Aarushhh/wikipedia-simple-splitted huggingface dataset:
About eight months after River and Simon have joined Serenity's crew, the ship's captain Malcolm "Mal" Reynolds takes River with him to rob a bank. While they are robbing the bank, Reavers attack. After they escape back to Serenity, Simon argues with Mal. Mal decides to leave Simon and River at their next stop. While at their next stop, River starts a fight that is started by a subliminal message broadcast by the Alliance in a commercial. Mal lets Simon and River keep traveling on Serenity while the crew talks to a techno-geek known as Mr. Universe. Mr. Universe lives on a planet inside a giant cloud of objects in space that does not let people see there is a planet there. Mr. Universe watches a video of the fight and finds the subliminal message. He also sees that River said the name "Miranda." Mal gets a call from Inara, a former passenger. He knows it is a trap, but also knows that she must be in danger. Mal goes to her. He is confronted by the Operative
. The Operative tells Mal that he will let him go if Mal turns River over to him. Mal refuses and they escape from the Operative and go back to Serenity. The crew finds out that "Miranda" is an unknown planet near the edge of the solar system. To get to Miranda, they would have to cross into Reaver territory. They think this is too dangerous. Serenity instead goes to Haven which is home to another former passenger, Shepherd Book. When they get to Haven, the crew sees that it has been attacked by the Alliance. They also see that Shepherd Book was hurt very bad and dying. The Operative sends a message saying he did it. He said he will keep doing things like it until River is given to him.
Mal orders that Serenity be made to look like a Reaver ship. They get the disguised ship through a fleet of Reaver warships. When they get to Miranda, the crew finds everyone that lived there is dead. There are dead bodies everywhere but they can not tell how the people died. The crew finds a video made after the disaster by an Alliance ship. It tells them that the Alliance made a chemical that was susposed to stop aggression and make the planet free of violence. The chemical worked so well that the people stopped doing everything, including eating, and let themselves die. In a tenth of a percent of the people, the chemical had the opposite effect. It turned them very aggressive and caused mental problems: they became the Reavers. Mal wanted to show this secret to all the worlds by using Mr. Universe's equipment. The Operative figures out where they are going and waits just outside of Reaver space with an Alliance fleet
. Knowing that the Operative is likely to be waiting for them, Serenity opens fire on one of the Reaver ships while coming back. The other Reaver ships chase after them. Serenity leaves Reaver space and pass through the cloud around Mr. Universe's planet while being chased by the entire Reaver fleet. There is a large fight between the Alliance and the Reavers. The fight lets Serenity's pilot Wash to fly down to the planet. The Operative's ship is destroyed, and he also goes to the planet in an escape pod.
Serenity crashes on the planet. While the ship is damaged very badly, the crew has survived. Just as everyone begins to relax, a Reaver harpoon hits Wash, and kills him. The crew leaves Serenity and finds a place to fight off the Reavers while Mal goes to get to Mr. Universe and send the message. Mal finds Mr. Universe has been killed and his equipment is destroyed. He finds a message that tells him about a hidden backup transmitter. The Reavers attack the crew, and make them move back. The crew tries to close a blast door, but it will not shut all the way. River dives through the hole in the door and closes it from the other side. This traps her with the Reavers. Mal gets to the other transmitter. The Operative gets there also and they fight. Mal wins but does not kill the Operative. He leaves him to watch the video from Miranda as it is being broadcast. Mal goes back to his crew. As he is told what River did, the blast door opens to reveal River standing unhurt on an large pile of dead Reavers
. A group of Alliance soldiers show up but the Operative orders them not to fight because of what he has seen on the video. The crew buried their dead and fixed Serenity. Serenity leaves the planet with Mal in Wash's seat as the pilot, and River as his copilot.
Cast 
 Nathan Fillion as Malcolm "Mal" Reynolds. A former soldier on the losing side of the Unification War, he live his life outside of the Alliance. Captain Malcolm Reynolds was named #18 in TV Guide's "25 Greatest Sci-fi legends" list in 2004.
 Gina Torres as Zoe Washburne (née Alleyne). Another veteran who fought alongside Mal in the war. Zoe is Wash's wife. She is very loyal to Mal.
 Alan Tudyk as Hoban "Wash" Washburne. The pilot of the ship, and Zoe's husband. He often acts as a voice of reason on the ship.
 Morena Baccarin as Inara Serra. She is a Companion who once rented one of Serenity's shuttles.
 Adam Baldwin as Jayne Cobb. A mercenary who is very good with weapons. Jayne is often the "main gun" for jobs. He is someone who is good in a fight. He seems dumb, but may be smarter than he lets on. As Whedon says many times, he is the person that will ask the questions that no one else wants to.
Jewel Staite as Kaywinnit Lee Frye. Kaylee, the ship's mechanic. She is known for always seeming bright and happy.
 Sean Maher as Simon Tam. Simon is River's brother. He rescues her from the Alliance. He and River are taken in by the crew of Serenity. A surgeon before the rescue, he is the doctor to the crew. His life is all about his sister's needs.
 Summer Glau as River Tam. River is a seventeen-year old genius with special powers. She and her brother are taken in by the crew of Serenity after he rescues her from an Alliance. The Alliance's hunt to find River is mainly what the movie is about. The movie is also the "story of Mal as told by River."
 Ron Glass as Shepherd Derrial Book. A shepherd, or preacher, with a mysterious past, Book was once a passenger on Serenity, but now lives on the planet Haven.
 Chiwetel Ejiofor as The Operative. An evil employee of the Alliance given the job to find River and Simon.
David Krumholtz as Mr. Universe. A "techno-geek" who is friends with the crew of Serenity, especially Wash. Mr. Universe lives with his "love-bot" wife and watches incoming signals from around the 'verse (universe).
Themes 
While the movie shows the Alliance as an all-powerful regime, Whedon is careful to point out that it is not that simple. "The Alliance isn't some evil empire", he says, but a largely benevolent bureaucratic force. The Alliance’s main problem is that it cannot and should not try to control all the different cultures that are a part of it. The crew of Serenity, and specifically Mal, show the idea that people should have the right to chose for themselves, even if those choices are bad.
The Operative is all that the Alliance stands for. He is, as Whedon described, the "perfect product of what's wrong with the Alliance". He is someone who is a force for good, who wants to help make his (and the Alliance's) image of a "world without sin." The Operative believes so much in this idea that he do anything to make create that world . Mal is the opposite. At the movie's beginning, he is a man who has lost all faith. By the end of the movie, however, Mal finally believes in something—freedom of choice—so strongly that he is willing to die to preserve it. Whedon has said that the most important line in the movie is Mal's to the Operative at its end: "I'm going to show you a world without sin." Whedon's point is that a world without sin is a world without choice, and that choice is what defines humanity. The Operative, who does only what he is told to do, and the inhuman Reavers, created by the Alliance's need to control people, are only two examples of this theme.

Notes
Notes

References
 DeCandido, Keith R.A. Serenity. August 30, 2005. .
 Whedon, Joss. Serenity: The Visual Companion. September 1, 2005. .

Other websites 

 
 Official website of the film
 Official Australian website 
 SerenityMovie.com  - A major Serenity fan site
 FireflyFans.net - Another major fansite
 Serenity  at Whedonesque.com
 

2005 action movies
2005 science fiction movies
American action movies
American science fiction movies
Movies based on TV series
Movies directed by Joss Whedon
Screenplays by Joss Whedon
Whedonverse
Hugo Award winning movies
Post-apocalyptic movies
Universal Pictures movies
Joinery often refers to the part of woodworking that involves the joining together of parts of wood.

Traditional wood joinery techniques use
the distinctive material properties of wood, often without mechanical fasteners. There are different types of joinery for different structures, for example the joinery used
to build a house is different from that used to make puzzle toys,
although elements overlap.

Wood is strong when stressed along the grain (longitudinally), but weak across it (radially and tangentially). It expands and contracts in response to humidity.
This change is very small longitudinally.  It is considerable, but unequal,
in the radial and tangential directions.

Images of different types of joints

Styles of joinery
Two of the most common traditions of joinery are Japanese and European. The Japanese in particular developed hundreds of types of joints and their furniture was often held together without glue or nails.

Related pages
Woodworking
References
 Bernard Jones (Ed.) (1980). The Complete Woodworker.   
 Peter Korn (1993). Working with Wood.   
 Sam Allen (1990). Wood Joiner's Handbook. Sterling Publishing. 
 Wolfram Graubner (1992). Encyclopedia of Wood Joints. Taunton Press. 

Woodworking
George Grenville (14 October 1712–13 November 1770) was Prime Minister of Great Britain. He was a member of the Whig Party. He was one of the few prime ministers who never was given a title of nobility.

Grenville was the second son of Richard Grenville and Hester Temple. His older brother was Richard Grenville-Temple.  Grenville went to school at Eton College and at Christ Church College, Oxford.  He entered Parliament in 1741 as member for Buckingham, and represented Buckingham until his death.

As Treasurer of the Navy in 1758 he introduced and carried a bill which established a fairer system of paying the wages of sailors. He stayed in office in 1761, when Pitt resigned, and in the administration of Lord Bute acted as Leader of the House of Commons. In May 1762 he became Secretary of State for the Northern Department, and in October First Lord of the Admiralty; and in April 1763 he became First Lord of the Treasury and Chancellor of the Exchequer.
While Prime Minister, his government oversaw the prosecution of John Wilkes and the passing of the American Stamp Act 1765, which led to the first disagreements between American colonies and Great Britain that led to the American Revolutionary War.  

After many years of being Prime Minister, he began to have disagreements with young king George III.  The king started to think that the Prime Minister was using him as a puppet.  The king convinced Rockingham to become the new Prime Minister and Grenville never held an office again.
Grenville was called the "gentile shepherd" because he bored the House by asking over and over again, during the debate on the Cider Bill of 1763, that somebody should tell him "where" to lay the new tax if it was not to be put on cider. Pitt whistled the air of the popular tune Gentle Shepherd, tell me where, and the House laughed. Though few excelled him in a knowledge of the forms of the House or in mastery of administrative details, he lacked tact in dealing with people and with affairs.

In 1749 Grenville married Elizabeth Wyndham (before 1731-5 December 1769), daughter of Sir William Wyndham. They had seven children.

1712 births
1770 deaths
Politicians from London
Whig party (UK) politicians
Prime Ministers of Great Britain
Harald Sigurdsson was also known as Harald of Norway (;  – 25 September 1066). He was also called Hardrada (, modern Norwegian:  ("stern counsel" or "hard ruler") in the sagas). 

Harald was King of Norway (as Harald III) from 1046 to 1066. Also, he unsuccessfully claimed the Danish throne until 1064 and the English throne in 1066. Before becoming king, Harald had spent about fifteen years in exile as a mercenary and military commander in Kievan Rus' and of the Varangian Guard in the Byzantine Empire.
When he was fifteen years old, in 1030, Harald fought with his half-brother Olaf against Cnut (Canute). Olaf sought to reclaim the Norwegian throne, which he had lost to the Danish king Cnut the Great two years before. In the battle, Olaf and Harald were defeated by forces loyal to Cnut.  Harald was forced into exile to the Kievan Rus'.  After some time in the army of Grand Prince Yaroslav the Wise, he moved on to Constantinople with his companions around 1034. In Constantinople, he commanded the Byzantine Varangian Guard. 

Harald got wealthy during his time in the Byzantine Empire. He shipped the money to Yaroslav in Kievan Rus' for safekeeping. He finally left the Byzantines in 1042. He arrived back in Kievan Rus' to prepare his campaign of reclaiming the Norwegian throne. In his absence Olaf's illegitimate son Magnus the Good had got the throne. Magnus had also become king of Denmark.
In 1046, Harald joined forces with Magnus's rival in Denmark the pretender Sweyn II of Denmark, and started raiding the Danish coast. Magnus, unwilling to fight his uncle, agreed to share the kingship with Harald, since Harald in turn would share his wealth with him. The co-rule ended abruptly the next year as Magnus died, so Harald became the sole ruler of Norway. 

Domestically, Harald crushed all opposition, and outlined the union of Norway under a national rule. Harald's reign was probably one of relative peace and stability, and he set up a viable coin economy and foreign trade. Probably seeking to restore Cnut's "North Sea Empire", Harald also claimed the Danish throne, and spent nearly every year until 1064 raiding the Danish coast and fighting his former ally, Sweyn. Although the campaigns were successful, he was never able to conquer Denmark.
Not long after Harald had renounced his claim to Denmark, the former Earl of Northumbria, Tostig Godwinson, brother of the English king Harold Godwinson, pledged his allegiance to Harald and invited him to claim the English throne. Harald invaded Northern England with 10,000 troops and 300 longships in September 1066, raided the coast and defeated English regional forces of Northumbria and Mercia in the Battle of Fulford near York. Although initially successful, Harald was defeated and killed in an attack by Harold Godwinson's forces in the Battle of Stamford Bridge, which wiped out almost his entire army. Modern historians have often considered Harald's death, which brought an end to his invasion, as the end of the Viking Age.  The famous Anglo-Saxon Chronicle records these events.

References

1015 births
1066 deaths
Kings and Queens of Norway
The Normans were Vikings who settled in northern France. There they made a kingdom called Normandy.

In 1066 the Normans attacked England and took over. The battle was called The Battle Of Hastings. They ruled England for about 300 years. There they built the Tower of London, Windsor Castle and many other stone castles.

Norman life

Clothes 
Normans wore woollen tunics and sometimes they wore a waistband to keep the tunic in place. The men also wore long cloaks.

Food 
Normans ate dairy, oatmeal porridge, green vegetables and sometimes meat. They often used honey as a sweetener and for mead (an alcoholic drink).

Castles 
Normans built many stone castles that often had moats around them to protect them from intruders.

Houses 
Norman houses had a wooden frame with sticks and twigs woven in between, which is called wattle, and then it was all covered in a layer of daub which was made from mud, wet clay, dung and straw. The roofs were usually thatched.
Normans in Ireland 
Diarmuid MacMurrough, King of Leinster kidnapped the King of Breifne’s wife. Then Rory O’Connor, the High King of Ireland fired him from being the King of Leinster. Diarmuid still wanted to be king so he hired some Normans, lead by Strongbow to help him get the throne back. Diarmuid had to pay Strongbow so he said that he could marry his daughter and become king when Diarmuid died. Strongbow agreed to this. They first came to Ireland at Bannow Bay, Wexford in 1169 and soon they got the throne back for Diarmuid. King Henry II, King of England and part of France, thought that Strongbow was getting too powerful since Strongbow wasn’t actually the king, so Henry decided to take over the whole of Ireland. He sent over some other Normans who arrived at Ireland in Baginbun, Wexford in 1170. Then King Henry II became King of Ireland as well.

While the Normans were in Ireland they built the original Dublin castle and many other stone castles.
Normans probably introduced rabbits and fallow deer to Ireland for meat and skins.

References 

Ethnic groups in Europe
Germanic tribes
Middle Ages
Normans
Captain is a military rank.  

Captains are officers in an army.  In a navy, the commander of an entire ship is called "Captain" even if he is actually a lower rank. A Navy Captain rank is equal to the army rank of colonel. Another type of captain may command a merchant vessel or other ship that is not in a navy. 

There are also captains in other uniformed organisations, including the police. A leader of a sports team is also called a captain, as well as the pilot of an airliner.

Military ranks
Law enforcement occupations
Ships
Wire rope consists of several strands laid (or 'twisted') together like a helix. Each strand is likewise made of metal wires laid together like a helix. Initially wrought iron wires were used, but today steel is the main material used for wire ropes.

History & materials
Modern wire rope was invented by the German mining engineer Wilhelm Albert in the years between 1831 and 1834 for use in mining in the Harz Mountains in Clausthal, Lower Saxony, Germany. It was quickly accepted because it was better than ropes made of hemp or to metal chains, such as had been used before.

Wilhelm Albert's first ropes consisted of wires twisted about a hemp rope core, six such strands then being twisted around another hemp rope core in alternating directions for extra stability. Earlier forms of wire rope had been made by covering a bundle of wires with hemp.
In America wire rope was later manufactured by John A. Roebling, forming the basis for his success in suspension bridge building. Roebling introduced a number of innovations in the design, materials and manufacture of wire rope.

Manufacturing a wire rope is similar to making one from natural fibres. The individual wires are first twisted into a strand, then six or so such strands again twisted around a core. This core may consist of steel, but also of natural fibres such as sisal, manila, henequen, jute, or hemp. This is used to cushion off stress forces when bending the rope.

Construction & specification
The specification of a wire rope type, including the number of wires per strand, the number of strands, and the lay of the rope, are is documented using a commonly accepted coding system, with abbreviations. For example, the rope shown in the figure "Wire rope construction" is designated:

6x19 FC RH OL FSWR
6x19 FC RH OL FSWR

Each of the sections of the wire rope designation described above is variable. There are therefore a large number of combinations of wire rope that can be specified in this manner. The following abbreviations are commonly used to specify a wire rope.

Other websites 
 Modern history of wire rope

Hardware (mechanical)
Ropework
Finnish mythology has several different kinds of Liekkiö ("flamey").  One of them is Ihtiriekko, a ghost of a bastard child.

Stories tell that a woman had sex with someone else than her husband. Maybe she did not even have a husband. She then get pregnant and gave birth to a baby. This way to make a baby was not accepted by church and society - that kind of baby is called bastard. Mother had to kill her bastard child to avoid being blamed by priests or other people. Mother then buried child outside graveyard and without priests blessing the body. The soul of the baby could not go to heaven because their body was not at a graveyard and was not blessed by a priest. This is why they became a ghost.

This ghost could make terrible noise until somebody dugs up their body and buries it in graveyard. Such ghost people are called Ihtiriekko. Ghosts could also be quiet, but they might be seen as a flame in forest, like will o' the wisp. Such ghost people are called Liekkiö.

Finnish mythology

es:Ihtiriekko
A bastard is a person who was born of parents who are not married to one another. It is considered by some cultures and individuals as a nasty or insulting word, or sometimes even profanity, with the term illegitimate being a little more polite. Some cultures see illegitimate children as dirty or bad, and only accept sexual relations between married couples.

Related pages
 Illegitimacy

Pejoratives
English profanity
In formal number theory a Gödel numbering is a function which assigns to each symbol and formula of some formal language a unique natural number called a Gödel number (GN). The concept was first used by Kurt Gödel for the proof of his incompleteness theorem. 

A Gödel numbering can be interpreted as an encoding where a number is assigned to each symbol of a mathematical notation, and a stream of natural numbers can then represent some form or function. A numbering of the set of computable functions can then be represented by a stream of Gödel numbers (also called effective numbers). Rogers' equivalence theorem states   criteria for which those numberings of the set of computable functions  are Gödel numberings.

Definition

Given a countable set S, a Gödel numbering is an injective function

with both f and  (the inverse of f) being computable functions.

Examples
Examples

Base notation and strings
One of the simplest Gödel numbering schemes is used every day: The correspondence between integers and their representations as strings of symbols. For example, the sequence 2 3 is understood, by a particular set of rules, to correspond to the number twenty-three. Similarly, strings of symbols from some alphabet of N symbols can be encoded by identifying each symbol with a number from 0 to N and reading the string as the base N+1 representation of an integer.

References 

 Gödel, Kurt, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", Monatsheft für Math. und Physik 38, 1931, pages 173–198.

Further reading
 Gödel, Escher, Bach: an Eternal Golden Braid, by Douglas Hofstadter.  This book defines and uses an alternative Gödel numbering.
Gödel's Proof by Ernest Nagel and James R. Newman.  This book provides a good introduction and summary of the proof, with a large section dedicated to Gödel's numbering.

Number theory
In mathematics, computer science and linguistics, a formal language is one that has a particular set of symbols, and whose expressions are made according to a particular set of rules. The symbol  is often used as a variable for formal languages in logic.

Unlike natural languages, the symbols and formulas in formal languages are syntactically and semantically related to one another in a precise way. As a result, formal languages are completely (or almost completely) void of ambiguity.

Examples 
Some examples of formal languages include:

 The set of all words over 
 The set , where  is a natural number and  means  repeated  times
 Finite languages, such as 
 The set of syntactically correct programs in a given programming language
 The set of inputs upon which a certain Turing machine halts

Specification 
A formal language can be specified in a great variety of ways, such as:
Strings produced by some formal grammar (see Chomsky hierarchy)
 Strings described or matched by a regular expression
 Strings accepted by some automaton, such as a Turing machine or finite state automaton
 Strings indicated by a decision procedure (a set of related yes/no questions) where the answer is 'yes'

Related pages
 Language for languages in general
 Syntax for the form of a language in general
 Semantics for the meanings in a language
 Natural language for languages that are not formal
 Computer language for application of formal languages in computing
 Programming language for the application of formal languages to program computers

References

Further reading

Other websites 
 http://icalp06.dsi.unive.it/  ICALP 2006 33rd International Colloquium on Automata, Languages and Programming.
 http://www.cs.auckland.ac.nz/CDMTCS/conferences/dlt/DLTConfSeries.html International Conferences on Developments in Language Theory

Mathematics
Theoretical computer science
Linguistics
In computer science, an alphabet is a finite non-empty set. The elements of an alphabet are called the letters or symbols of the alphabet.

An example of an alphabet is  which may be used for Morse code or {begin, if, else, for, while} which may be the keywords of a Programming language.

The set of natural numbers is not an alphabet because as it is not finite.

The alphabet which is used the most in computer science is {0,1}. It is called the binary alphabet because it contains two symbols. An alphabet can be used to make a string (or word). This is a finite Sequence of letters from the alphabet. For example, a string of length 5 over {0,1} is 01101.

The empty string is the string containing no letters (it is often written as ). The empty string is a string over any alphabet.

If we have an alphabet called , then we write the set of all strings that can be made from  as . This is called the Kleene star (or Kleene closure) of . It is named after the mathematician Stephen Cole Kleene.
The Kleene star of the binary alphabet is . The three dots after 001, show that we cannot write the Kleene star of an alphabet in full because it is an infinite set.

Alphabets are important because they are used in studying formal languages, finite automata and very difficult questions in computer science about what can be computed and what can not.

Related pages
Formal language
Syntax
Semantics

References
References 

 Arto Salomaa, Formal Languages, (1973): Chapter 1
 Michael A. Harrison, Introduction to Formal Language Theory, (1978): Chapter 1.2
 John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley Publishing, Reading Massachusetts, (1979). .
 György E. Révész, Introduction to Formal Languages, (1991): Chapter 1.1
 Grzegorz Rozenberg and Arto Salomaa, Handbook of Formal Languages: Volume 1. Word, Language, Grammar, (1997): Chapter 2.1
 Dan A. Simovici and Richard L. Tenney, Theory of Formal Languages with Applications, (1999): Chapter 2.1
 Keijo Ruohonen, Formal Languages, (2009): Chapter 1.1
 John Martin: Introduction to Languages and the Theory of Computation (2010): Chapter 1.5

Computer science
The empty string is the unique string of no characters over some alphabet Σ. It is written as ε or λ. The length of this empty string is 0. 

In simple words, given some characters of an alphabet, the empty string is the word that can be made if no letters are used. There is of course only one such word.

Under concatenation, the empty string is the identity element of the free monoid on Σ. That is, for any string s, sε = εs = s.

Representations 
In many programming languages, the empty string is written with two double quotes: "". The empty string is also sometimes noted by the Greek letter λ.

Implementation 
In C, the empty string is represented by a character array with a null character in the zeroeth position. Note that all strings in C are terminated by a null character.

Computer science
Mathematics
Old Possum's Book of Practical Cats is a book of poems about cats. The cats in these poems act like humans. It is by T. S. Eliot. It was first sold in 1939. Andrew Lloyd Webber used most of the poems in his musical Cats.

Contents of Old Possum's Book of Practical Cats by T. S. Eliot:
 The Naming of Cats
 The Old Gumbie Cat
 Growltiger’s Last Stand
 The Rum Tum Tugger
 Mungojerrie and Rumpelteazer
 Old Deuteronomy
 The Pekes and the Pollicles
 Mr. Mistoffelees
 Macavity: The Mystery Cat
 Gus: The Theatre Cat
 Bustopher Jones: The Cat about Town
 Skimbleshanks: The Railway Cat
 The Ad-dressing of Cats
 Cat Morgan Introduces Himself (added in the 1962 edition and not included in the musical)

References
Old Possum's Book of Practical Cats 

1939 books
20th-century British poems
Concatenation is a simple concept from linguistics, mathematics and computer science. It is a way of making a new word (or string), by joining two (or more) other strings. For example, the concatenation of "snow" and "ball" is "snowball". In most languages if we write  x = "snow" + "ball", then the value of x will be "snowball". But to do the same in SQL we would write "snow"||"ball".

Computer science
In mathematics, the identity element (or neutral element) of a set is a special element of that set. It is special because if it is combined with another element of that set, it does not change the other element.

With addition, the identity element is 0, because adding 0 to some number does not change the number. With multiplication, it is 1. In a group (an algebraic structure in mathematics), the identity element is sometimes denoted by the symbol .

Further Examples

Related pages 

 Identity (mathematics)
 Null vector
 One
 Zero

References 

Algebra
Abstract algebra
An inverse function is a concept of mathematics. A function will calculate some output , given some input . This is usually written . The inverse function does the reverse. Let's say  is the inverse function of , then . Or otherwise put, . An inverse function to  is usually called . It is not to be confused with , which is a reciprocal function.

Examples
If  over real , then 

To find the inverse function, swap the roles of  and  and solve for . For example,  would turn to , and then . This shows that the inverse function of  is .

Not all functions have inverse functions: for example, function  has none (because , and  cannot be both 1 and -1), but every binary relation has its own inverse relation.

In some cases, finding the inverse of a function can be very difficult to do.

Related pages
 Inverse element
 Inverse triangle function
 Inverse hyperbolic function
 Invertible matrix
 Reciprocal

References 

Functions and mappings
Set theory
In mathematics (particularly set theory), a countable set is a set whose elements can be counted. A set with one thing in it is countable, and so is a set with one hundred things in it. A set with all the natural numbers (counting numbers) in it is countable too. This is because even if it is infinite, someone who counts forever would not miss any of the numbers. The sets which has the same size as the natural numbers are therefore called countably infinite. The size of these sets are then written as (aleph-null)—the first of the aleph numbers. Sometimes when people say 'countable set' they mean countable and infinite. Georg Cantor coined the term.

Examples of countable sets 

Countable sets include all sets with a finite number of members, no matter how many.
Countable sets also include some infinite sets, such as the natural numbers. Since it is impossible to actually count infinite sets, we consider them countable if we can find a way to list them all without missing any. The natural numbers have been nicknamed "the counting numbers", since they are what we usually use to count things with.

You can count the natural numbers with 

You can count the whole numbers with 

You can count the integers with 

You can count the square integer numbers with

A more-complex example
The rational numbers are also countable, but its counting becomes tricky. We can't just list the fractions as (0/1, 1/1, -1/1, 2/1, -2/1...) since we will never get to 1/2 this way. However, we can list all of the rational numbers in the form of a table. The horizontal rows are the numerators, while the vertical columns are the denominators. We can then zigzag through the list, starting at 1/1, then 2/1, then 1/2, then 1/3, then 2/2, then 3/1, then 4/1, then 3/2, then 2/3, etc.  If we keep this up, we will get to all of the numbers on the table in due time. Each time we hit a new rational number that is new, we add it to the list of counted numbers. We don't want to count numbers twice, so when we hit 3/6, for example, we can skip it, because we already counted the rational number 1/2. In this way, we produce an infinite list with all the rational numbers. Therefore, the rational numbers are countable.

Not all counting schemes will yield a countable list
Suppose the integers are counted differently, as
This does not prove that the integers are uncountable, but it does illustrate what one might call a "failed" effort to count a set, because it is never possible to reach .  Not all sets are countable. For example, the interval  and the set of real numbers can be proven to be uncountable.

Related pages 

 Cantor's diagonal argument
 Cardinality
 Uncountable set

References

Set theory
A computable function is an idea from computer science. A function is computable if there is an algorithm that can work out its result in a finite number of steps.

Computability theory is all about such functions.

Theoretical computer science
A pharmacist is a person who supplies drugs to people, often  prescriptions from a doctor but sometimes on their own.  

Pharmacists have to be trained and have knowledge about the drugs package. Many work in a pharmacy.Pharmacists interact with customers, give the prescribed medication and telling them about the drugs. 

Some work in hospitals where they may deliver the drugs to the different parts of the hospital and give people the drugs they need to take home. 

Some work with general practitioners where they may check that people are getting the right drugs.
Pharmacists is the one who checks the works of the pharmacy technician. Pharmacy Technician works under the supervise of the Pharmacists, Pharmacy Technician are the one who pulls out the medicines according to the prescription written and they are the one who counts the medicine, after they finish counting and putting it inside a container for medicines purpose only. Once the Pharmacy Technician finished counting the medicine and putting it inside a container then, the Pharmacist will check the medicine in the computer to make sure the medicine that is dispensed is correct. 

Pharmacists can also help with recommending over the counter medication like when someone has sore throats or a common cold they can recommend medications that anyone can buy with a prescription from the doctor. Pharmacists can also help with vaccines, burning the covid-19 pandemic they help with giving vaccines to those who did not want to go to the hospitals.
Pharmacists can also help when a person gets changed to a new medication the pharmacist can help with giving them the new instructions as to how to use the medications. The pharmacist also helps by telling the patient the side effects of the new medication. Pharmacists  help by calling the doctor if the patient has concerns about the new medication.

In the COVID-19 pandemic in the United Kingdom many pharmacists were vaccinating people.  They have also been doing Influenza vaccines for several years.  There are plans for them to do more of this work.

Related pages
 Pharmaconomist
 Pharmacy
 Pharmacologist

References

 
Healthcare occupations
In Greek mythology, Thoosa was the name of the mother of the cyclops Polyphemus.

Nymphs
Perch is the name of a freshwater perciform fish belonging to the genus Perca. 

Perch have "rough" scales.  On the front end of the fish, there are two dorsal fins. The first one is spiny and the second is soft. There is also an anal fin, which is also spiny, and a caudal fin.

Species 
There are three living species in this genus:

 Perca fluviatilis Linnaeus, 1758 (European perch)
 Perca flavescens Mitchill, 1814 (Yellow perch)
 Perca schrenkii Kessler, 1874 (Balkhash perch)

Habitats 
Perch are carnivores, They choose waters where smaller fish, shellfish, and insect larvae are plentiful. 

They are found in parts of the United States in freshwater ponds, lakes, streams, or rivers. These fish can be found in fresh water all over the world. They live in the Great Lakes region, in particular Lake Erie. 

The fish like bodies of water with vegetation and debris. In the spring when the perch spawns, they use vegetation to hide their eggs from predators.

Related pages 
 Percidae
 Perciformes
References 
 "Perca Linnaeus 1758 (perch)".
 Lydon, Alexander Francis (1879), Perca fluviatilis, retrieved 2022-05-10

Other websites 

 Media related to Perca at Wikimedia Commons
 Is perch a good fish to eat? If so, what's the best way to cook it?

Perciformes
Edible fish
Puce is a medium grayish red-violet colour. 

Puce colours may be pale grayish red-violet, grayish red or brownish-purple colours.  

Basically, puce colours are reddish purple colours mixed with gray or brown.  A wide range of tones of puce are shown below. 

Chinese dried plums, a favorite snack among Chinese people worldwide, can be said to be puce coloured.

Where the name came from
The name is from the French word puce which means "flea".  Some people say that the colour name comes from the colour of a squashed flea or the colour of a flea full of blood. Other people say that colour name comes from the flea's droppings of digested blood, which spread out in deep red stain when water contacts them.  Still others say that the colour name means the colour of the belly of a flea. 

On the other hand, the colour name may refer to blue-lavender of the Pennyroyal flower, also named puce in French. The name may come from the use of strong-smelling Pennyroyal to ward off fleas.
The Oxford English Dictionary (OED) dates the use of "puce" (in couleur puce)in English from 1787. The first recorded use of puce as a color name was in the 14th century, in the French language.

Meaning of puce
 The colour puce and/or its various tones are used to signify something that is odd,  unusual, or bizarre. 
 Puce and its tones are favourite colours among those of the Goth subculture.
Tones of puce colour comparison chart
 Light Lavender Blush (Lavender Blush Light (Xona.com color list)) (Hex: #FFF9FB) (RGB: 255, 245, 251)
 Lavender Blush (web color) (Hex: #FFF0F5) (RGB: 255, 240, 245)
 Light Melanie (Melanie Light (Xona.com color list)) (Hex: #F4E5ED) (RGB: 244, 229, 237)
 Light Kobi (Kobi Light (Xona.com color list)) (Hex: #F5D3E6) (RGB: 245, 211, 230)
 Light Can Can (Can Can Light (Xona.com color list)) (Hex: #EBCBD6) (RGB: 237, 203, 214)
 Light Pale Red-Violet (Xona.com color list "Pale Violet-Red Light") (Hex: #F0B7CD) (RGB: 240, 183, 205)
 Light Puce (Puce Pink) (Hex: #FFAFC8) (RGB: 255, 175, 200)
<li style ="background-color:#ef9bb9;"> Light Cabaret (Cabaret Light (Xona.com color list)) (Hex: #EF9BB9) (RGB: 239, 155, 185)<li>
 Light Red-Violet (Xona.com color list "Violet-Red Medium Light") (Hex: #E79EC5) (RGB: 231, 94, 197)
<li style ="background-color:#e79fc4;"> Kobi (Xona.com color list) (Hex: #C79FC4) (RGB: 231, 159, 196)<li>
Light Blush (Blush Light (Xona.com color list)) (Hex: #DE98B2) (RGB: 222, 152, 178)
 Light Night Shadz (Night Shadz Light (Xona.com color list)) (Hex: #D98AA8) (RGB: 217, 138, 168)
 Light Rouge (Rouge Light (Xona.com color list)) (Hex: #D58EB5) (RGB: 213, 142, 181)
<li style = "background-color: #d597ae;"> Pale Persian Lilac (Ridgway) (Hex: #D597AE) (RGB: 213, 151, 174) <li>
 Can Can (Xona.com color list) (Hex: #D591A4) (RGB: 213, 145, 164)
 PUCE (Hex: #CC8899) (RGB: 204, 136, 153)
 Persian Lilac (ISCC-NBS) (Hex: #C17E91) (RGB: 193, 126, 145) 
 Turkish Rose (Xona.com color list) (Hex: #B57281) (RGB: 181, 114, 129)
 Rose Gold (Hex: #B76E79) (RGB: 183, 110, 121)
 English Lavender (Pantone TPX 17-3617) (Hex: #B48395) (RGB: 180, 131, 149)
 Light Cosmic (Cosmic Light (Xona.com color list)) (Hex: #BB8CAA) (RGB: 187, 140, 170)
 Lavender Brown (Medium Vanda) (Plochere "Vanda") (Plochere) (Hex: #AA8A9E) (RGB: 170, 138, 158)
 Pharlap (Xona.com color list) (Hex: #A3807B) (RGB: 163, 128, 123)
Bazaar (Xona.com color list) (Hex: #98777B) (RGB: 152, 119, 123)
 Rose Dust (Crayola Silver Swirls) (Hex: #9E5E6F) (RGB: 158, 94, 111)
 Mallow Purple (ISCC-NBS) (Hex: #A8516E) (RGB: 168, 81, 110)
 Deep Puce (Puce (Maerz & Paul)) (Hex: #A95C68) (RGB: 169, 92, 104)
 Puce Orange (Hex: #D66F6C) (RGB: 214, 111, 108)
 Dingy Dungeon (Crayola Silly Scents) (Hex: #C53151) (RGB: 197, 49, 81)
 Light Black Rose (Black Rose Light (Xona.com Color List)) (Hex: #B12B7F) (RGB: 177, 43, 127)
 Strong Red-Purple (ISCC-NBS) (Hex: #9A366B) (RGB: 154, 54, 107)
 Vietnamese Mauve (Hex: #993366) (RGB: 153, 51, 102)
 Red-Violet Eggplant (Hex: #990066) (RGB: 153, 0, 102)
 Twilight Lavender (Crayola Silver Swirls) (Hex: #8A496B) (RGB: 138, 73, 107)
 Light Bulgarian Rose (Bulgarian Rose Light (Xona.com color list)) (Hex: #9A393D) (RGB: 154, 57, 61)
 Cordovan (Pantone color planner) (Hex: #893F45) (RGB: 137, 63, 69)
 Solid Pink (Xona.com color list) (Hex: #893843) (RGB: 137, 56, 67)
 Copper Rose (Hex: #996666) (RGB: 149, 102, 102)
Dark Chestnut   (Hex: #986960) (RGB: 152, 105, 96)
 Rose Taupe (ISCC-NBS) (Hex: #905D5D) (RGB: 144, 93, 93)
 Mauve Taupe (ISCC-NBS) (Hex: #915F6D) (RGB: 145, 95, 109)
 Medium Puce (Hex: #8E616A) (RGB: 142, 97, 106)
<li style="background-color: #755258; color: #ffffff"> Galaxy (Resene color list) (Hex: #755258) (RGB: 117, 77, 82) <li>
<li style="background-color: #763950; color: #ffffff"> Cosmic (Xona.com color list) (Hex: #763950) (RGB: 118, 57, 93) <li>
 Puce Red (Puce (ISCC-NBS)) (Hex: #722F37) (RGB: 114, 47, 55)
 Internet Puce (color of the puce website www.puce.com) (Hex: #681C23) (RGB: 104, 28, 35)
 Black Rose (Xona.com color list) (Hex: #67032D) (RGB: 103, 3, 45)
 Bottle Puce  (Hex: #631800) (RGB: 99, 24, 0)
 Rose Ebony (ISCC-NBS) (Hex: #674846) (RGB: 103, 76, 71)
 Deep Tuscan Red (Hex: #6642D) (RGB: 102, 66, 77)
 Dark Liver (Hex: #534B4F) (RGB: 83, 75, 79)
 Purple Taupe (ISCC-NBS) (Hex: #504040) (RGB: 80,  64, 77) 	 
 Dark Puce (Puce Pantone TPX 19-1518) (Hex: #4F3A3C) (RGB: 79, 58, 60)
French Puce (Puce (Pourpre.com)) (Hex: #4E1609) (RGB: 78, 22, 9)
 Bulgarian Rose (Xona.com color list) (Hex: #480607) (RGB: 72, 6, 7)
Related pages
 List of colors

References
Scarlet is a slight brilliant red color.  It is a color of the rainbow.  It is redder than vermilion.  The color's name comes from the Persian saqirlat. 

An early recorded use of scarlet as a color name in the English language dates to 1250.

Meaning of Scarlet
  
 Traditionally, scarlet is the color of flame.  People also call the color of the blood of a living person scarlet, even though the actual color of blood is crimson.  

 Scarlet may represent sin.

 Scarlet represents sensual pleasure and fun.  Scarlet represents partying.

Tones of scarlet color comparison chart

Related pages
List of colors

References
The word league can mean one of the following:
 An association, such as the League of Nations
 Sports league, a type of competition often used in games like football and rugby
 League (unit), an old unit of measurement which is equal to the distance a human walks in one hour or some other time interval
Worship is a word often used in religion.  It means to have much respect.  If someone prays or says thank to God, people say that they are worshipping God. Worship can also be used as the name for a church service or similar event. This can be called an act of worship.

The Quran talks about worshipping Allah.
Claudius ; 1 August 10 BCE – 13 October 54 CE) was the fourth Roman emperor. He ruled from 24 January 41 AD to his death in 54 AD. His great-uncle was the first emperor, Augustus, and his uncle was the second emperor Tiberius. His nephew was the third emperor, Caligula. His maternal grandfather was Mark Antony.

Claudius had some kind of disability, in speech and walking, and his family kept him from public office until he was 38. Claudius' infirmity may have saved him from the purges of Tiberius' and Caligula's reigns; enemies did not see him as a serious threat. He was declared emperor at the insistence of the Praetorian Guard after Caligula's assassination. He was then the last adult male of his family.
Assassination of Caligula 
On 24 January 41 CE, Caligula was assassinated by a broad-based conspiracy. There is no evidence that Claudius had a direct hand in the assassination, although it has been argued that he knew about the plot. In the chaos following the murder, Claudius witnessed the German guard cut down several uninvolved noblemen, including some of his friends. He fled to the palace to hide. According to tradition, a Praetorian named Gratus found him hiding behind a curtain and suddenly declared him emperor. A section of the guard may have planned to seek out Claudius, perhaps with his approval. They reassured him that they were not one of the groups looking for revenge. He was put under their protection.
Expansion of the empire 
Under Claudius, the empire expanded for the first time since the reign of Augustus. The provinces of Thrace, Judea and three other provinces were annexed during his term. The annexation of Mauretania, begun under Caligula, was completed after the defeat of rebel forces, and divided into two provinces. The most important new expansion was the conquest of Great Britain (). In 43 CE, Claudius sent four legions to Britain. The island was an attractive target for Rome because of its wealth – particularly mines and slaves. It was also a haven for Gallic rebels and the like, and so could not be left alone much longer. Claudius himself traveled to the island after the completion of initial offensives, bringing with him reinforcements and elephants.
The Senate granted him a Roman triumph for his efforts: in the Roman Empire only members of the imperial family were allowed such honors. Claudius later lifted this restriction for some of his generals. When the British general Caractacus was captured in 50, Claudius granted him his life. Caractacus lived out his days on land provided by the Roman state, an unusual end for an enemy commander.

Claudius conducted a census in 48 CE that found 5,984,072 Roman citizens, an increase of about a million since the census conducted at Augustus' death.
Marriages and personal life
Claudius married four times. His first marriage, to Plautia Urgulanilla, occurred after two failed betrothals. During their marriage she gave birth to a son, Claudius Drusus. Unfortunately, Drusus died of asphyxiation in his early teens, shortly after becoming engaged to Junilla, the daughter of Sejanus. Claudius later divorced Urgulanilla for adultery and on suspicion of murdering her sister-in-law Apronia. When Urgulanilla gave birth after the divorce, Claudius repudiated the baby girl, Claudia, as the father was one of his own freedmen.

Soon after (possibly in 28 AD), Claudius married Aelia Paetina, a relative of Sejanus, if not Sejanus's adoptive sister. During their marriage, Claudius and Paetina had a daughter, Claudia Antonia.
Some years after divorcing Aelia Paetina, in 38 or early 39 AD, Claudius married Valeria Messalina, who was his first cousin once removed and closely allied with Caligula's circle. Shortly thereafter, she gave birth to a daughter Claudia Octavia. A son, first named Tiberius Claudius Germanicus, and later known as Britannicus, was born just after Claudius' accession. This marriage ended in tragedy. Messalina was regularly unfaithful to Claudius and manipulated his policies in order to amass wealth. In 48 AD Messalina married her lover Gaius Silius in a public ceremony while Claudius was at Ostia. The result was the execution of Silius, Messalina, and most of her circle. Claudius made the Praetorians promise to kill him if he ever married again.