What does this technique called? Also, what's the proper notation for this? The audio link is attached below. https://voca.ro/19p4jeWEK5g8 Edit: It sounds like fast arpeggio repeated over and over again with the same voicing.

“Pay careful attention to him and obey his voice; do not rebel against him, for he will not pardon your transgression, for my name is in him.” ‭‭Exodus‬ ‭23‬:‭21‬ ‭ Is that saying the messenger has the ability to forgive but won’t or is it saying the messenger won’t forgive because he can’t? u...

Is it possible to use this single supply, non-inverting, summing op-amp configuration to sum multiple arbitrary DC voltages at unity gain? I've used the inverting summing op-amp config on bipolar power supplies to sum AC and DC input voltages (paired with a second op-amp to 'un-invert' them) but ...

I recognize that the diaeresis is not in the common English language anymore, but I was wondering if Beelzebub was ever spelt Beëlzebub, as I have found quite recently that I was pronouncing Beelzebub incorrectly as I didn't realize that there was a vocal syllable split in between the two e's. Go...

My house was built in the 1950s. I was redoing my bathroom, and I noticed there was a pipe coming out of my pipe. Someone tapped onto the 1/2 inch cold-water faucet bib. What could be the reason for this? Whatever was on the other side of the tap isn't there anymore it was copper tube crimped and...

I would like to express argument $d$ through $f$ and $B$ and to get $d(f,B)$ $$f(d,B)=B\left(\left(\frac{1}{4}-\frac{d}{B}\right)\left( 1-\left(1- e^{-30d/B} \right)^8\right)+\frac{2/B}{3+1/B^2}\left(1- e^{-30d/B} \right)^8\right)$$ How to do it in Mathematica (analytically or numerically)? Clear...

Lets say Bob writes an AI that has the ability to replicate, learn and has a predisposition towards self preservation. As the AI gets smarter, it realizes that it needs to clone itself in order to avoid being shut down. Since it has access to the internet. It teaches itself how to replicate simil...

Suppose a sinner confesses his sins to a priest, receives absolution, completes the penance, but the priest talks about his confessed sins with others. Is the absolution still valid?

I came up with a cryptic clue that I'd like to use, but I'm not sure if it's valid. Less hair?—nonsense! (10)

I recently came across a definition in the dictionary Hobson-Jobson. It's basically a big collection of English words and Anglicizations used or found in India. The entry that's been stumping me is the one for the word 'orombarros,' a word that looks strange even when I know what it means. Oromb...

I'm an avid tauist (tauday.com) and I don't like the fact that Mathematica displays equations with $\pi$ instead of $\tau=2\pi$. I know that I can "force" it to display $\tau$ by e.g. Sum[ArcTan[1/n^2],{n,1,Infinity}] /. [Pi] -> [Tau]/2 (with backslashes) but writing "/. [Pi] -> [Tau]/2" (with ba...

I saw this a real long time ago- I'd say early-mid 80's though I suspect the cartoon itself was much older. An anthropomorphic duck dressed up like a scientist (complete with nerd glasses) was narrating over animated shorts one of which revolved around cavepeople (though they were depicted as hum...

Expanding $\arctan$ around 0 as a Taylor series yields $$ \arctan x = \sum_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{2n+1} $$ for $x$'s that are in the region of convergence. All even terms vanish, which is due to the symmetry $\arctan (-x)=-\arctan x$, i.e. $\arctan$ is an odd function. Now expanding ...

There is a button menu on the edge of my stock Pixel 5 / Android 13 screen that do nothing and are constantly in the way, but I can't figure out how to make it go away. Probably the same problem that is preventing them from launching an app is also preventing configuration. I don't know what thes...

Let's say TikTok is banned tomorrow by Congress. How would they be able to actually enforce the ban, assuming TikTok refused to cooperate? They could definitely convince Apple and Google to remove it from their app stores, however there's also a browser version and Android phones support sideloa...

I am using Manta (https://github.com/Illumina/manta/blob/master/docs/userGuide/README.md) but whenever I try to specify the --exome command using the following code I get the error below: The code in my script: # Accept path to reference fasta file as a parameter: reference=$1 # Accept input an...

I'm looking at this but I'm trying to adapt it to my case where I don't hardcode the variable name. In fact, I'm combining logic from a previous question of mine. Something like this: shopt -s extglob export var=abc_def__123__456 echo ${var/%__*} # does this variable (abc_def) exist? echo This i...

If an Airworthiness Directive is published for your aircraft which makes it illegal to operate until complied, and your aircraft is sitting in the Alaskan wilderness with the closest facility hours away, what is the correct procedure? Would it be against the law to fly it directly to the facility...

I am new to R studio. I tried to use the regression model. I used the semi-log model due to the normality. I summarised the results of the regression. And I found that two variables (called v1 and v2) had 0 predict (estimate) values. V1 and V2 are continuous variables as the control variables. An...

I have a project I am doing where I have to control three simple peristaltic pumps with an Arduino. Originally I started with cheap $13 6 V pumps powered with 9 V batteries which only worked for a day, then wouldn't even work when connected directly to the battery. The circuit works in Tinkercad,...

A Langford sequence is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n, n in which there is one number between the two 1s, there are two numbers between the two 2s, and more generally the two copies of each number k have k numbers in between them. An example would be: 3 1 2 1 3 2 ...

I am learning about control strategies for DC-DC converters. While I find voltage mode control easy to understand, I struggle to understand current mode control. Is the idea here to control the output voltage by controlling the inductor current? If so, what is the relation between them?

I have been seeing small puddles of water in the kitchen. On further investigation I see this water line sticking out from the wall. I don’t see an individual shut off for this and it just started leaking. Any suggestions? I’m assuming it’s an old cap that needs to be replaced, but what are my op...

I met someone at a conference and we had a good conversation. We emailed after for a bit. He is the associate editor of a reasonably well respected journal. He asked me to referee a paper and I just said yes without thinking much about it - he went to my talk and we talked for awhile so I assumed...

Would Paul's comment include all tyrannical governments without the people rising up against them? Rom 13:1 (BLB) Let every soul be subject to the authorities being above him. For there is no authority except by God; but those existing are having been instituted by God. Rom 13:1 (KJV) Let ev...

I am currently writing a review paper (for the first time) on an emerging topic, and the problem is that almost all the that I found regarding this topic are preprints on arxiv. I wanted to know if including them in the review paper is okay or not. This paper is going to be a chapter in my thesis...

I wrote code that solves the subset sum problem via the LLL algorithm, as given in chapter three of the Handbook of Applied Cryptography https://cacr.uwaterloo.ca/hac/ I ran the code on ten random sets, each with positive integers from one to $2^n$, each with a random subset adding up to a target...

What is Judaism's view on using psychedelics (like peyote, ayahuasca, magic mushrooms or cannabis) to receive mystical visions or gain insights? I am well aware of a growing trend nowadays among many people and some cultures (like various Native American tribes) of using what are known as psyched...

Basically, I want to decisively put an end to any idea that lasers could be used in my space combat in any large degree. One of the solutions I've thought of is a world having advanced armour (either through a coating or something else) that is resistant enough to lasers (or I guess heat because ...

The Knowledge Domain cleric's Channel Divinity: Read Thoughts feature (PHB, p. 59-60) lets you read a creature's surface thoughts, and states that while you do so: During that time, you can use your action to end this effect and cast the suggestion spell on the creature without expending a spell...

I'm looking for Bruce W. Jordan's thesis: On the diophantine arithmetic of Shimura curves. Thesis, Harvard University, 1981. I could not find the pdf at the following site. https://www.math.harvard.edu/graduate/dissertations/ I could not find it in my university library either. Would it be possib...

I was visiting the Museum of Science and Innovation in Chicago (highly recommended) and I took the tour of the complete U-Boat that they have housed there. It's extremely well-preserved inside and quite fascinating. However, the guide was not able to shed any light on the quite spectacular number...

The equation of state for and ideal gas states, $PV = mRT$. Since entropy is a state variable, can the equation of state be rewritten in terms of entropy?

One of the annoying problems with most urban fantasy series I've read is that they seem to mostly try to avoid discussing the fact that most of their fearsome magical foes could be felled with a simple gun. Many works just ignore guns entirely and never explain why we should fear the guy that ca...

I’m working on updating the switch to an existing run. It’s a two way switch connected to an outside light. My wife took the receptacle apart and I’m left with the wiring. I see the 12/2 wire as expected but the previous installer apparently marked with a permanent marker in black one side of the...

I think this story was less than 10 pages long, and published in the Scithers era of Asimovs. The main character, a scientist of some sort, I think, receives from a mysterious personage (I don't remember whether it was in person or a delivery) an immensely powerful device (possibly a duplicating ...

If somebody said to me, "I have to work until Friday", would that mean that he still had to work on Friday or would that mean that Friday was already his day off?

Are there any Jurisdictions around the world that allow for consent to be after the fact ? or is there defences that allow for consent obtained after an act to be a defence (as in the accuser or victim clearly being permissive or even indulgive in an act)

In GCM, GMAC, the additional associated data (AAD) (as well as outputs of subsequent blocks) is multiplied by a polynomial H in GF(2^128). This appears to be doing some secure hashing. Is that what's happening, and if so, is this a general hashing method that's used elsewhere?

I recently read this passage form a website and I just can't work out the math. Overall, it says you can be 93.75% confident of having the true median parameter within an interval, obtained from a random sample of 5 out of a 10 000 population. Could someone guide me to obtain this value? Here's t...

My wife and I lived in Massachusetts as our primary residence for 2022. However my wife started a new job that is based in New York and works remotely in 2022. However, this job required her to have a New York based address so she filled out her W4 with her parent's New York address. Where/how do...

Given the following problem $$u_{tt}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$ $$u(x,0)=f(x)$$ $$u_t(x,0)=g(x)=0$$ Where $ f(x)=y_0(x) $ $y_n$ are the Eigenfunctions that defined as $ y_n(x)=\exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x) $ By separation we assume $$u(x,t...

In Jewish and Christian tradition, it is said that God created humans from dust. In Islam, it is said from a clot. Why is that difference? Are the two terms just metaphors?

I am writing a review for a journal. In the instructions, it contains the following quote: "Your comments may be forwarded in their entirety to the author by the Review Editor, so state your opinions impersonally and objectively". What does this mean? Are opinions not by definition personal and s...

I have a Python script that I am currently using to (excuse the confusing description) rename a given object's material's image-datablock-names to their actual filenames. It works correctly, for a single selected object. When selecting multiple objects it only executes on the first object. Is the...

I have encountered a text (a specification) in which this: FFT(f(x)) = f(FFT(x)) is clearly presumed (for the functions they are applying). This is, I believe a composite function and the property sought is commutativity (of the composite function). Here's what chatGPT had to offer: Regarding t...

I have recently purchased a home in Illinois. The yard was in terrible condition before. There were big bushes growing all around the yard (as shown in picture two). Now there are only patches of grass growing. There’s also a large tree that drops a lot of acorns which hinders the growth of gra...

I have been looking around for an answer to this question but can't really come up with anything. Given some oracle, $U$, that maps $| 0 \rangle$ to $| \psi \rangle$, is there some algorithm that determines whether $| \psi \rangle$ is entangled or separable? I think there must be an algorithm for...

Let us take $$ \mathbb{N} := \{ 1, 2, 3, \ldots \}, $$ and let the function $f \colon \mathbb{N} \longrightarrow \mathbb{N} \times \mathbb{N}$ have the following values: $$ \begin{align} & f(1) := (1, 1), \\ & f(2) := (1, 2), f(3) := (2, 1), \\ & f(4) := (1, 3), f(5) := (2, 2), f(6) := (3, 1), \\

The party, which includes a bard and a wizard both with counterspell, will soon be facing a marid. The marid's total time on the battlefield will likely largely depend on whether or not he is able to get off his conjured water elemental to act as a blocker. The marid has Innate Spellcasting with...

In some polylines stored in PostGIS, I found Z values equal to NaN. For example: LINESTRING Z (30 10 0, 10 30 nan, 40 40 nan) I want to replace the 'nan' with 0 to prevent subsequent errors.

I encountered the following exercise in calculus course: Let $U$ be a convex open subset of $\mathbb{R}^n$ and $f \colon U \to \mathbb{R}^n$ differentiable. Suppose that $\lVert Df(\mathbf{x}) - I_n \rVert < 1$ for all $\mathbf{x} \in U$ where $I_n \colon \mathbb{R}^n \to \mathbb{R}^n$ is an ide...

I've built an over voltage protection circuit according to this schematic by Maxim: If the load is low power consumption like MCU or other ICs, it works just fine. If the load is higher for example, 350mA (maybe DCDC circuit,) the circuit starts to draw 2x current of the load (would be up to 700...

And God helped him against the Philistines, and against the Arabians that dwelt in Gurbaal, and the Mehunims.(2 Chronicles 26:7) Question- I have a question concerning the location of Gur-baal. I am reading multiple commentaries and they all have different answers. Some say its Gur a place in P...

In the TV show, Succession, Ep 1, Season 1, Roman Roy teases a boy by promising one million dollar if this boy could hit a home run in a baseball game. It ends up with Roman tearing up the one million dollar check into pieces in front of the boy. Logan Roy sends his lawyer over to the boy and his...

My minimal demo is given as follows \documentclass{article} \usepackage{amsmath,amssymb} \begin{document} $$ \begin{aligned} \text{quantitative} &= \left\{ \begin{gathered} \text{continuous}\\ \text{discret} \end{gathered} \right. \\ \text{qualitative} &= \left\{ \begin{gathered} \text{nomina...

What does the real value of Sliver polygon represent? it's not the area of the polygon it's not the perimeter is not the area of the bounding box so I ask if anyone can tell me what it represents, I can't find anything useful in the documentation. https://docs.qgis.org/3.28/en/docs/user_manual...

For my new paper, I need to use the notations and definitions of another paper that I wrote in 2019. The notations and definitions take about 3 pages. I really don't know what to do, can I copy and paste the notations for the convenience of the reader? Or simply just reference the notations? It i...

I feel like there is something wrong with my circuit. I'm trying to do an AC sweep simulation to find the transfer function frequency response from input to output.

I know for the same user name, we can do: ssh-keygen ssh-copy-id to skip entering the password. However, in my understanding, this is for remote and client servers both have the same user name. However, the user name in the remote server didn't in my client server, how can I do ssh-copy-id here...

For any $C^\ast$-algebra $A$, don't we have the isomorphism $\mathcal{H}_A \oplus \mathcal{H}_A \cong \mathcal{H}_A$? In some places, it is only mentioned when $A$ is $\sigma$-unital. But $\mathcal{H}_A \cong A \otimes l^2$, and since tensor product commutes with direct sums, we should be getting...

Type the first line of following code and press enter key. RowBox[{"-", "(", "3", "+", "5", ")"}] // DisplayForm -(3+5) -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ The output is -(3+5). Now drag and copy the output and paste it to a new line. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+...

I tried to use GDB to debug Emacs. More specifically, I want to observe the behavior of a function written in C. vertical-motion is a built-in function in ‘C source code’. However, the name of a C function cannot contain a - (i.e., minus sign). So GDB will complain when I type break vertica...

When I try to load WFS layer it shows blank area, even there is some information in attribute table. And instead on vector layer it shows new icon. Here is the source: https://www.avoindata.fi/data/fi/dataset/oulun-kaupungin-aanestysaluejako Here is WFS link: https://e-kartta.ouka.fi/TeklaOGCWebO...

I need a website where I can find free chess ebooks? I would like to see a list of free books to download or read online.

I searched for information on data scientist pay by country but was unable to find any. I am aware that the US pays data scientists an absurdly high salary (well, maybe not "insanely high" by American standards), but I seldom ever hear about any other nations, probably with the exception of the U...

I am trying to understand how channels work. I created a blank 8bit RGB document in Photoshop and filled the background layer with 50% gray. But however, when I navigate to channels and click on R, G or the B channel, I can see that the channels are not 50% gray. They are somewhat a lighter shade...

I'd like to print out two minus signs just after each other, like this -- (as in the C operator to subtract one). Doing -- gives one longer - sign. I've tried \char"2D\char"2D but that also just gives one longer - sign. How can this be done?

My parents insist they remember contrails being significantly shorter around 1980s. From my research it seems this might be the result of several factors such as climate change, advancements in aviation technology (engine design, fuel types) or changes in common aviation procedures. Of course, th...

$$\int_0^4 \frac{\left(y^2-4 y+5\right) \sin (y-2)}{2 y^2-8 y+11} d y$$ Here is my attempt $$ \begin{aligned} & y-2=t \Rightarrow d y=d t \\ & y^2-4 y+4=t^2 \Rightarrow 2 t^2=2 y^2-8 y+8 \\ & {y^2-4 y+5=t^2+1} \\ & 2 y^2-8 y+11=2 t^2+3 \\ & 2 y^2-8 y+10+1=2 t^3+3 \\ & 2\left(y^2-4 y+5\right)+1=2 ...

Reluctant DBA here. Do I really need a backup when using REPAIR_ALLOW_DATA_LOSS? I am well aware MS recommends doing a backup. What's the worse that could happen if I run a DBCC CHECKTABLE using REPAIR_ALLOW_DATA_LOSS? A bit of background. A client wants to migrate the DB used by our software fro...

Data I have a set of locations for weather stations (download easily from here: https://archive.ceda.ac.uk/cgi-bin/midas_stations/search_by_county.cgi.py?county=SHROPSHIRE&minyear=&maxyear=). Problem I want to plot them in QGIS, but when I import as CSV file, it places them in the completely wron...

I have 100 .cif files. I want to convert them all to .vesta files through vesta software (https://jp-minerals.org/vesta/en/download.html). I know I can choose them one by one and convert them. Is there any method better than this? Example of .cif file: data_image0 _cell_length_a 18.685 _cel...

In the following MCE, a tcolorbox is equipped with two rectangles drawn as overlays. The color of these rectangles is supposed to be the same as the bottom color of the tcolorbox. It works well with the color e.g. blue but not with cyan: why? \documentclass{article} \usepackage{tcolorbox} \tcbus...

I know that 10..01 can’t be a perfect square, since it is 2 mod 3, but 10..09 can a perfect square, since it is 1 mod 3. Am I correct?

According to https://dba.stackexchange.com/a/307373/156984, both text[] and text[][] have the same internal type _text. If the internal type of both is the same, how can I then actually differentiate them? SELECT * FROM pg_type; just returns one row, representing both types. I would expect it to ...

I am rebuilding a 6 cylinder BMW engine. The engine had 300,000KM on it. I want to balance the rotating assembly as I want to increase the RPM redline from 6500 to 7000. Upon measuring the pistons after completely cleaning, the below tables are the result. As can be seen, cylinder 4 piston is an...

My potency to provoke, a smile or weeping, Repugnance in my core, I carry its keeping. With a fresh dawn, I set forth to explore, Guided by directions to engulf and implore. Roughly, we are benign cysts, not to fear, Held back, a young lover, I hear. What am I?

According to Griffith's Introduction to Quantum mechanics in section 1.5 Momentum, he said that " the expectation value is the average of repeated measurements on an ensemble of identically prepared systems, not the average of repeated measurements on one and the same system" So, my question is w...

How should I show that the function $f$ defined below is strictly increasing for $x\in(0,1)$? I have considered its first derivative, but it seems too complicated to deduce $f'>0$ from there. $f(x)=\frac{3x^2+4x(1-x)+4(1-x)^2}{4x^2}\ln^2{(1-x)}$ $f'(x)=\dfrac{\ln\left(1-x\right)\left(3x^3+\left(2...

Since, estimator is a function on a statistical(or any?) data to estimate an unknown parameter, will it be valid (or is one allowed to) to define your own estimator, like your own parameter..

The Web page for RSGB dx cluster doesn't have column headings. May be dumb question but what are they?

The introduction of int uncaught_exceptions() noexcept; in C++17 instead of bool uncaught_exception() noexcept; begs the question whether it is possible to have more than one exception at the same time. According to the en.cppreference.com: Return value The number of uncaught exception objects ...

If such a receptacle exists, what is the (US) NEMA designation for a 250V receptacle with a terminal on the back for hot#1, and one for hot#2, a ground terminal, and also a place to attach neutral, where the receptacle is prong-compatible with an L6-20P plug? And are such receptacles available wi...

I was inspired by this great question. Can you place each number from 1 to 8 twice into a 2x8 grid, such that each pair of numbers $k$ are separated by Manhattan distance $k$?

Some monsters, (e.g. the Death Knight) have a reaction called Parry which enables them to increase their AC. Are there any character options that work the same way, i.e. increase AC as a reaction? I am looking for class features, feats, and magic items from official sources that can do this. Some...

I've seen numerous sources, including the RSPCA, making claims along the lines that cats in the UK have a "right to roam", are "free spirits", and therefore that cat owners cannot be held liable for their cat's actions that cause damage. However, there appears to be no actual law that supports t...

I am building a common source amplifier as shown below. As you can see below, the Vsource signal is good sine, but after the capacitor the sine is totally canceled and I get only the DC bias. I am supposed to see the sine with a DC offset after the C2 capacitor. Where did I go wrong?

Most things I've seen claim that 気になる is an intransitive verb and that one major difference from 気にする is the transitivity. This includes examples from this site. However, a native speaker recently mentioned to me that 彼を気になる is fine. Upon further questioning, said native speaker felt that わんこを気にな...

I am currently looking for a language to program a game for my FYP which is to program the game "The game of nim". I am currently looking at pygame for this program, I hope someone can give me suggestions on any other language. I did made a simple python program which use console to show the rock...

The Italian term barista (bartender) entered the English language in 1992 and its usage has considerably increased since then according to Google Books: "bartender in a coffee shop," as a purely English word in use by 1992, from Italian, where it is said to derive ultimately from English bar (n....

Is it correct to assume that if there is only one object in the void (really empty void), then its location (the answer to the question “where” this object is) cannot be established? You need at least two objects to be able to tell where each one is. Or is it theoretically possible to specify whe...

I have a Tektronix TDS640a scope that overall works very well for its age. I also have OEM 500 MHz probes, P6139B. When sampling at or above 25 us, my waveforms look "normal": nice flat signals, with maybe 1 or 2 pixels of "noise". I have the bandwidth filter on here, but I don't really need it f...

This is a theoretical question since I've come across this type of problem many times. Suppose an amplifier is powered between 12 V and -12 V, so the signal output can reach a maximum of 12V. If I am not expecting my signal to be more than a few hundred millivolts, then I should be able to safely...

商人ギルドに店を登録した時にも口添えをしてくれ、商人ギルドから開業資金を借りると、その利子と初年度のギルド会費が相殺されることも教えてくれた。工費がかからなかったとはいえ、貯金は材料費でほとんど持っていかれていたので良かった。初年度のギルド会費が払はらえず営業権剝奪ということもこれで心配ない。 Does this mean that the interest of the debt will waiver the guild's fee? Or does it mean that both of them will be cancelled?

I stumbled across this post: Is it ethical/legal to publish Master thesis manuscript as a journal paper? Let me quote the top poster. However, an MSc thesis is typically 50-100 pages long. A paper is (in a dense journal format) typically 8-12 pages long. Let's make a generous estimate for 20 pag...

Let $A$ be a complex unital Banach algebra, and let $A^\times$ denote the set of (two-sidedly) invertible elements of $A$. Let $\exp : A \rightarrow A^\times$ denote the exponential map. My question is, in general is the exponential map surjective onto $A^\times$? What I understand so far is as f...

This question is taken from a very challenging calculus problems book called the Advanced Problems in Mathematics by Vikas Gupta And I have absolutely no clue on how to approach questions of the kind. My initial thought since y is composite function was to check for a graph similar to the outerm...

The 3rd-level feature of the UA Kensei Monk subclass, Path of the Kensei, reads as follows: You gain proficiency with three martial weapons of your choice. A martial weapon is considered a kensei weapon for you if you’re proficient with it. Whenever you wield a kensei weapon, you choose whethe...

I have a list of twenty different 125-component vectors. I have a bunch of other 125-component vectors which are known a priori to be expressible as a linear combination of these twenty. I want a way to input a 125-component vector and return a 20-component vector which is the coefficient of each...

I am designing a device based on TO-247 MOSFETs. The power is pretty high - about 50W per package, so it's going to be either water-cooling or something big with fins and fan. All is great, except they have the drain connected to the thermal pad. So common heatsink should somehow isolate between ...

Define a Skolem sequence to be a permutation of the sequence of 2n numbers 0, 0, 1, 1, 2, 2, ..., n-1, n-1 in which there are no numbers between the two 0s (the 0s are in adjacent positions), there is one number between the two 1s, there are two numbers between the two 2s, and more generally the ...

Shown below are 3 boxes A, B and C Box A shows 4 rows. Each row has a 3 letter blank. The 3 letters form a single word (same word for all 4 rows). After filling the blanks you should get 4 separate words. Box B shows 3 rows. Each row has a 2 letter blank. The 2 letters form a single word (same...

I'm repeating a bit of set theory these days and was a bit perplexed by the axiom schema of replacement, for which I can't really seem to find a substantial application. After all, if $F: A \to B$ is a function between sets, the image will exist due to separation. I read on WP about some implicat...