It is generally assumed that pairwise comparisons are transitive. Most agree on what transitivity is, though there is debate about the transitivity of indifference. The rules of transitivity are as follows.
This is linked to (xPy or xIy) being a total preorder, P being the related strict weak order, and I being the related equivalence relation.
Some believe that indifference (lack of preference) is not transitive. Consider the following example. Suppose you like apples and you prefer apples that are larger. Now suppose there exists an apple A, an apple B, and an apple C that are the same except for the following. Suppose B is larger than A, but it is not possible to see this without an extremely sensitive measuring device. Also suppose C is larger than B, but this also can't be seen without a sensitive measuring device. However, the difference in sizes between apples A and C is large enough that you can see it. In psychophysical terms, the size difference between A and C is above the just noticeable difference ('jnd') while the size differences between A and B and B and C are below the jnd.
You are confronted with the three apples in pairs without a sensitive measuring device. Because of this, when shown only A and B, you have no preference between apple A and apple B; and you are indifferent between apple B and apple C when shown only B and C. However, when the pair A and C are shown, you prefer C over A.
If pairwise comparisons are transitive by the four rules shown above, then pairwise comparisons for a list of alternatives ("A", "A", "A", ..., "A", and "A") can take the form:
For example, if there are three alternatives "a", "b", and "c", then the 13 possible preference orders are:
If the number of alternatives is n, and indifference is not allowed, then the number of possible preference orders for any given "n"-value is "n"<nowiki>!</nowiki>. If indifference is allowed, then the number of possible preference orders is the number of total preorders. It can be expressed as a function of n:
where "S"("n", "k") is the Stirling number of the second kind.
Madeleine Riffaud
Madeleine Riffaud (born 23 August 1924) is a French poet, journalist, war correspondent and a member of the French Resistance. She was born in Arvillers, France. Riffaud was awarded the National Order of Merit.
She began operating for the French Forces of the Interior at the age of 18 under the codename "Rainer". On July 23, 1944, at age 19, she became known for the killing of a German officer, whom she shot dead. Shortly afterwards, she was captured by the Gestapo and was nearly executed.
After the war ended in 1945, she became a journalist for , a French newspaper.
Marie-José Chombart de Lauwe
Marie-José Chombart de Lauwe ("née" Wilborts; born 31 May 1923) is a French sociologist, activist and World War II resistance fighter. She was born in Paris. In 2008, she was honored with the Legion of Honour.
During World War II, she was arrested by the Gestapo to La Santé Prison. She was nearly executed.
In 1954, she began working for the National Centre for Scientific Research. In 1996, she became Chair of the Fondation pour la Mémoire de la Déportation.
Irish Home Rule
Irish Home Rule was a proposed system of government in Ireland, in which Ireland would have its own government inside the United Kingdom. Until 1920, Ireland was ruled directly by the British government. British members of parliament tried to pass bills for Home Rule in 1896, 1893, and 1912, but they never got enough votes to pass. Irish Nationalists supported Home Rule, and Irish Unionists opposed it.
The 1886 bill was supported by the Liberal Party, but did not get enough votes in the House of Commons. The 1893 bill got enough votes to pass in the House of Commons, but not the House of Lords. William Gladstone was an important supporter of both. The 1912 bill also passed in the House of Commons, but not the House of Lords. In 1912, Unionists in Ulster signed a document called the Ulster Covenant, and made an army called the Ulster Volunteers, to fight against Home Rule.
Although many Nationalists wanted Home Rule, some thought it was not good enough. Most members of the party Sinn Féin wanted Ireland to be completely separate from Great Britain. Sinn Féin became the most powerful party in 1916 and made their own government in Dublin, the Dáil Éireann. Irish Nationalists fought in the Irish War of Independence against the British government from 1919-1921. In 1920, Britain passed a law that said there would be two parliaments, one for Northern Ireland, and one for Southern Ireland. This was a form of Home Rule. However, the Southern Ireland parliament never met. The war did not end until the 1921 Anglo-Irish Treaty, which created the Irish Free State. The Irish Free State still had the same king as Britain, but had a separate government.
Frinkcoin
"Frinkcoin" is the 13th episode of the 31st season of "The Simpsons". It was first shown on television in the United States on the Fox network on February 23, 2020. In the episode, Professor Frink makes a new cryptocurrency. The episode was watched by 1.84 million people when it was first shown on television.
The Simpson family are eating at a vegan restaurant, wanting Lisa to pick them for a project at school. She chooses Professor Frink because he wants to help the world with science. At Springfield University, Lisa interviews Professor Frink. Frink says he is making a new cryptocurrency called Frinkcoin.
Frinkcoin becomes well known, making Frink the richest man in Springfield. Mr. Burns is angry because he is no longer the richest man in Springfield. Frink feels lonely, so Marge says that he should go to Moe's Tavern. Frink gets every question correct in Moe's trivia questions, so they become friends with Frink. Frink shows his friends Springfield's best places. Smithers gets a team of people to create a cryptocurrency for Mr. Burns. The team creates an equation to make Frinkcoin worth nothing, but it will take thousands of years to calculate. Instead, Mr. Burns tells Frink that his friends only like him because he is rich.
Burns brings the equation to Springfield for a crowdsourcing solution. Frink finds out that his friends only like him because he is rich. Frink solves the equation himself, but only Lisa knows. Frink loses all of his money, but he is happy to be friends with Lisa and to go back to his university.
Dennis Perkins of "The A.V. Club" gave the episode a score of B and says that the episode "uses the cryptocurrency concept as an excuse for a largely successful exercise in side-character development." "Den of Geek" gave the episode a 4 out of 5 stars and says "'Frinkcoin' is a satisfying episode" and that Lisa and Frink's actions add up to a "solid half hour investment."
The Mephisto Waltz
The Mephisto Waltz is a 1971 American horror movie directed by Paul Wendkos and based on the novel of the same name by Fred Mustard Stewart. It stars Alan Alda, Jacqueline Bisset, Barbara Perkins, Bradford Dillman, Curd Jürgens and was distributed by 20th Century Fox.
Ace High
Ace High (, literally translated as "The Four of the Hail Mary") is a 1968 Italian western movie directed by Giuseppe Colizzi and starring Eli Wallach, Bud Spencer, Terence Hill, Brock Peters, Kevin McCarthy, Bruno Corazzari, Rick Boyd. It was distributed by Paramount Pictures and is the second part of the Italian western trilogy.
Postal Index Number
Postal Index Number is also called as Pincode. It is used in India For Post office Numbering or post office system. It is also used for couriering in India. It is used by
India Post and many courier Company. It is six digit long code to identify the city or area
Esme &amp; Roy
Esme & Roy is an American/Canadian animated children's television show created by Dustin Ferrer and Amy Steinberg. The series is produced by Canada-based animation studio Nelvana and "Sesame Street" creator Sesame Workshop, in association with Corus Entertainment.