There is an infinite sequence of functions $g_1,g_2,\ldots$, each of them is $\Bbb R\to\Bbb R$. Prove that there exists a finite set of functions $f_1,f_2,\ldots,f_n$ such that any function $g_k$ can be expressed as a composition $f_{k_1}\circ f_{k_2}\circ\cdots\circ f_{k_m}$.
I'm painting geometric stuff and know how to mask out straight-lined shapes using tape on canvas (image on the left). However, have always wondered what would be a clean effective way, or most common way, of masking out circular, elliptical, anything non-linear shaped (image on the right). Is the...
I just helped someone with this issue so I thought I'd post this to help anyone having the same issue as there seems to be no question here about it.
Issue: in the Notification area of the desktop you will get a notification about an available update but opening Discover or even using apt or apt...
Formally, I understand that infinite series are not defined by adding up "infinitely many" terms, but are instead defined as equalling their limit. As user Brian M. Scott outlined in an answer to a similar question (Why is an infinite series not considered an infinite sum of terms?), it is easier...
I have a 1662 version of the Aeneid, with Latin and French on facing pages, with the French having been translated by M. de Marolles, Abbé de Villeloin, [additional book info continues: À Paris, Chez Gvillavme De Lvyne, Libraire - Iuré au Palais, en la Gallerie des Morciers, à la Iustice, M. DC. ...
What I mean is an engine whose thrust is on the order of tens to hundreds of Newtons with an ISP "well" above that of chemical engines. I don't require this engine to be space ready - if it has to plug into a mega watt generator and only works on the ground at the moment that's fine - but it must...
So I'm a pianist looking at one of my favorite concertos ever, the Rachmaninoff 2. I had been listening to some symphonic works prior to it, so for some reason I noticed that in the concerto, there was a distinct lack of trumpet lines. Here's a copy: http://imslp.simssa.ca/files/imglnks/usimg/c/c...
This is the last exercise of a quite challenging exercises paper a friend who is taking calculus has which I'm trying to help. I already helped her doing the other bunch. But this got me. I will appreciate anyone help to see my work and to tell me if is right or If I need to correct something.
T...
Almost all aircraft piston engines are four-stroke engines, with one power stroke per piston every other crankshaft revolution and a great deal of intricate moving parts which are only too happy to break. Two-stroke engines, in contrast, have a number of features that would seem to make them exc...
We find many references in the Talmud to what could be perceived as a Sanhedrin, like Chachamim or Beis-Din, or that Hillel and his descendants were the Nessi'im (of a Sanhedrin presumably), but I don't recall a reference to an specific institution of Sanhedrin, with a team of 71/23 (full-time) j...
If $u$ is harmonic and bounded in $B_1(0)\setminus\{0\}$, then can we say that $u$ is harmonic in $B_1(0)$? I believe the answer is yes and I think the way to show it is by the Mean Value Property... but there is a problem. For $|x|<1/2$ and $|x|<r<1/2$, how do we know that $\frac{1}{|B_r|}\int_{...
I have become a TA for a professor who teaches differential equations. The course is basically a self study course where students are to use their previous knowledge to explore and teach themselves differential equations. There is no book for the class which makes this hard for some students. I a...
It seems Apollo missions carried some variety of gray tape, likely Duct Tape or similar. There's the scene in the movie Apollo 13 and the reality behind it discussed in the video below.
Question: How often has duct tape or similar gray tape been used during crewed space missions? What were a few...
A is a special snowflake, though for all the wrong reasons. You see, he was born with a special ability that allowed him to see premonitions of his and his loved ones' future in the form of still images. Of course, future here isn't immutable, and premonitions change as new information comes in.
...
So in the Summer, I was offered to work on a paper with a doctor at my local university. The main goal of the paper is to try and predict the amount of displacement when pressure is applied to a 3D-printed ball of titanium using machine learning. The thing is that the main focus of the paper is a...
I am building an RGBW controller for my room. I will be using an ESP32 with 4 MOSFETs for each channel. I want to know which is best for fast switching. Do I need to use a MOSFET driver IC such as ICL7667 with IRFZ44n or is it better to use lower VGS MOSFET such as AO3400, or something entirely ...
During a project at my work I needed a convenient way to store values taking up the smallest amount of bits necessary, not in memory but later when they're serialized into an array of unsigned short ints. For instance, a value that could be between 0 and 7 was only supposed to be 3 bits long. I e...
If one were to probe with an oscilloscope using the short ground spring clip attachment, and use the ground pad of a decoupling capacitor as the ground, would the measurement be thrown off at all by currents moving to ground through the capacitor? Or is something like a test point pad on the top ...
It is stated that a convert is in the same regard considered a Jew as a native born. Rashi on Dvarim 26:11 states that a convert cannot recite the declaration כי באתי אל הארץ נשמע ה׳ לאבתינו לתת לנו. Why is that? At conversion a convert receives a Jewish neshama, thus making him part of the Jewis...
Piskarev felt one of the elderly, venerable-looking gentlemen grab one
of his coat buttons and submit a most just observation for his
judgement, but he rudely thrust him aside, without even noticing that
he was wearing a fairly important order around his neck.
Can anyone explain to me ...
When we use the integral to calculate the work done by the spring force, then according to my interpretation, we are only calculating the work done by the outermost point on the spring. Why don't we sum (integrate) the work done by all the points?
Am I missing something? Help me out please.
A tool that runs day and night sometimes posts crucial information to the wall. Is there any way to redirect this output to a file for when I'm asleep? Alternatively, does wall keep a log of messages posted to it or is there a way to enable it?
Why isn't the consonant л pronounced in "солнце" ( it is pronounced ['sont͡sə]] instead of [ˈsolnt͡sə] ) ? Is that a result of a pronunciation rule or is it an exception?
I live in a Townhouse in NC, in a community under a HOA management. I've been doing some improvements on my patio. One of them that I couldn't find a solution is what to do with the condensed water from the AC draining. My AC is installed in the attic. 2 drain lines come from it. One is the ...
I stumbled across this page describing the energy of a given object in orbit.
It describes 'total energy' as:
$$E_{k} + E_{p} = E_{\mathrm{total}} $$
where
$$E_k = \frac{1}{2}mv^2$$
and
$$E_p = \frac{-GMm}{r}$$
Towards the bottom of the page it states that if total orbital energy exceeds zero...
I need to draw a simple animated flow chart that describes the flow from each node to node.
In the picture timeframe, denotes how the flow of the animation.
Applications has disappeared from the sidebar in Finder and I don't know how to get it back.
The direction of the force will always be perpendicular to velocity and pointing to the opposite side of the rotation direction. In plain terms, any object traveling in the rotation plane: up (toward the axis), down (from the axis), Westward (spinward) or Eastward (counter-spinward) will seem ...
In a few months I'm switching to a health insurance plan with a $1,600 deductible. After the deductible is met, the plan pays everything, i.e. 0% coinsurance.
As of now, I see a physical therapist each week at a cost of $250. Under the new plan, will I have met my deductible after seven visits ...
I'm looking for a "meta-command" xyz such that:
(echo "foo"; echo "bar") | xyz rev
will return:
foo oof
bar rab
I'd like to avoid temporary files, i.e. I'm looking for a solution neater than:
tempfile=$(mktemp)
cat > $tempfile
cat $tempfile | rev | paste $tempfile -
(And of course I want...
How should the two As be played with the left hand? Why is the second A even necessary?
I encounter a small but annoying problem with the following MWE
\documentclass{article}
\usepackage{hyperref,cleveref}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{thm}\label{good}
Cleveref is good
\end{thm}
\section{Proof of \Cref{good}}
It is trivial.
\end{document}
The com...
I have the following limit:
$$
\lim_{x\to 7}\dfrac{x^2-4x-21}{x-4-\sqrt{x+2}}
$$
I could easily calculate the limit = 12 using the l'Hopital rule.
Could you please suggest any other ways to solve this limit without using the l'Hopital rule?
Thank you
I'm writing a Javascript function for an array, based on a geographic sequence. \$[1, 2, 4, 8, 16]\$, etc.
This function needs to populate the next number in the sequence
$$item_n = item_{n-1} * 2$$
If there are more than \$10\$ items in the array, remove the first
(smallest) number.
...
Proverbs 26:4 says, "Answer not a fool according to his folly, lest thou also be like unto him."
The very next verse, verse 5, says, "Answer a fool according to his folly, lest he be wise in his own conceit."
To answer or not to answer?
This seeming contradiction has me scratching my head. I w...
When designing an exam, would you mention the maximum score per question or not? Is it common practice?
In my view this promotes cherry-picking. This could be seen as a way to prioritize or to satisfice (leaving questions open since "they are not worth it").
Is there any scientific proof/p...
So I'm designing a game. I want to include not just the exported models but the original blender file as well. Am I able to do this without having permission or a licence?
I have a 2011 rs Chevy camaro and I do not have the wheel lock key for the wheel lock. The wheel lock has 7 spline but are uneven and I can't find it anywhere.
These are three-dimensional Nurikabe puzzles. In each case, the four squares represent the layers of a $4\times4\times4$ cube. The goal is to shade some cells in each layer so that the resulting space satisfies the rules1 of Nurikabe:
Numbered cells cannot be shaded.
Unshaded cells a...
In case Brexit has already happened, can it be reversed after a short time?
Legally, the answer is no, I think.
But I can imagine a situation where, during the first few days after Brexit, all participants unanimously agree it should not have happened.
It is at least possible that the first da...
When travelling in the UK, I often see this sign when there are roadworks:
This results in a few questions:
What does this exactly mean and are there specific reasons when is used?
Where will you be recovered to?
Does this replace breakdown cover?
“We have long ago paid the goblins of Moria,” said Thorin.
From chapter 1 of the book The hobbit by Tolkien. What does it mean? Did the goblins pay for their murder or did the dwarves stopped paying them thoughts?
Not a native speaker so some expressions I have to look up, this one I could ...
There's no directory above /, so what's the point of the .. in it?
Latin:
The third-person plural present active indicative form of amare (to love): amant
Participle: nominative ama-ns (genitive ama-ntis)
Gothic:
The third-person plural present active indicative form of frijon (to love): frijond
Participle(noun): frijonds (friend)
Ols Slavic:
The third-pers...
Is there a way to convert the DateObject whose FullForm is:
date1 = DateObject[List[2019,9,14,0,0,0],"Instant","Gregorian",-7.`]
into the following DateObject:
date2 = DateObject[List[2019,9,14],"Day","Gregorian",-7.`]
My list has DateObjects with "Instant" granularity, but I need to use Ca...
Could you please provide some sources about that?
Or maybe there is some rule of thumb to detect if some setting is “High magic” or “Low magic”?
I was watching Professor Gilbert Strang's lecture on Linear Algebra, and in the video, he talks about when we can or cannot say that linear combinations of vectors span the entire region in that dimension.
He said that if we had nine vectors, each of dimension 9, and if the vectors were all ra...
I'm reading the book "Methods of Nonlinear Analysis" written by Pavel Drábek. In this book there's the following proposition:
Let $\gamma$ be a positively oriented Jordan curve,
$\sigma(B)\subset \text{int}\, \gamma $ ($\sigma(B)$ is the set of
all eigenvalues of $B$), and let $f$ be a h...
Please tell me which one is the most correct usage of 迎えにいく
両親が国へ帰るので、空港へ迎えに行きます。
迎えに行きますから、駅に着いたら、電話してください。（The answer is this one but I do not understand why?)
この荷物を郵便局へ迎えに行きます。
今年の夏休みは子供を海へ迎えにきます。
(2) is the correct answer according to the textbook, but I think that (1) is also correct, ...
Imagine you have a function like this:
function compute(uint256 a, uint256 b) external pure returns (uint256) {
return a % b;
}
Does the EVM revert when b is 0?
I have used ln to write symbolic links for years but I still get the order of parameters the wrong away around.
This usually has me writing:
ln -s a b
and then looking at the output to remind myself.
I always imagine to be a -> b as I read it when it's actually the opposite b -> a. This feel...
I went to a library the other day and found Roald Dahl's Matilda. I started reading, and I found what I think might be a typo (but maybe not---Roald Dahl has a quirky writing style):
My transcription:
如果那天我正好是诗情勃发，我还可能这么写：”虽说稀奇，却是事实，...
Here's my attempt at disassembling this:
If ...
I noticed recently that I tend to try and impress others and gather attention, especially with women (I'm a man). I see this as problematic because unlike other sources of craving and attachment, its hard to avoid others.
Thus, I'd like to understand the nature of the craving/grasping/etc. proc...
With refence to Comma-Separated return arguments in C function [duplicate]
,
x=x+2,x+1;
will be evaluated as
x=x+2;
However, in case of the following code
#include<stdlib.h>
#include<stdio.h>
int fun(int x)
{
return (x=x+2,x+1); //[A]
}
int main()
{
int x=5;
x=fun(x);
prin...
Can someone please tell me what I have done wrong here? I can't see what is wrong and have asked many people far smarter than me who also can't spot the error.
I found this program and I was wondering how can I add on a left brace as in the systeme package or in the cases environment? Also is it possible to left align the right-hand side of the equal sign ?
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{4}
2x & {}+{} &...
Specifically, what do the lightning bolt, fist, lightning bolt, and x2 mean?
What did the first ever Hunger Games look like?
Was it like how on YouTube terror assassinations go down, or did they lock them in dangling prisons on top of a volcano and drop them in, or was it some other way?
I'm looking for answers from the movies or books.
I can't understand the circled symbol and didn't manage to google it. It looks like a variable resistance and a capacitor. What does it mean?
I was preparing $\ce{Mn3O4}$ but it was when characterized by XRD, a $\ce{Mn2O3}$ phase existed. Now how can I convert $\ce{Mn2O3}$ to $\ce{Mn3O4}$?
About 20 years ago, I had a book that was definitions of colorful, interesting, unusual, and oddly specific words. One of the words described someone who engaged in (and possibly enjoyed, but I don't remember) the act of destroying or vandalizing monuments.
In this line from the poem "Tête de faune" by Rimbaud, how do I know who "recueille"? Is it "le Baiser" or "le Bois"? To whom does the "qui" refer?
If it is refering the "Bois", how do I refer to the "Baiser"?
I have a piece of latex code:
\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{matrix}
\definecolor{arbitrary}{rgb}{0.9,1,1}
\begin{document}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\b...
Isn't white giving up too much (one tempo in the opening and the bishop pair) for too little (a doubled pawn)?
For example, after
[fen ""]
1. e4 c5 2. Nf3 Nc6 3. Bb5 g6
Bc6 is the second option in Lichess Masters database
I ran into a scenario where JavaScript behaves in a way that is somewhat baffling to me.
Let's say we have an object with two keys foo & bar.
a = { foo: 1, bar: 2 }
Then, I have an array of strings, in this case one 'foo'
b = ['foo']
I would expect the following:
a[b] == undefined
a[b[0]]...
I followed that instruction add optix device for installing Nvidia driver, Optix and compiling Blender. No errors but also no Optix in Blender. Here is debug:
CPU flags:
AVX : TrueAVX2 : True
AVX : True
SSE4.1 : True
SSE3 : True
SSE2 : T...
In Chapter Ten of Deathly Hallows we are presented with the story of Kreacher's escape from Voldemort's cave:
“How did you get away?” Harry asked, and he was not surprised to hear himself whispering.
Kreacher raised his ugly head and looked Harry with his great, bloodshot eyes.
“Ma...
Why is the stock market so unpredictable? If you think about, most of the things we do in a day are pretty predictable. Waking up, deciding what sites to browse, etc. So if we have a good model about how. People behave on a day to day basis, why can't this be transferred to stocks?
I have compiled a document with
\usepackage[showframe]{geometry} to produce the document below with some dimensions of interest annotated in red. What is the difference between dimensions a and b, or between g and h? Basically what do the lines coming from show frame indicate? I had thought t...
Can you place 5 queens on a 11x11 chess board such that they can attack every empty square?
It turns out this problem was answered here:
http://golovolomka.hobby.ru/books/gik/04.shtml
Can you find another solution?
Good luck with this!
Where is the place shown below?
A \fill is 0pt plus 1fill by definition (in LaTeX kernel), but why 1.5\fill gives 0.0pt (the same for other multipliers)?
Example:
\documentclass{article}
\usepackage{expl3}
\begin{document}
\ExplSyntaxOn
\skip_log:n { \fill }
\skip_log:n { 1 \fill }
\skip_log:n { 1.5 \fill }
\skip...
I am a physicist with a limited knowledge of electronic. I usually study my problems extensively on Internet before asking for a help. This means that here I will present both the questions and probable solutions and I would like you to confirm or correct what I wrote.
I would like to obtain a...
I tried searching on my own but can’t even come up with proper search terms.
Prior to medical transition, do people undergo testing for conditions like Congenital Adrenal Hyperplasia or XXY? Although in some cases it’s visually clear that somebody is intersex, in others such as XXY, the person ...
Output Distinct Factor Cuboids
Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors.
Explanations
A cuboid's volume is the product of its three side lengths. For example, a cuboid of volume 4 whose side lengths are integers can h...
I am trying to implement a kind of email verification system with a node.js server with no state.
The strategy
User sends his email to the server
Server generate a 4 digits code based on the email address and sends it to the user via email.
User sends back the received code via email + the em...
A late question inspired by Finger sequence – find the continuation
How should the grid above the '10' be coloured?
Is there a source to the idea of "When it rains it pours" (misfortunes or difficult situations tend to follow each other in rapid succession or to arrive all at the same time) in Judaism?
If I make a link pointing to a shared hosting IP address, does it have any effect on all domain hosted on it?
I've seen this plane but I don't know its name.
I want to install boruta in my anaconda environment, but if I execute
conda install boruta
It displays,
PackagesNotFoundError: The following packages are not available from current channels:
- boruta
Current channels:
- https://repo.anaconda.com/pkgs/main/linux-64
- https://repo.anac...
Anywhere in history did slaves have slaves? (Assuming this wasn’t a common occurrence)
Was there a slave hierarchy?
I read the slavery wikipedia entry, it mentions that in various cultures slaves have retained some rights.
But anywhere in the world, anytime in history, have slaves retained en...
Let $V$ be a (finite-dimensional) vector space and $A \colon V \to V$ a linear map.
Is it true that, if $v$ is an eigenvector of $A\circ A$, then $v$ is an eigenvector of $A$?
I know the converse statement is true.
Im noob here. I tried to make a sci-fi car but when I render it, its like this(see photo).
I dont want these black lines
Doing PhD in new field that does not have enough resources in it.
Most of the information I find are articles written in websites such as medium.com
I really feel awkward citing a website article, as I feel it is not good enough.
It is not from university, it has just the author name, not muc...
There is a lot of information about how to safely unplug USB hard drives. However, the articles tend to stop at the part where the operating system says it is safe to unplug, or where you're sure nothing is writing to the drive, etc.
Relevant set up:
Windows 10 PC or Windows 10 notebook
Extern...
I feel like with today's movies, it would be easy to fill a small booklet with production notes, pictures and background information. Is there a particular reason why programmes (as available for theatre performances) never caught on in cinema?
Suppose a program uses an API which has two implementations:
An MIT implementation which uses GPL libraries
A newer version of it which no longer uses any GPL libraries
Neither is distributed along with the program, one is already present on the system. I don't know which version the programs...
Your task is pretty simple. Given two floats, bitwise xor the binary representation of them, and output that as a float.
For example,
Normal: 16.7472 ^ 123.61 = 7.13402e-37
Binary: 01000001100001011111101001000100 ^ 01000010111101110011100001010010 = 00000011011100101100001000010110
Normal: 2....
Is there a theorem in Real Analysis similar to Cauchy's theorem/Cauchy's Integral Formula from Complex analysis?
If not, then why? What is it about the complex space that makes Cauchy's theorem true?
I'm cross-compiling for an embedded Linux board, based in BCM5892 ARM11 processor.
I need to know about architecture detail of this processor(‘armv6’, ‘armv6j’, ‘armv6k’, ‘armv6kz’, ‘armv6t2’, ‘armv6z’, ‘armv6zk’) for feeding -mcpu flag for compiling my application, but there is no such informa...
In here, i want to show this entropy exist or not exist, namely i
should calculate the integral of $\int_0^c\frac{1}{x\log^2\frac{e}{x}}\frac{1}{2} \log\frac{e}{x}\,dx$. If the result is $ <\infty$, we can say the entropy exists, otherwise it does not exist.
\begin{equation*}
\int_0^1f...
One version of the Pigeonhole principle says that if the cardinality of a set $A$ is greater than that of a set $B$, then there can be no one-to-one function that maps from $A$ to $B$.
Another version says: If $n$ elements are partitioned into $m$ subsets, then at least one subset must contain ...
Yeh I still can't give out the first hint... Bring it on! :D
This puzzle will provide a screenshot in somewhere on Google Earth, please try your best to identify where the location is. The reasons to find out the location should be part of your answer.
Will give a zoom-out image as the next...
In the article here : https://abcnews.go.com/Health/Healthday/story?id=4507808&page=1 it is claimed that
Short-haul flights are usually pressurized at 5,000 to 6,000 feet while long-haul flights are closer to 8,000 feet, according to Thibeault, [M.D., medical advisor, IATA].
But why would t...
Are all men created equal according to Hinduism? Is this predominant western belief based on the Vedas?
This belief is fundamental to most modern Western countries, and it is the second sentence of the US Declaration of Independence:
We hold these truths to be self-evident, that all men are ...
I have seen "engine skirt" and "engine nozzle" both used for the bell-shaped end of a rocket engine. Is there a difference?