the-french-artist/wikipedia_20220301.simple_sentence_split huggingface dataset:
At first, it is a just a voice telling what has happened.
It then is shown to be a school room where the voice was that of the teacher.
They next showed that this was all just memories in one of the character's mind.
Since the budget was not very large, physical special effects were used as much as possible.
They made as sets and props as they could to use less CGI effects.
The most technically challenging scene was the mule skiff chase.
Because it would cost too much, a gimbal (a hydraulic turntable) and CGI, like the pod race scene in Star Wars Episode I: The Phantom Menace could not be used.
The production team to find other ways to do things.
They built a trailer connected to the "hover craft" in the movie and shot the scene while riding up a highway north of Santa Clarita.
Serenity visual effects supervisor Loni Peristere said in a Los Angeles Times article: "Traditionally this would have been, like, a 30-day shoot.
I think we did it in five."
One item from the television show that could not be used again was the original set of the inside of the ship Serenity.
It had to be built for the movie, using images from the Firefly DVD set.
The company that did the graphics for the series also had to change the computer model of Serenity.
The television model was not good enough for high-definition cinema screens and HD DVD.
Five hundred years into the future, mankind has left Earth.
All the people moved to a new large star system.
The system is controlled by the Alliance.
Away from the "core planets" people like the crew of the cargo ship Serenity can make a living if they stay away from Alliance ships and the Reavers -  space-faring cannibals who raid the planets of "the Rim."
One of the Alliance's projects is the creation of a group of warriors with mental powers.
The star of this project is teenager River Tam.
After her older brother Simon rescues her, the Alliance Parliament sends "The Operative", a man with no name, rank or official existence after them.
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.
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).
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.
DeCandido, Keith R.A. Serenity.
August 30, 2005. .
Whedon, Joss.
Serenity: The Visual Companion.
September 1, 2005. .
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
Movies based on TV series
Movies directed by Joss Whedon
Hugo Award winning movies
the distinctive material properties of wood, often without mechanical fasteners.
There are different types of joinery for different structures, for example the joinery used
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,
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.
Bernard Jones (Ed.) (
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.
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.
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.
1770 deaths
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 Kievan Rus' (early form of Russia).
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.
1015 births
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
The Normans wore woollen tunics and sometimes they wore a waistband to keep the tunic in place.
The men also wore long cloaks.
Normans ate dairy, oatmeal porridge, green vegetables and sometimes meat.
They often used honey as a sweetener and for mead (an alcoholic drink).
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.
Captains are officers in an army.
In a navy, captains command an entire ship.
A Navy Captain is equal to the army rank of colonel.
Another type of captain is a commander of a ship who is not in the military.
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.
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:
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.
Modern history of wire rope
Stories tells 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.
Soul of baby could not go to heaven because his/her body was not at graveyard and was not blessed by a priest.
This is why she became a ghost.
This ghost could make terrible noise until somebody dugs up his/her body and buries it in graveyard.
Such ghost people call Ihtiriekko.
Ghosts could also be quiet, but she/he might be seen as a flame in forest, like will o' the wisp.
Such ghost people call Liekkiö.
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 today, 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.
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.
Given a countable set S, a Gödel numbering is an injective function
with both f and  (the inverse of f) being computable functions.
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.
Gödel, Kurt, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", Monatsheft für Math.
und Physik 38, 1931, pages 173–198.
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.
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.
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
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'
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
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
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 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.
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
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.
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.
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.
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)
Concatenation is a simple concept from computer science.
It is a way of making a new word (or String), by putting together two other Strings.
Given the words foo and bar, the two new words foobar and barfoo can be made that way.
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
fa:عمل دوتایی#عضو خنثی
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.
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.
Inverse triangle function
Inverse hyperbolic function
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
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
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.
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.
A pharmacist is a person who works in a pharmacy.
Pharmacists have to be trained to work there, and have knowledge about the drugs package.
Pharmacists interact with customers, give the prescribed medication and telling them about the drugs.
Pharmacologist
In Greek mythology, Thoosa was the name of the mother of the cyclops Polyphemus.
Perch is a type of fish.
Perch are the fish in the genus Perca.
Perch have "rough" scales.
When looking through a microscope, the scales look like a plate with growth rings and spikes on the top edges.
On the top side of the fish, there is a mouth, a pair of nostrils, and two lidless eyes.
On the bottom sides are the operculum, which are used to protect the gills.
Also perch have a lateral line system, which a set of sense organs that are sensitive to vibrations in the water.
They have a pair of pectoral and pelvic fins.
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 considered spiny, and a caudal fin.
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.
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 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>
PUCE (Hex: #CC8899) (RGB: 204, 136, 153)
Persian Lilac (ISCC-NBS) (Hex: #C17E91) (RGB: 193, 126, 145)
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)
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)
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)
Dark Chestnut   (Hex: #986960) (RGB: 152, 105, 96)
Medium Puce (Hex: #8E616A) (RGB: 142, 97, 106)
<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)
Bottle Puce  (Hex: #631800) (RGB: 99, 24, 0)
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)
Scarlet is a slight brilliant red colour.
It is a colour of the rainbow.
It is redder than vermilion.
The colour'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 colour of flame.
People also call the colour 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
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.
Claudius ; 1 August 10 BC – 13 October 54 AD) 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.
Despite his lack of experience, Claudius proved a good administrator and a great builder of public works.
His reign saw an expansion of the Empire, and the conquest of Roman Britain.
He took a personal interest in the law, and he presided at public trials.
Claudius suffered setbacks in his personal life, one of which may have led to his murder.
He married four times, and the marriages did not turn out well.
Claudius' relative and adopted son Nero succeeded him as emperor, and undid much of his good work.
Assassination of Caligula
On 24 January 41 AD, 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.
The Senate quickly met and began debating a change of government.
When they heard of the Praetorians' claim, they demanded that Claudius be delivered to them for approval.
He refused, sensing danger.
Eventually the Senate was forced to give in and, in return, Claudius pardoned nearly all the assassins.
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 AD, 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 AD 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.
The attempted coup d'état by Silius and Messalina had probably made Claudius realize the weakness of his position since he did not have an obvious adult heir, Britannicus being just a boy.
Agrippina's son Lucius Domitius Ahenobarbus (the emperor Nero) was one of the last males of the imperial family.
Future coup attempts could rally around the pair, and Agrippina was already showing such ambition.
In any case, Claudius accepted Agrippina, and later adopted the newly mature Nero as his son.
Nero was made joint heir with the underage Britannicus, married to Octavia and heavily promoted.
Nero was popular with the public as the grandson of Germanicus and the direct descendant of Augustus.
Death, deification, and reputation
The consensus of ancient historians was that Claudius was murdered by poison, and died in the early hours of 13 October, 54 AD.
Accounts vary greatly, but nearly all implicate his last wife, Agrippina, as the instigator.
Agrippina had motive in ensuring the succession of Nero before Britannicus could gain power.
Claudius was described as physically repulsive, weak, and easily manipulated by his wives and companions by Suetonius, but this historian cannot be entirely trusted.
The surviving works of Claudius present a different view.
They paint a picture of an intelligent, scholarly, well-read, and conscientious administrator with an eye to detail and justice.
Thus, Claudius becomes an enigma.
Since the discovery of his letter to the Alexandrians in the last century, much work has been done to rehabilitate Claudius and determine where the truth lies.
Scholarly works and their impact
Claudius wrote copiously throughout his life.
Besides the history of Augustus' reign, his major works included an Etruscan history and eight volumes on Carthaginian history, as well as an Etruscan dictionary and a book on dice playing.
Claudius is the last person known to have been able to read Etruscan.
His first wife was Etruscan.
Finally, he wrote an eight-volume autobiography.
Unfortunately, none of these major works survive.
They do live on as sources for the surviving histories of the Julio-Claudian dynasty.
Suetonius quotes Claudius' autobiography once, and must have used it as a source numerous times.
Tacitus may have used him for some of the more antiquarian passages in his annals.
Claudius is the source for numerous passages of Pliny's Natural History.
Pliny credits him by name in Book VII 35.p83
Many of the public works instituted in his reign were based on plans first suggested by Julius Caesar.
Levick believes this emulation of Caesar may have spread to all aspects of his policies.
In literature and film
The best known fictional representation of the emperor Claudius were the books I, Claudius and Claudius the God (published in 1934 and 1935) by the poet Robert Graves.
They were both written in the first-person, as if they are Claudius' autobiography.
Graves' plot suggested there were recently discovered, genuine translations of Claudius' writings.
Claudius' genuine surviving letters, speeches, and sayings were incorporated into the text (mostly in the second book, Claudius the God) in order to add authenticity.
Graves's two books were the basis for an I, Claudius TV series by the BBC.
The series starred Derek Jacobi as Claudius and was broadcast in 1976 on BBC2.
It was a substantial critical success, and won several BAFTA awards.
The series was later broadcast in the United States on Masterpiece Theatre in 1977.
The DVD release of the television series contains The Epic that Never Was documentary.
Claudius has been portrayed in movies on several occasions.
I, Claudius (1937, Director Josef von Stromberg), unfinished; Charles Laughton as Claudius was a great performance.
The surviving reels were featured in the BBC television documentary The Epic that never was (1965), revealing some of Laughton's most accomplished acting.
Also, minor portrayals in Demetrius and the Gladiators (1954) and Caligula (1979).
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10 BC births
54 deaths
Nero (Nerō Claudius Caesar Augustus Germanicus; 15 December 37 AD – 9 June 68 AD) was the fifth and last Roman Emperor of the Julio-Claudian dynasty.
He was born Lucius Domitius Ahenobarbus.
Nero was the adopted son of his grand-uncle Claudius.
He became emperor on 13 October 54, after Claudius died.
Claudius was probably assassinated by Nero's mother Agrippina the Younger.
Agrippina had motive in ensuring the succession of Nero before Britannicus (Claudius' natural son) could gain power.
Nero as Emperor
During his reign, Nero focused much of his attention on diplomacy, trade, and improving the cultural capital of the empire.
He ordered the building of theatres and promoted athletic games.
His reign included a successful war and negotiated peace with the Parthian Empire; the suppression of a revolt in Britain; and the beginning of the First Roman–Jewish War.
In 64, most of Rome was destroyed in the Great Fire of Rome.
In 68, the rebellion of Vindex in Gaul and later the acclamation of Galba in Hispania (Spain) drove Nero from the throne.
Facing assassination, he died by suicide on 9 June 68.
Nero's rule is often associated with tyranny and extravagance.
He is known for a number of executions, including those of his mother and stepbrother.
Nero is known as the emperor who played a fiddle while Rome burned.
In reality, the violin had not yet been invented, Nero wasn't in Rome at the time, and when he heard of the fire he returned to direct relief efforts.
He also persecuted Christians.