and also the same thing for B and B'

hint 2: if two sets are equal then their complements must also be equal

>>14788101
Thank you, but I still wonder, say [math]A[/math] has no greatest element, [math]A'[/math] a smallest element, [math]B[/math] no greatest element, but [math]B'[/math], contrary to [math]A'[/math], no smallest. Would [math](A=B)\Rightarrow (A'=B')[/math] still follow?

>>14788115
then B|B' is not a dedekind cut because by definition a dedekind cut is a partition on Q (that is, every element of Q must be either in B or B')

How do I find references/bibliography for the shit I'm writing for my bachelor's thesis?

>>14788144
Give example.

>>14788286
Wdym? I'm writing about point-set triangulations, convex hulls, etc.

Since the shape and volume of a container has no effect on hydrostatic pressure, would fluid from two raised containers double the pressure or would stay the same same?

>>14788296
Bibliography is for stuff you cite. So I am asking for an example of what you want to cite.

>>14788144
bibTeX

>>14788317
I'm pretty much reading the Wikipedia and re-elaborating it in my mother tongue, adding and removing things as I see fit.
For example, https://en.wikipedia.org/wiki/Convex_hull
The first paragraph after the title, and the first paragraph after "Definitions".

>>14788350
You shouldn't learn mathematics from wikipedia, you should learn from books.
But if you really wanna insist on this you can cite whatever wikipedia is citing and pretend you read the original source.

>>14788379
It's not that I *want* but also I don't know how to look for books on the subject matter.
I just wanna be done with my thesis and move on.

>>14788440
>It's not that I *want* but also I don't know how to look for books on the subject matter.
The MAA has an excellent book list that you can browse by subject and rating
https://www.maa.org/press/maa-reviews/the-basic-library-list-maas-recommendations-for-undergraduate-libraries
Once you find the book you want you can easily get the pdf from ligen.is

>>14788457
>ligen.is
meant to type libgen.is

>>14788144
convex sets/hulls are a very basic and widespread concept, even in undergrad topics, e.g.
>convex optimization (the feasible region is often convex)
>functional analysis (krein milman thm)
>cs algorithms (given 100 points, figure out which ones form the boundary and which ones are on the interior)
so there are lots of places to look but they are in diverse areas. afaik there is no purely “convex hull theory” book

>>14788472
meant for >>14788350

>>14788457
Thanks, I'll check it out.

>>14788472
The convex hull theory is simply the part I wanted to write about right now. The actual subject of the thesis is the application of mesh generation algorithms to a cloud of points.

I'd really appreciate any (further) help or tips, since the subject encompasses a lot of areas I'm having a tough time focusing and finding the right concepts to write about.

>>14776276
What second major should I get as CS student?
I'm unable to decide whether I want to do EE or Physics.
I definitely want to learn electronics at a deep level because it would be the applications and implementations of both my CS knowledge and signal processing knowledge, but I also want to go for physics because I aim for a PhD in QC.

>>14787204
>in Europe
look for swiss unis maybe?
the swiss love physics and put a lot of money into it, there are a bunch of worldwide known laboratories you can work at and many technical schools and good unis to teach and do research at.
Anyone doing math of physics always find their purpose in Switzerland.

>>14788666
thank you, i'll check that out (have nothing to do with experiment tho)

>>14788661
>PhD in QC
you want EE for that

Anyone here good at Linear Algebra?

Let [math]\varphi[/math] be an endomorphism on [math](\mathbb{Z}^n,+)[/math] prove that [math]\varphi[/math] is injective iff [math]\mathbb{Z}^n / \text{im} (\varphi)[/math] is a finite group.

I only managed to do one direction.

>>14789205
Did you tensor the endomorphism with [math]\mathbb{Q}[/math]?

>>14789250
What is a tensor?
I did extend it to a linear map [math]\varphi'[/math] on [math]\mathbb{Q}^n[/math] by defining
[eqn]\varphi' \left( \sum_{k=1}^n a_k e_k \right) = \sum_{k=1}^n a_k \varphi(e_k) [/eqn]
If this is what you mean.

Then if [math]\varphi[/math] isn't injective then neither is [math]\varphi'[/math].
So [math]\varphi'[/math] isn't surjective either and I can find a
[eqn] \begin{pmatrix} \frac{p_1}{q_1} \\ \vdots \\ \frac{p_n}{q_n} \end{pmatrix} \not \in \text{im}(\varphi') [/eqn]
All multiples of it aren't in the image either so I can multiply it with all the denominators to get an element that has infinite order in the group [math]\mathbb{Z}^n / \text{im} (\varphi)[/math].
A group that has an element with infinite order can't be finite.

>>14789302
Yeah, that's roughly how tensoring with Q goes.
For the other way around, consider the boomer interpretation of things. [math]\mathbb{Z}^n / im ( \phi )[/math] is a finite group if, for any element [math]v \in \mathbb{Z}^n[/math] you can add and subtract elements of [math]im ( \phi )[/math] from it to drag it into a "canonical" finite subset of [math]\mathbb{Z} ^n[/math]. This finite subset can, for the sake of convenience, be something like [math]\{ v \in \mathbb{Z}^n : \| v \| < \lambda \}[/math].

Hint: use the extension to Q again.

>>14789205
just generalize inverse operation

Hey bros, did I do this correctly?

>>14789205
I'm no good at being clever, but its obviously true because the generators and module dimensions, so you may be able to cram the square into the round hole with force.

>>14789409
And please look at this one as well. Cymath gives a different answer. I don't know why I'm wrong.

>>14789205
I crammed the square into the round hole by putting [math] \phi [/math] into matrix form, but the 4chan TeX window just deleted everything AGAIN upon going to copy.

>>14789409
Looks good.
>>14789488
Also looks good.
>Cymath gives a different answer.
Wolframalpha gives the same but it flips (z - x).

>>14781105
Tenks enon, I think I got it much more than before, but still need to practice/read a bit.

>>14789302
>>14789336
Did you get stuck? I can give you extra hints or the complete proof if you want.

imagine there's an afterlife where you can't feel physical pain anymore. do you think that would include emotional pain, too? is there a substantial difference between the two?

>>14789302
Wrote this earlier but 4CHAN deleted it. For the other direction you can do this. Put [math] \phi [/math] in matrix form in the obvious way. Argue [math] \phi [/math] is injective iff [math] \det \phi \neq 0 [/math]. Now if [math] \phi [/math] is injective then by Cramer's rule [math] \phi( \phi^{-1} \det \phi) [/math] is a diagonal matrix with non-zero integer entries on the diagonal. Also [math] \phi^{-1} \det \phi [/math] has integer entries. It follows for [math] k = 1,...,n, \exists m_k \in \mathbb{N}, m_k e_k \in \phi(\mathbb{Z}^n) [/math]. It easily follows [math] \mathbb{Z}^n /\phi(\mathbb{Z}^n) [/math] is finite.

>>14791006
People rarely commit suicide over physical pain. That's why everyone on /sci/ should watch Kemono no Souja Erin!

Is it possible to make money from stochastic calculus on your own terms instead of having to work for a major company? I am too socially inept for finance.

https://www.youtube.com/watch?v=z1EpzTu_-5I

This video is incorrect. Right?

Using E=mc^2 (units: J, kg, m^-1), then converting joules to kilotons or megatons of TNT:

>40% more powerful
Nope, only 30% more powerful - 15 KtTNT vs 21 KtTNT

>1 Kg is more powerful than the Tsar bomb (50 MtTNT)
Nope, 1 kg -> 21.51 MtTNT. 2 kg -> ~40 MtTNT

Antimatter bombs would be more effective on Earth than in the vacuum of outer space.

>>14791275
Correction
m*s^-1

>>14791275
Well the annihilation of 1kg of anti-matter means 2kg of matter in total (since it has to cancel with normal matter) so:

E = 2 x c^2 = 1.8 x 10^17 J = 4.3 x 10^5 ktTNT = = 430 MtTNT

>>14791306
What I was thinking:

300 million squared is 90 thousand trillion.
(300,000,000 * 300,000,000 *1 = 9 x 10^16 J)

2 kg = 18 x 10^16 J

This thing -
https://www.justintools.com/unit-conversion/energy.php?k1=joules&k2=megatons-of-TNT
- says that
180000000000000000 J
=
43.02103250478 Megatons Of TNT

Did I mess up? What did I mess up on? Maybe you miscalculated, but IDK.

Antimatter bombs don't work well in outer space because there is not a lot of matter there to bump into.

>>14791306
>>14791335
Decimal place of final number was off by one.
>https://en.wikipedia.org/wiki/TNT_equivalent
>The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules (4.184×10^15 J).
>kiloton . . . ^12 J

1.8 x 10^17 / 4.184 x 10^15 =
43.021032504780114722753346 MtTNT

1.8 x 10^17 / 4.184 x 10^12 =
43021.03250478011472275334 KtTNT
=
4.3 x 10^4 KtTNT
(not 10^5)

All the schemes I’m talking about are integral.
I’m going through hartshorne and I can’t find where one symbol is defined.
For an integral scheme X, we define K(X) to be the local ring of the generic point of X. K(X) is called the function field of X.
My problem is later in section 6 of chapter 2 Hartshorne is using both K and K*, K should be the function field defined above but I can’t find a definition of K*

>>14783929
nta but where's this from?

>>14791524
Analysis I by Amann/Escher, a highly abstract German undergrad analysis textbook which features commutative diagrams in the second or third chapter

>>14789724
Thank you fren. Cymath is good most of the time and shows the steps for free, but I guess it spergs out from time to time.

Has anyone here read Dieudonne's Treatise on Analysis? It's 9 volumes of analysis. Seems to be crazy comprehensive.

>>14776276
>>14776276
Electric Machinery and Power System Fundamentals by Chapman, does this book exist on the internet? (yes, I have looked libgen & torrent. 2001 print only 1 edition book, so I'm thinking not.)

Why is it necessary to take the [math]n[/math]th composition here?

What strategy should I use for "give example" question?

>>14791842
Firstly (a) and (d) are clearly impossible.
Hint: For (a) apply Bolzano-Weierstrass to the bounded subsequence and for (d) use the fact that the set of acculmulation points of a sequence is always closed in a metric space.

For (b) you can constuct a sequence [math](a_n)[/math] where [math](a_{2k+1})[/math] is a subsequence that converges to 0 without including 0 or 1 and [math](a_{2k})[/math] is a subsequence that converges to 1 without including 0 or 1.

Similiar thing for (c). Constuct [math](a_n)[/math] so that the subsequence where n is odd converge to 1. Then let the subsequence where n is divisible 2 but not by 4 converge to 1/2. Then let the subsequence where n is divisible 4 but not by 8 converge to 1/3. And so on. You can glue any countable amount of sequences into one sequence like that.

>>14791435
I'm no algebraic geometer but if R is a ring, R* is typically used to denote the set of invertible elements of the ring

>>14791869
I didn't ask for a solution.

>>14776276
I got told by a /sci/entist in the math thread to post my question here.

>>14792258

>big math word problem (dra/g/on maid edition)
Ilulu lives in your computer and she is bored (See attached figure. It's your Ilulu. Take her to the Maid Library, fren). She wants to go to the Maid Library and read some books, because Ilulu likes books, old DVDs and vending machines filled with healthy snacks.

Ilulu goes to the Maid Library and wanders into the INFLATING section. She's walking around eating some trail mix she got out of the vending machine and casually looking at the covers of books to figure out which one has the coolest cover.

Ilulu finds a book called MAGIC-COIN that has some excited looking anime maids on the cover playing with a cool looking, glowing gold coin.

Maid Books in the INFLATING section are non-deterministic. The magic of the INFLATING section causes any chapter of the book which is read to have a copy of the read chapter re-inserted into it.

The MAGIC-COIN Maid Book originally represents a fair coin. It contains two chapters. One reading "HEADS!" and another reading "TAILS!". So 50/50 on what you get. Ilulu reads the book and gets "HEADS!". A copy of that chapter is inserted into the MAGIC-COIN Maid Book.

Now the book has three chapters. "HEADS!", "HEADS!" and "TAILS!". So now the book has a 2/3rds chance of "HEADS!" and a 1/3rd chance of "TAILS" when read. Ilulu opens the book again and gets another "HEADS!". A copy of "HEADS!" Now 3/4ths of the book is "HEADS!"

As the number of times ilulu reads the MAGIC-COIN Maid Book approaches infinity, is it possible to converge to a point where MAGIC-COIN will have a 100% chance of being either "HEADS!" or "TAILS!"? What are the odds of that happening? What happens if it doesn't converge?

Bros, how can I stop feeling stressed out and sad before exams? I got a terrible viral fever that kept me bedridden for 3 days, then the medicine I got for that gave me gastritis. Still, I prepared well. I still feel stressed out and sad. How to stop and be happy instead. I don't want this feeling to go away, I'll fail out of college if I didn't have a panic episode before exams, just want it to not be too harsh.

>>14792294
The solution for an equivalent problem is here
https://staff.math.su.se/daniel.ahlberg/notes-urns.pdf

a-ano, how to do this?

>>14792361
Sounds like you got anxiety nigga.

Try jogging, getting at least eight hours of sleep, and looking into cognitive behavioral therapy to deal with intrusive thoughts.

>>14792435
The denominator is something like [math]a+b[/math], so you can multiply both the numerator and denominator by [math]a-b[/math] so that the denominator becomes [math]a^2-b^2[/math] which eliminates the square root in the denominator.

>>14792435
Numerator has no square roots. Problem solved.

>>14792461
I reckon my attempt is wrong?

>>14792478
forgot pic

>>14792484
You should have [math]x-25[/math] in the denominator.

>>14776276
How many unique paths can you trawl a cubes edges without overlapping? Especially if the cube has no origin.

>>14792491
But [math]2\sqrt{x}-\sqrt{x}[/math] evaluates to [math]\sqrt{x}[/math] leaving the denominator as [math]\sqrt{x}+5[/math]

>>14792501
The problem is small enough to brute force it.
Write the cube as a graph and let your PC do a DFS on it to count the number of paths.

>>14792509
Yes, and you should multiply numerator and denominator by [math]\sqrt{x}-5[/math], not [math]\sqrt{x}+5[/math]

>>14792425
Thank you for the paper, fren. I am not a high level enough mathematician to read it. Do you know some papers I can read to get good enough to read that paper?

I did go ahead and build the library section for Ilulu though. She wants to do an experiment because she is bored and likes science and thinks experiments are fun, so I am going to make her read the book a billion times.

Also can someone give me like a simple English answer from the paper? I want to see if my experiment confirms their paper.

If I read it right the ratio converges to a random variable between 0 and 1?

>>14792674
you'll need to read several combinatorics books.

>>14792674
The dra/g/on maid board tags don't work here. Also I haven't made loops yet so I hope you /sci/entists don't mind recursion to a billion, and plain-text code for the experiment:

>SLAM code to test INFLATING Maid Books:

:+ MAGIC-COIN ." HEADS! " | ." TAILS " ;
: LB 10 EMIT ;
: ONE MAGIC-COIN LB ;
: TEN ONE ONE ONE ONE ONE ONE ONE ONE ONE ONE ;
: HUNDRED TEN TEN TEN TEN TEN TEN TEN TEN TEN TEN ;
: THOUSAND HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED HUNDRED ;
: TEN-THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND THOUSAND ;
: HUNDRED-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND TEN-THOUSAND ;
: MILLION HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND HUNDRED-THOUSAND ;
: TEN-MILLION MILLION MILLION MILLION MILLION MILLION MILLION MILLION MILLION MILLION MILLION ;
: HUNDRED-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION TEN-MILLION ;
: BILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION HUNDRED-MILLION ;

>>14792695
Ok, which ones? And do I have to read stuff before those?

>>14792720
Did you ever go beyond high-school math?

>>14792484
Yeah, that's wrong. [math](\sqrt x+5)\cdot(\sqrt x+5) = x + 5+2\cdot5\sqrt x[/math]; you forgot the cross term.
Remember, [math] (a+b)^2 = a^2+b^2+2ab [/math], while [math] (a+b)\cdot (a-b)=a^2-b^2[/math], which is why you should multiply with the conjugate.

>>14792720
Ilulu is reading the MAGIC-COIN Maid Book one billion times and writing it to file.

Ilulu is happy to do an experiment. I hope 16GB RAM is enough.

>>14792723
Yeah, but I think I took a wrong turn at Calculus and got lost somewhere in Laplace Transforms.

Nothing as cool as this and it was a ling time ago.

How do you prove prove that [math]\emptyset : \emptyset \rightarrow \emptyset[/math] is a bijection?

During a supernova that creates a black hole, why is there a supernova? Why doesn't it all fall right into the black hole?

>>14792911
It's trivially injective because it doesn't map two different elements in [math]\emptyset[/math] to the same element in [math]\emptyset[/math] (since the set doesn't have any element).
Surjection is more subtle, but it is because for every element [math]y[/math] in [math]\emptyset[/math] there exists an element in [math]\emptyset[/math] that [math]\emptyset[/math] maps to [math]y[/math] (the empty set doesn't have any element so there is no element for which the surjection property isn't true).

>>14791900
I think you’re right. I’m probably just overthinking it

>>14792887
The end result was my computer getting hot and crashing.

I redesigned the program to just count the instances instead on trying to make a file, and turned off console printing.

Still ran out of memory because the Maid Book got too big, so I reran at 100 million.

I also redefined ONE to not print a linebreak.

New results are attached. Maybe 100 million isn't enough to see something cool? How do we science this more?

>>14792911
As is so often the answer, the first step is to write down all definitions of the objects involved in the question

>>14792616
Why is that, anon. I know the rule, but not the reason.

I've always gotten filtered by probability and combinatorics. I'm shiny hunting in Pokemon. Each battle represents a bernoulli trial in which I have a 1/8192 chance of encountering a shiny pokemon. The trials are independent.

With that being the case, what is the function representing "if I have k battles, I should have P probability of having encountered a shiny by now"

since it's a geometric distribution, it should be
[math]P = \sum _{n=1}^{k}\:(1 - \frac{1}{8192})^k\cdot \frac{1}{8192}[/math]
right?

>>14793126
It's a binomial distribution.

[eqn]P = 1 - \left(\frac{8191}{8192} \right)^k [/eqn]

>>14792973
When the star initially collapses into a heavier element core it produces an insane amount of neutrinos in the process. Something like a 1/10 of the stars mass is converted within a few seconds into a neutrino wind that blows away the outer shell, that's your supernova. Depending on how much mass is left over will dictate if the remnants collapse into a white dwarf, neutron star or a black hole.

However if the star is really massive, at least 15 solar masses, you can get direct collapse into a black hole without a supernova occurring. Obviously these are much, much harder to detect.

>>14793100
The denominator is a sum of two elements [math]a[/math] and [math]b[/math] and you want to get rid of the square root on one of the elements.
The trick is to transform [math]a+b[/math] into [math]a^2-b^2[/math] so it can be done. Now remember that [math](a+b)(a-b) = a^2 - b^2[/math]. Since you already have [math]a+b[/math] at the denominator, you just have to multiply by the difference [math]a-b[/math] and the trick is done.
[eqn]\frac{1}{\sqrt{x}+5} = \frac{1}{\sqrt{x}+5}\cdot\frac{\sqrt{x}-5}{\sqrt{x}-5} = \frac{\sqrt{x}-5}{(\sqrt{x}+5)(\sqrt{x}-5)} = \frac{\sqrt{x}-5}{x-25}[/eqn]

>>14793204
Thank you.

>>14761949
>What's the opposite of a sigmoid curve?
>>14776414
>Opposite of a sigmoid curve
lmao
the function would be the inverse of a sigmoid function, i.e. -ln(1-x), I know it as the logistic function.

>>14762357
There are a lot (a lot) of people in the field that should not be there. think business/psych/whatever majors that take a 1 year degree or bootcamp and hope to work there, which tarnishes the reputation a little.
if you know your stuff it's just applied mathematics really, and I imagine it should be regarded as well as that here.

>>14791181
finance people are quite different from quants, which is where you would use this stuff. actuaries also, and neither field is well known for its extraverted people.
FWIF, I doubt you can make some money on your own from what you read in those books.
All the quants ive talked to say the university level autism is largely useless in their job; they just teach new hires in their company what they need to know.

I need to calculate the probability of having to wait maximum of X amount of time when you have known times for a minute of being able to go or having to wait.
How do I calculate the probability?
I have tried googling ways to calculate this, but none of them seem right for this. Any help would be appreciated.

>>14793433
Your first sentence is quite unclear
>known times for a minute of being able to go or having to wait
What does this mean?

>>14793459
Ah, I meant that in a minute you have known times for having to wait and being able to go. So for a minute ofr example a 40 second waiting window followed by a 20 seconds of being able to go, and that repeating.

>>14791842
Usually I try to picture how an example should go in my head and any obstructions that appear.
There are some completely braindead outliers like a) but b) is a good example of how you can just visualize a sequence ping ponging between 0 and 1 without ever touching them.

If you get stuck go back through your text and look for example construction techniques it uses. Stuff like stitching two sequences together by putting the entries of the first in the odds and the entries of the second in the evens.

>>14793496
Still unclear. ESL?

>>14793508
40 seconds of not being able to go, followed by 20 seconds of being able.

>>14793518
Okay, so after 40 seconds you are able to go with probability 1.

>>14793522
Yes, but with what probability do you have to wait a MAXIMUM of 20 seconds. I want to know how to calculate that.

>>14793527
You said 40 seconds then 20 seconds. So 100%. Where's the random element to make it a probability?

>>14793527
Well, you just said you have to wait 40 seconds before you can go for 20 seconds. So, you must always wait 40 seconds, so never a maximum of 20.
Or do you mean you have this structure of minutes forever repeating, and you `enter' at a random point in time? Because then the probability is 2/3.

>>14793533
>>14793534
Yeah my dumb ass forgot to add that you enter at a random point and from that point having to wait a maximum of X time.

>>14793537
Yeah, so you enter at a random point in the interval [0,60].
We say that in [0,40] you have to wait, and that in [40,60] you can go.
Clearly, if you arrive in [20,60] (probability=2/3 if uniform arrivals), you wait at most 20 seconds, and otherwise you must wait longer.

If I'm learning programming/data science with a side interest in ML, how useful would it be through a pure probability textbook? My courses teach statistics but don't require that. I have "mathematics for machine learning" that just has one chapter on it

>>14793547
Very useful. I do not recomment the measure theory autism, but the harvard course on probability by blitzstein should be perfect. There are full lectures on youtube, and the book is free online with excellent exercises.

>>14793541
Alright, I understood it now, thank you.

>>14793547
Outside of knowing about things like false positives, true negatives etc I've never had to use any pure probability in my years of coding or related ML work. That's just my personal experience, other people's may vary.

>>14793553
alright thanks. But what is it useful for? What areas should I focus on?

>>14793009
This time I ran it 200 million times, and the ratio is different!

Is the random variable convergence different each time? Or is 200 million too few times to see convergence?

>>14793567
A lot of machine learning heavily uses bayesian statistics, which that book nicely builds towards.
I guess it depends; if you are content with fitting a base xgboost on everything then you don't need to know probability (or anything else for that matter).
If you want to get some ideas, I recommend the book Pattern Recognition and Machine Learning by Bishop. It's nice.

>>14793579
300 million times!

The ratio is way more in favor of one side than the other now!

>>14793738
400 million!

More than 10x as many TAILS! flips than heads.

>>14793579
>>14793738
>>14793776
this isn't your blog. take your meds

>>14793776
450 million times, and this one is much closer than 50/50?

We are hitting the limits of the science computer. 500 mil runs me out of memory.

>>14793784
>fan mail
Thanks fren. I like doing science experiments and getting Ilulu to read the MAGIC-COIN Maid Book 450 million times was a lot of fun.

Too bad the science computer doesn't have the memory for a bigger list of Maid Books.

I think I will come to this board to look for more problems which are computable with SLAM. Playing with my /sci/ence frens was a lot of fun.

Thank you for reading my experiment.

>>14793325
There are lots of possible sigmoids, each with its own inverse. E.g.

y=1/(1+e^-x) <=> x=-log(1/y-1)
y=x/√(1+x^2) <=> x=y/√(1-y^2)
y=(2/π)atan(x) <=> x=tan((π/2)y)

let's say g-d trolls us by suddenly changing the direction and speed that the earth is moving through space, what would we experience on the surface?

When will the range-ban on Australians end?

>>14794082
Assuming a god did it then nothing at all. Not until we either freeze to death or burn to a crisp when our orbit changes.

>>14794121
we wouldn't feel any kind of inertia or anything?
like what if the earths orbit accelerated to 2x speed within a few hours

>>14794134
Why would a god care about trivial details like inertia?

If you're asking about acceleration then don't bring a deity into the conversation. Some big ass (fantastical) thrusters would work just as well. It wouldn't take much g-force, probably around 0.05g, to accelerate the earth to double it's speed relative to the sun in a few hours.

>>14794149
okay what if a giga nigger planet flew through our solar system and fucked up the earths orbit, so suddenly we changed direction and speed
what would people on the surface experience?

>>14794162
they'd feel nothing. it's takes a fuck ton of mass to exert a noticeable gravitational acceleration. you'd have to park the moon over your house before you experienced a difference.

Is digit ratio valid predictor of prenatal hormones? I have high digit ratio and masculine face

Scientifically speaking, what would the mortality rates of young rich black men be if they had no access to drugs and sex?

Scientifically speaking, if I suddenly became rich at 18 and had no interest in sex or drugs I'd be doing absurdly retarded shit like trying to tame honey badgers and trying to reproduce cartoon scenes irl.

>>14776276
would still like confirmation if this is the right way to think about it (previous thread)

>>14773243

>>14794304
>if they had no access to drugs and sex?

Why get rich then?

If you ask the square root of 4 and want ±2 instead of just +2 (the principal root), how would you phrase that?

>>14776278
xy = 6/12 = 1/2
x + y = 6/12 = 1/2

>>14794975
{x | x^2=4}

A book I'm reading from 1991 claims that subatomic particles "die" and reappear constantly at the rate of 10^22 times a second. Is there any truth to this?

What the fuck is homotopical algebraic geometry?

is there a name for words that only make sense when you're comparing multiple things?
like "difference".
it makes sense to say "there's a difference between X and Y", but not "X has a difference", and even "X is different" only makes sense in contexts where there's a stated or implied Y.
or am I just a completely wrong ESLfag who's missing something?

Are these GR lecture notes any good? https://jila.colorado.edu/~ajsh/courses/astr5770_18/grbook.pdf

>>14793229
Thank you, fren. I understand now.

Is it normal to forget about simplifying basic stuff after not doing math for a few months? I picked it up fairly quickly, but felt really dumb for simplifying basic algebra stuff wrongly.

>>14793833
Anytime friend. I really enjoy your work.

>>14794992
Well QFT would say that a particle is constantly changing into a cloud of virtual particles and then reforming. However virtual particles aren't real, they can't be observed, and are instead just mathematical tools used to perform QFT calculations. So yes, you could say they die and reappear if you were speaking pop-sci.

My lab manual says the Cp/Cv ratio is 5/3 for air which would be true for a monatomic gas, but it''s assuming that the molecules are diatomic in the mass calculations...If they are Diatomic shouldn't the ratio be 7/5?

>>14795419
Yes that's a mistake, the Cp/Cv ratio for air is roughly 1.4 or 7/5.
If you calculate the sound velocity with 5/3 you obtain something like 375 m/s for 20°C which is abnormally high since the actual velocity is closer to 344.

I have heard an anon say here before that you learn QFT as fast as possible and only in the process of learning QFT learn about all the prerequisites. Apparently, a lot of undergrad physics is irrelevant to modern physics, and studying it non-linearly would be better. Thoughts?

>>14795258
It's pop philosophy trying to use physics to support it. So he's talking about "virtual particles"?

>>14795864
Quantum Electrodynamics is experimentally verified, and probably the most successful theory in physics
https://en.wikipedia.org/wiki/Precision_tests_of_QED
QFT tries to build on that but it does have its shortcomings,like the virtual particle BS. There's an alternative derivation of Dirac's Equations by Dennis Morris using Quaternions and they achieve much of the same without resorting to the "virtual particle"" (read God) cope:
https://youtu.be/8Qv0zJdsW7s

>>14795840
> learn QFT as fast as possible
It's often claimed to be the single hardest topic any physicist can study and that isn't a joke, it isn't normally taught at undergrad level because it requires a lot of pre-requisite knowledge of other fields first (pun intended)

>>14795864
Sounds like it.

>>14795913
Whoosh right over my head.

>>14795925
QFT assumes theres some particle that is instantaneously created and annihilated that transfers momentum from the parent baryon to the leptons. This process is supposed to happen so fast that we can never detect them. This is about as good as saying God did it.

>>14795949
rip wrong diagram but the point still stands, its assuming some particle we cant detect is transfering momentum from parent particles to the products

>>14794969
Good food and hiring maids/butlers/personal chefs to cater for you.

>>14795925
Good because that was a schizo post

>>14795975
sweaty, all scientists are schizos
the metric by which we measure intelligence itself is pattern recognition ability
pattern recognition is what scientists do for a living

Did/do physicists really believe that human consciousness is something magical with a special ability of making wave functions collapse?

>>14796272
Yes, experiments show that if you only let non-conscious animals like flies observe the double slit experiment then they see a very different result than when there's a human observer too.

>>14796272
Nope, only non-physicists believe that. Observation makes the wave function collapse but what a physicist means by observation is any interaction between two particles.

>>14796286
That's not even a god shit post, what a waste of characters. Do better.

Chembros, how does greek lettering work when referencing the positions of functional groups on rings? I'm working with an old reference on dyestuffs that uses this notation. For example, it mentions α-γ-dimethylquinolinium iodide, is this equivalent to 1,3-dimethylquinolinium iodide? Some of the things I've found online suggest it goes backwards.

V(X) = pi * ((xi - E(x)))^2

V(X) = pi * ((xi^2 - 2*xi*E(X) +E^2(x))
V(X) = pi * xi^2 - 2*pi*xi*E(X) + pi * E^2(x)
= E(x^2) -2 * E^2(X) +

>>14796433
>>14796433
>>14796433
Koenig Huygens formula

Where I am wrong please?

>>14796353
>Nope, only non-physicists believe that.
https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
It seems Von Neumann thought so. Also
>Prominent physicists have gone so far as to suggest that astronomers observing dark energy in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's cat scenario

>>14796433
I found it

Pi = 1

Right thank you

How do i dispose of DCM and THF. Just let it evaporate outside?

so how do you anons write your notes from physics books?

What ive been doing is mainly writing down every relevant equation and constants.

>>14791297
One coffee cup full (volume) of antimatter plus the same volume of normal matter would make an immense explosion, especially if both the antimatter and matter was in the form of neutronium. Said neutronium antimatter bomb would explode with the force of <s>35</s> 35000 Chicxulub impactors. <s>Or maybe</s> it was 35,000 of that asteroid that wiped out the dinosaurs. The bomb would explode with a force of 3.5 trillion megatons of TNT = 3.5 billion gigatons of TNT. Chicxulub impactor = 100,000 gigatons of TNT.