title: Address

text: When written in the Latin alphabet, the address begins with the smallest geographical area and ends with the largest one as in the Anglicized example in the table. Macrons (as on ō and ū) may be omitted.


title: Address

text: Japanese-style envelopes are vertically aligned and the address is written from top to bottom, then right to left. Western-style envelopes are horizontally aligned and the address is written from left to right, top to bottom.


title: Address

text: The official languages of Macao are Cantonese and Portuguese. For domestic mail within Macau, the address may be written entirely in either Portuguese or Chinese. For overseas mail going out from Macau, the address may be written in the language of the destination country, provided that the city name and the country name are in English. However, for overseas mail from Macau to mainland China, Hong Kong, Taiwan or Singapore, the address may be written entirely in Chinese. While traditional Chinese characters are commonly used in Macau, simplified Chinese characters are also understood by Macau's postmen. Note that Macau does not use any postal codes.


title: Address

text: An address written in Portuguese should begin with the street name and end with the area in Macau, as in the following example for domestic mail within Macau.


title: Address

text: An address written in Chinese should begin with the largest unit and end with the smallest unit, as in the following example for a piece of domestic mail within Macau. Traditional Chinese characters are used in this example.


title: Address

text: For mail to Macau from overseas, "Macau" should be added at the end of an address written in Portuguese, and "Macao" at the end of an address written in English; should be added at the beginning of an address written in Chinese.


title: Address

text: The postal code is a unique street identifier, and always consists of four numbers followed by a space and then two capital letters. PostNL, which is appointed by the Dutch government to carry out the UPD (Dutch for "Universal Postal Service"), recommends putting two spaces between postal code and town. Also, the name of the town should be written in capitals.


title: Address

text: Because the Dutch postal code uniquely identifies a street, a shortened format may also be used. This method only needs the postal code and the number. The ideal format for this method is the number after the postal code, meaning that this: '5631 AV 1092' will still get the letter delivered to the correct location.


title: Address

text: It is also possible to replace the street name line with a PO box (e.g. "postbus 1200") or freepost number (e.g. "antwoordnummer 150"), which have their own postal code.


title: Address

text: Note that no space or full stops exists between P and O in PO Box or R and D in RD. One should put only one space between the town/city and the postcode.


title: Address

text: Note for Wellington metropolitan area, users should use the city name (i.e. Wellington, Lower Hutt, Upper Hutt, Porirua), not the metropolitan area name. For example:


title: Address

text: The city in this case is important, as if Wellington is used instead of Lower Hutt and the postcode is unclear (note only the first digit differs), someone's private mail could accidentally be sent to the New Zealand Parliament Buildings instead (or vice versa).


title: Address

text: One anomaly about this system is the Wellington Mail Centre, which is addressed as "Wellington Mail Centre, Lower Hutt 5045", due to its location in the Lower Hutt suburb of Petone.


title: Address

text: The first line, "Recipient (Person or Entity)", is the legal recipient of the item being sent. The Recipient's name must be marked on the mail box in order for the item to be delivered.


title: Address

text: The postal code (always four digits) is mandatory. If a PO box is used (e.g. Postboks 250 Sentrum), it replaces "Street name + Number". PO box addresses have postal codes which differ from those used for street addresses. Some areas do not have street names. For these areas, "Street name + Number" is replaced by a local designation determined by the Norwegian postal service.


title: Address

text: Physical addresses only exist in major urban centers like those of Greater Muscat, Sohar, Salalah, Sur and Nizwa.


title: Address

text: The Philippines follows Western conventions on addressing. Addresses in the Philippines either uses these formats.


title: Address

text: Some streets have names not containing the word "street". Then the full description is written with initial caps, e.g. "Zaułek Marii" ("Court of Mary") or "Aleje Ujazdowskie" (plural for "Ujazdowskie Ave."). If the first word of name is "Aleje" it may be abbreviated to "Al." (with initial capital).


title: Address

text: The abbreviation "m." (meaning "mieszkanie" = "flat") can be used instead of "/" before the flat number.


title: Address

text: Some large buildings occupy two or more cadastral plots. Sometimes to maintain consistency all numbers are included in address. The very well-known example is the address of Polish Radio Three: "ul. Myśliwiecka 3/5/7" (occupying three neighbouring plots). In examples like in above table the number "4/6" is ambiguous and not knowing the locality you cannot tell if "6" is the apartment number or the building is large.


title: Address

text: When using a p.o. box the abbreviation "skr. poczt." may be used and "nr" ("no.") may be omitted. Polish Post allows the box user to register an alias for their name. In such case it is written instead of the real name of the recipient. It is required to write the full name of post office including a number if it exists.


title: Address

text: The postal code always consists of five digits separated with a hyphen (in the "XX-XXX" format), i.e. 00-486 (00 = Warsaw); 20-486 (20 = Lublin), etc. The first digit signifies the postal district, the second: the code zone, the third: the code sector, the fourth and fifth signify the post office and its area of operation. Usually the code is unique on the street level for cities and the town level for smaller towns and villages. Contrary to popular belief the name after postal code is a locality of addressee, not their post office. So if a small town has no street names you do write its name twice. The post office location (and a number if there are many) is written only on letters to p.o. box or "poste restante".


title: Address

text: Postal codes have the codice_1 format. Street name and the number is traditionally separated by a comma, but nowadays CTT recommends just a blank space, or two blank spaces for extra clarity; this is to avoid OCR mistakes. The º after the number is the ordinal for floor number. Usually followed by "Esq." (Left, abbr from "Esquerdo") or "Dir." (Right, abbr from "Direito"), or an apartment letter (A, B, C, etc.). PO Boxes are called Apartado, followed by a number (e.g., Apartado 1001).


title: Address

text: Not all of Qatar's roads and buildings are numbered, Q-Post doesn't deliver to any street addresses, and no postal codes are used in Qatar.


title: Address

text: In Russia, the address must be written in Cyrillic or Latin alphabet, in usual format (from most specific to general).


title: Address

text: "Note: sub-region and region/oblast names are void if the city is Moscow or Saint Petersburg or if it is sub-region administrative center."


title: Address

text: Some neighbourhoods may be planned in such a way that some, or most, apartment buildings face no named street. In this case, a number of expedients can be used. In older neighbourhoods, such as the historical center of Moscow, a "main" building may have the same number as one or more "subsidiary" buildings accessible via driveways behind the main building. They will be addressed as, for example, ul. Lenina, d. 123 (that is, 123 Lenin St). An address may also cover one or more subsidiary buildings behind the main building, addressed as ul. Lenina, d. 123, str. 2 (123 Lenin St, Unit 2, where str. (abbreviation for строение, stroenie) means a '(subsidiary) building'. In newer areas with more regular street plans, apartment buildings that face no named street may be designated with Cyrillic letters appended to the building number, such as 123-а, 123-б, etc., in alphabetic order.


title: Address

text: In some microraion neighbourhoods, with few, if any, buildings facing named streets, the name (or more likely number of the microraion (planned housing development)) would be used instead of the street name; thus someone may live at 4-th microrayon, d. 123, kv. 56, that is, 123 - 4th Microraion, apt. 56.


title: Address

text: In addition to 5-digit postal code, another line can be added containing PAK, a six-digit number which encodes the town, street and house number section.


title: Address

text: Generally, the last line "SINGAPORE" is omitted when posting within the country. Addresses are usually written in the English language.


title: Address

text: Street numbers can be written as orientation numbers (related to street) or descriptive numbers (unique within the town) or as a combination separated by a slash (descriptive/orientation). Descriptive numbers are also used within small villages that do not have named streets.


title: Address

text: If the delivery is intended exclusively for a specific person at a company site, the address should begin with the individual's name and the company name should follow. The standard format of addresses enables anyone at the company to receive the delivery.


title: Address

text: http://www.posta.sk/potrebujem/spravne-napisat-adresu ("How to write addresses correctly", in Slovak, with pictures)


title: Address

text: The simpler the code, the bigger the locality: 1000 Ljubljana, 2000 Maribor (big cities); 1310 Ribnica, 9250 Gornja Radgona (mid-sized towns); 4263 Bohinjska Bela, 8262 Krška vas (smaller settlements, including villages).


title: Address

text: Some cities have more than one post office, thus having multiple postcodes (usually in the x1xx format). For example, Ljubljana which has a "general" postcode 1000, also has additional ones, ranging from 1101 to 1133 (for some reason, however, omitting 1103 and 1105), Kamnik has 1240 and 1241, etc. Albeit they exist, it is not necessary to use them - usually the "general" postcodes are used.


title: Address

text: The abbreviations are: g. for "gospod" (Mr), ga. for "gospa" (Mrs), and gdč. for "gospodična" (Miss) - all always capitalized if in the beginning of the line.


title: Address

text: Common abbreviations are: c. for "cesta" (Street), and ul. for "ulica" (Road) - both always capitalised if in the beginning of the line.


title: Address

text: South Korea uses a system similar to Western addressing, but previously used a system similar to Japanese addressing. South Korean addresses start with the largest unit (country, province), as with other East Asian countries.


title: Address

text: 5ºB means 5th floor (Spanish: quinto), door B. Also, there may be door number, printed as 1ª (primera-first). Suffixes "o" and "a" derives from Spanish words piso (floor) which is masculine and puerta (door) which is feminine.


title: Address

text: Some doors may be indicated with the abbreviations Izq. or Dcha., to indicate either left (Izquierda) or right (Derecha). Streets and avenues can be indicated with the abbreviations C. (for calle) and Av. (for avenida).


title: Address

text: Sri Lanka uses a five-digit postal code. Generally, the last line "SRI LANKA" is omitted when posting within the country. Addresses are usually written in English and Sinhala.


title: Address

text: The postal code is always a five-digit number divided into groups of three and two (e.g. SE-414 73) with the prefix SE (ISO-code for Sweden) used only if sent from abroad. It is also possible to replace the street name line with a PO box (e.g. Box 51).


title: Address

text: The canton abbreviation (SO, VD in the examples) is needed only for cities/town that have the same name but in another canton for example: Renens and Renan which were both, in the past, called Renens, the difference stays today and Renens is often mentioned as Renens VD.


title: Address

text: In Taiwan, addresses are regulated by the Department of Household Registration, while mails are handled by the Chunghwa Post. As a result, senders are required to write addresses in different formats in different situations.


title: Address

text: Some neighbourhoods in Ukraine may be planned in such a way that some, or most, apartment buildings don't face a named street. In this case, a number of expedients can be used. In older neighbourhoods, a "main" building may have the same number as one or more "subsidiary" buildings accessible via driveways behind the main building. They will be addressed as "vul. Bandery, d. 123" ("123 Bandera St") An address may also cover one or more "subsidiary buildings" behind the main building, addressed as "vul. Bandery, d. 123, bud. 2" ("123 Bandera St, unit 2", where "bud." (abbreviation for будинок, "budynоk") means a '(subsidiary) building'). In newer areas with more regular street plans, apartment buildings that don't face a named street may be designated with Cyrillic letters appended to the building number, e.g. "123-а", "123-б", etc., in Cyrillic alphabetical order.


title: Address

text: In some "microraion" neighbourhoods, with few, if any, buildings facing named streets, the name (or more likely number of the "microraion" (planned housing development)) would be used instead of the street name; thus someone may live at "4-th microrayon, bud. 123, kv. 56", i.e. "123 - 4th Microraion, apt. 56".


title: Address

text: Not all of the roads and buildings in the UAE are numbered consistently and no postal codes are used in the United Arab Emirates. All mail by post are delivered only to PO boxes in the United Arab Emirates. If delivering to a street address it is customary to include recipient's telephone number should the delivery driver need to make a phone call to ascertain the address or let the recipient know that the package is already delivered.


title: Address

text: The locality is required only where its absence would cause ambiguity, for example where a post town or postcode district includes two streets with the same name. Royal Mail specifies that post towns should be written in block capitals. Until 1996 a postal county (or permitted abbreviation) was required after the post town, unless it was a special post town, for example London. The post town and postcode should each be on a separate line. Historically, each line of an address ended with a comma and was indented from the previous line. Royal Mail discourage this usage and specify that all lines should start from the same point and not be staggered or aligned to the centre. The postcode identifies, from left to right, increasingly smaller units of the postal delivery system. The first half of the postcode, known as the outward code, contains the postcode area and postcode district. The second half, known as the inward code, contains the postcode sector and postcode unit.


title: Steven Berghuis

text: Steven Berghuis (born 19 December 1991) is a Dutch professional footballer who plays for Eredivisie club Ajax and the Netherlands national team. He can play as either a winger or attacking midfielder.


title: Steven Berghuis

text: Berghuis made his debut for the Netherlands in 2016, and represented the national team at UEFA Euro 2020 and the 2022 FIFA World Cup.


title: Steven Berghuis

text: Berghuis came through the youth system at FC Twente, following spells with the youth clubs of local amateur club WSV Apeldoorn, then Eerste Divisie side Go Ahead Eagles. As a 16-year-old, he scored WSV's only goal in a 4–1 friendly match defeat to Feyenoord.


title: Steven Berghuis

text: One year later, Berghuis joined Twente, and in June 2010, he signed a professional contract lasting until 2012. In January 2011, Berghuis was called-up to the first team by manager Michel Preud'homme at the training camp in La Manga. He then made his first team debut for Twente on 19 January 2011 as a substitute in a 5–0 Eredivisie win over Heracles.


title: Steven Berghuis

text: On 23 June 2011, Berghuis scored his first goal for the club in a pre-season friendly against Eerste Klasse D team DOS '37. One week later, he scored one of Twente's ten goals in another warm-up fixture against Derde Klasse side DSV '61. On 14 July 2011, he scored his first goal against foreign opposition, scoring Twente's second in a 4–3 friendly win over Turkish Süper Lig side Fenerbahçe.


title: Steven Berghuis

text: After being promoted to the first team for the 2011–12 season, Berghuis signed a contract extension with Twente lasting until 2014. He then played in Twente's 2011–12 UEFA Champions League qualifying legs against Romanian club Vaslui on 26 July and 3 August 2011, during which Twente won 2–0 on aggregate. He also played in the 2011 Johan Cruyff Shield; despite being sent-off, Twente won the match 2–1 against Ajax. He started the club's first Eredivisie match of the 2011–12 season, against NAC Breda. On 21 September 2011, he then scored four goals against Zwaluwen '30 in the KNVB Cup, where Twente won 8–1. Berghuis scored his first Twente goal in a 6–2 win over Utrecht on 4 December 2011.


title: Steven Berghuis

text: On 20 January 2012, Berghuis joined VVV-Venlo on loan until the end of the 2011–12 season. Two days later, he made his VVV-Venlo debut, starting and playing the full match in a 2–1 win over Feyenoord. On 18 February, he scored his first goal for VVV-Venlo, in a 4–1 win over De Graafschap. In the last match of the season, Berghuis scored his second goal—as well as setting up another—in a 4–2 win over parent club Twente. On 13 May, he scored twice in the second legs of the play-offs in a 4–2 victory over Cambuur. By the end of the 2011–12 season, in all competitions, he had made 21 appearances and scored 4 goals.


title: Steven Berghuis

text: On 20 June 2012, Berghuis joined AZ for a reported £400,000 transfer fee from Twente, after which he signed a contract keeping him at AZ until 2017. Upon joining the club, Berghuis said he expected to develop more as a player at AZ. He made his AZ debut playing 16 minutes after coming on as a substitute in a 1–0 loss against Anzhi Makhachkala in the qualification round first leg of the 2012–13 UEFA Europa League on 23 August. One week later, on 2 September, he made his Eredivisie debut for the club, playing 13 minutes in a 5–1 loss against PSV.


title: Steven Berghuis

text: Berghuis played the season predominantly as a left winger and as a substitute, only completing 90 minutes on four occasions, contributing only one assist in the league due to the form of Icelandic player Jóhann Berg Guðmundsson, who scored two and assisted six goals in the season at left wing. In his first season, Berghuis made 27 appearances in all competitions and helped the side win the KNVB Cup over PSV in the tournament final.


title: Steven Berghuis

text: The 2013–14 season could be considered Berghuis' breakthrough season as he featured more in the starting 11, although he still had to compete with Gudmundsson. He scored his first AZ goal in a 3–0 win over Go Ahead Eagles on 15 September 2013, then scored again on 1 December in a 3–2 loss against NEC. In the KNVB Cup, Berghuis played a role in the first two rounds, scoring in a 4–1 win over Sparta Rotterdam, followed-up by three assists in a 7–0 win over Achilles '29 in the third round. In the second half of the season, Berghuis recorded two two-goal games, against NAC Breda on 18 January 2014 and RKC Waalwijk on 2 March. Berghuis later added a goal—as well as setting-up another—in a 3–0 win over Heerenveen in the 2013–14 UEFA Europa League play-off competition as part of the Eredivisie format for European competition qualification. Despite suffering from an injury in January 2014, Berghuis finished the 2013–14 season with 41 appearances and 10 goals in all competitions.


title: Steven Berghuis

text: In the 2014–15 season, Berghuis scored three goals to begin the campaign, against Heracles, Ajax and Dordrecht. However, in the first half of the season, Berghuis was plagued by injuries, making just seven appearances. By February 2015, Berghuis scored seven more goals in the Eredivisie, including a brace against Heerenveen. He also scored an important goals against Groningen and Willem II. At the end of the 2014–15 season, Berghuis scored 11 goals in 25 appearances in all competitions.


title: Steven Berghuis

text: On 27 July 2015, Berghuis joined recently-promoted English Premier League club Watford for an approximate £4.6 million transfer fee from AZ. Prior to the move, Berghuis made an emotional farewell to the club's management at its training camp. Upon joining the club, he was given the number 20 shirt.


title: Steven Berghuis

text: Having missed out due to an injury at the start of the season, Berghuis made his Watford debut on 15 August 2015 against West Bromwich Albion, coming on as a late substitute in a 0–0 draw. However, competition for spots saw Berghuis unable to secure a place in the Watford first team, largely because he was unable to feature in Watford manager Quique Sánchez Flores' preferred 4–2–3–1 formation. Sánchez Flores said he was not impressed with Berghuis' performances despite having high expectations of him. After two months omitted from the first team squad, Berghuis made his first appearance in the third round of the FA Cup in a 1–0 win over Newcastle United. It was not until on 20 April 2016 when he returned to the first team, setting up the lone Watford goal in a 3–1 loss against West Ham United, followed up by setting up another goal in a 3–2 win over Aston Villa. Following his appearances in the first team, Sánchez Flores praised Berghuis for his determination and hard work. At the end of the 2015–16 season, Berghuis had made 13 appearances in all competitions.


title: Steven Berghuis

text: Ahead of the 2016–17 season, Berghuis' first-team opportunities became further limited following the arrival of new manager Walter Mazzarri.


title: Steven Berghuis

text: On 1 August 2016, it was announced Berghuis had been loaned to Feyenoord for the 2016–17 season. He made his Feyenoord debut as a second-half substitute in a 5–0 win over Groningen in the opening match of the Eredivisie season. On 27 August, he scored his first Feyenoord goal, in a 4–1 win over Excelsior. By the end of 2016, Berghuis went on to score three more goals, against Oss, AZ and Vitesse. With his impressive display at Feyenoord that saw them top of the table, there were rumours of Berghuis returning to Watford in January 2017. However, Watford manager Walter Mazzarri denied he was planning on recalling Berghuis prematurely. Subsequently, Berghuis scored his fifth goal of the season on 29 January in a 4–2 win over NEC. On 5 April, he provided three assists in an 8–0 victory over Go Ahead Eagles, followed-up by scoring two goals on 9 April in a 2–2 draw against PEC Zwolle. Berghuis later helped Feyenoord win the Eredivsie for the first time since 1999. Despite suffering from an injury, Berghuis made 37 appearances and scored 7 goals in all competitions. At the end of the 2016–17 season, Berghuis expressed hope he would join Feyenoord for another season rather than return to Watford.


title: Steven Berghuis

text: On 31 July 2017, Feyenoord announced the permanent signing of Berghuis, with Berghuis signing a four-year contract. On 22 April 2018 he played as Feyenoord won the 2017–18 KNVB Cup final 3–0 against his former club AZ.


title: Steven Berghuis

text: On 23 September 2018, Berghuis made international news when he feigned injury by diving to the ground after a light pat on the head from Utrecht's Willem Janssen. When Berghuis eventually got back on his feet he continued to fake injury by holding his head.


title: Steven Berghuis

text: On 16 July 2021, Ajax announced they had agreed a deal with Feyenoord to sign Berghuis, subject to a medical, on a four-year deal for an undisclosed fee. The move caused controversy in the Netherlands due to rivalry between the two sides, especially between their fans. For several years, away supporters have not been allowed at matches between the clubs. He scored his first goal for the club in a 5–1 away win over Sporting CP in Ajax's first group match of the 2021–22 UEFA Champions League.


title: Steven Berghuis

text: Berghuis has achieved international recognition for Netherlands at under-19 and -21 level. In October 2009, he was called-up by the under-19 squad for the first time, then made his U19 debut on 9 October 2009 against France, scoring in a 4–2 win. He played two matches in the 2010 UEFA European Under-19 Championship, scoring the winning goal in a 1–0 group stage victory over England.


title: Steven Berghuis

text: In May 2011, Berghuis was called-up by the U21 team for the first time. He scored on his U21 debut in a 2–0 friendly match victory over Israel on 27 May 2011. He also scored in his second appearance in the same month in a 5–0 friendly win against Albania.


title: Steven Berghuis

text: In February 2012, Berghuis was called-up by the Netherlands U20 squad for the first time. He made his U20 debut as a starter before being substituted-off in the second half of a 3–0 win over Denmark on 29 February 2012. Berghuis made four appearances for the U20 side.


title: Steven Berghuis

text: In May 2015, Berghuis was called-up to the Dutch National team. However, he did not play and twice was an unused substitute.


title: Steven Berghuis

text: One year later, in May 2016, Berghuis was again called-up to the senior Netherlands squad. His call-up met with criticism because he had played just 222 minutes at Watford during the 2015–16 season. He made his "Oranje" debut on 27 May as a second-half substitute in a 1–1 draw against the Republic of Ireland.


title: Steven Berghuis

text: On 27 March 2021, Berghuis scored his first goal for the national team, scoring the opening goal in a 2–0 win against Latvia during the 2022 FIFA World Cup qualifiers.


title: Steven Berghuis

text: Steven is the son of footballer Frank Berghuis, who played for Volendam, VVV-Venlo and Cambuur, among others, and also earned one cap for the Netherlands senior international team. His brother Tristan Berghuis was also a Dutch youth international. He plays in a youth team affiliated to Vitesse, and in 2011 had trials with Chelsea and Tottenham Hotspur.


title: Steve Wilkos

text: Steven John Wilkos (; born March 9, 1964) is an American television personality, a veteran of the United States Marine Corps and a former law enforcement officer with the Chicago Police Department. He has been hosting "The Steve Wilkos Show" since 2007, and was director of security on "Jerry Springer" from 1994 to 2007. He had previously substituted for Springer as host on several occasions before being given his own talk show.


title: Steve Wilkos

text: Born in Chicago, Wilkos grew up in what is now the Roscoe Village neighborhood in North Center, Chicago, and is one of four children. His parents are Jeanette (née Pelikan), a beauty school instructor, and Stanley Wilkos, a former police officer who was in the Korean War as an army paratrooper. He graduated from Lane Technical High School in 1982.


title: Steve Wilkos

text: In October 1982, Wilkos joined the United States Marine Corps, serving in South Korea, Japan, Illinois, Virginia, and South Carolina before being discharged in March 1989.


title: Steve Wilkos

text: Wilkos joined the Chicago Police Department in 1990, where he was stationed at various times in the Logan Square, Chicago, Humboldt Park, and Near West Side neighborhoods.


title: Steve Wilkos

text: In May 1994, the producers of "Jerry Springer", taped in Chicago at that time, needed security guards, so they decided to hire Wilkos and other off-duty police officers to work part-time for the show. Wilkos recruited several fellow officers for the job, and he retired from the force in 2004 and worked exclusively for the show beginning in 2001.


title: Steve Wilkos

text: "Entertainment Weekly" reported that Wilkos became a professional wrestler with the Maryland Championship Wrestling during a temporary production hiatus of "Jerry Springer". In 2005, Wilkos appeared as a guest on "Check, Please!", a restaurant-reviewing program on Chicago's PBS station, WTTW. In 2006, after Springer began what would be a seven-episode stint on "Dancing with the Stars", Wilkos filled in for him in the meantime and Springer later recruited Wilkos to substitute for him each Monday, calling him "the obvious choice."


title: Steve Wilkos

text: Beyond "Jerry Springer", he has made cameo appearances on the MLB Network. He's also appeared on TV series "Between Brothers", "The Wayans Bros." and in the movie "" as a security guard for Jerry Springer.


title: Steve Wilkos

text: In January 2007, NBC Universal Television officially announced that Wilkos would host a talk show of his own based at NBC Tower in Chicago. The self-titled program premiered on September 10, 2007, and received high ratings. Steve is known for his abrasive approach to solving disputes on his self-titled show, tackling many different issues like child abuse, molestation, and cheating partners.


title: Steve Wilkos

text: Wilkos expressed disapproval with the first season of the talk show, as he reflected: "All I did was yell at everybody and throw people off the stage. There was no level of emotion -- just hardcore yelling." Wilkos said this was how he was produced by his original executive producer, but that his wife encouraged him to be himself and go with his "gut."


title: Steve Wilkos

text: Like other tabloid talk shows, "The Steve Wilkos Show" aired primarily on affiliates of Fox, MyNetworkTV and The CW. Only scattered ABC, CBS and NBC affiliates in smaller markets aired it to fill their timeslot. The CW Plus has aired "The Steve Wilkos Show" since 2007, airing weekdays between 8am-10am.


title: Steve Wilkos

text: He married his third wife Rachelle Consiglio, the executive producer for "Jerry Springer" as well as his own show, in 2000. They have two children. They lived in Park Ridge, Illinois until moving to Darien, Connecticut in 2009 when "The Steve Wilkos Show" moved production to nearby Stamford. In 2015, Wilkos sold his Park Ridge home for $750,000. Wilkos also owns a summer house in Camp Lake, Wisconsin.


title: Steve Wilkos

text: Wilkos identifies as a Republican. In an interview after the 2016 election, Wilkos described candidates Clinton and Trump as "so flawed" and said that they were both "poor" candidates, but said he was "glad" that Trump won.


title: Steve Wilkos

text: On January 21, 2018, Wilkos was involved in a rollover crash near his home and was charged with drunk driving. He has asked a judge for an alternative punishment which would result in charges being dismissed upon completion of an education and treatment program.


title: Tulsa King

text: Tulsa King is an American crime drama television series created by Taylor Sheridan with Terence Winter showrunning for Paramount+. The series stars Sylvester Stallone, marking his first leading role in a scripted television series. Stallone plays a Mafia capo who just got out of prison and is sent to Tulsa, Oklahoma, where he tries to set up a criminal organization. It premiered on November 13, 2022. In November 2022, the series was renewed for a second season.


title: Tulsa King

text: Dwight "The General" Manfredi is a New York Mafia capo who just completed a 25-year prison sentence. Upon release, his boss sends him to Tulsa, Oklahoma, to establish criminal operations there. Not knowing anyone in the area, The General seeks a new crew to help establish his empire.


title: Tulsa King

text: "Tulsa King" was first announced in December 2021 as "Kansas City", a new Paramount+ series created by Taylor Sheridan and showrun by Terence Winter. Sylvester Stallone was cast in the lead role, where he made his scripted television debut. It was ordered to series by February 2022, and the title and concept were reworked to take place in Tulsa instead of Kansas City, Missouri, with Max Casella, Domenick Lombardozzi, Vincent Piazza, and Jay Will added to the cast. In May, A.C. Peterson, Andrea Savage, Martin Starr, and Garrett Hedlund were cast. Dana Delany was added in June. In August, Annabella Sciorra was added to the cast.


title: Tulsa King

text: Sheridan created the series during the COVID-19 pandemic, taking a week to come up with the idea, write the pilot, and recruit Stallone to the project. Some filming occcured in Tulsa on March 29, 2022, at Tulsa International Airport. Most interior filming occurred in Oklahoma City at Prairie Surf Media, which also hosted the production offices for the entire first season; most other exterior location filming also occurred there.


title: Tulsa King

text: The series premiered on November 13, 2022, on Paramount+. The first two episodes of "Tulsa King" are scheduled to receive special linear television airings on Paramount Network on November 20 and 27, serving as a lead-out for the fifth season of "Yellowstone". On November 30, 2022, Paramount+ renewed the series for a second season.


title: Tulsa King

text: The review aggregator website Rotten Tomatoes reported a 78% approval rating and an average rating of 6.5/10, based on 40 reviews. The website's critics consensus reads, ""Tulsa King"s stale comedy sometimes feels like ordering spaghetti with marinara and instead getting egg noodles and ketchup, but Sylvester Stallone still commands the screen with his swaggering charm." On Metacritic, it has a weighted average score of 65 out of 100 based on 28 critics, indicating "generally favorable reviews".


title: Tulsa King

text: James Delingpole, writing in "The Spectator", wondered "how morally warped does an audience have to be to root for a character whose primary goal is to transform somewhere relatively sweet and innocent into yet another urban cesspit?" and wrote that "the worrying suspicion arises that our perceived nostalgia for Stallone is being asked to do all the heavy lifting here." He concluded that "writers Taylor Sheridan and Terence Winter could have exploited all this in a storyline that didn't leave such a nasty taste in the mouth."


title: Tulsa King

text: The premiere episode that aired on Paramount Network on November 20, 2022 had 3.7 million viewers, "making it the best new linear cable premiere of 2022".


title: Salomón Rondón

text: José Salomón Rondón Giménez (; born 16 September 1989) is a Venezuelan professional footballer who plays as a striker for the Venezuela national team, and is currently a free agent.


title: Salomón Rondón

text: After starting out at Aragua, he went on to spend most of his career in Europe, appearing in La Liga with Málaga, the Russian Premier League with Rubin Kazan, Zenit Saint Petersburg (winning the 2015 national championship with the latter club) & CSKA Moscow, and the Premier League with West Bromwich Albion, Newcastle United and Everton. A Venezuela international since 2008, Rondón is the country's all-time top goalscorer with 38 goals, and he represented his country in four Copa América tournaments.


title: Salomón Rondón

text: Born in Caracas, Rondón's sporting idols growing up were Ronaldo and Michael Jordan. He made his debut in the Venezuelan Primera División at the age of 17, appearing for Aragua FC against Carabobo FC on 8 October 2006; on 8 April of the following year he scored his first goal(s) for the club, in a 2–2 draw against Caracas FC.


title: Salomón Rondón

text: In the summer of 2008, Rondón was signed by UD Las Palmas in Spain, and made his official debut on 5 October in a 1–2 away loss against Deportivo Alavés in the Segunda División. Almost a year after his arrival, on 2 September 2009, he netted his first goal, in a Copa del Rey match against Cádiz CF – becoming the youngest foreign player to ever score for the club, at the age of 19 years, 11 months and 17 days – and finished the season with ten goals in 36 games, as the Canary Islands side narrowly avoided relegation.


title: Salomón Rondón

text: On 19 July 2010, Málaga CF signed Rondón for a record €3.5 million transfer fee. He scored his first goal for the Andalusians exactly two months later, in a 1–2 home defeat against Sevilla FC in La Liga. Four days later, he opened the score in a 2–0 win at Getafe CF, adding a third the following week in a 2–3 home loss to Villarreal CF.


title: Salomón Rondón

text: On 1 May 2011, Rondón contributed with one goal as Málaga came from behind at home to defeat Hércules CF 3–1. That was his 13th goal of the campaign, with which he surpassed the record of goals from a Venezuelan footballer in the Spanish top flight previously held by Juan Arango; the team finally escaped relegation, with the player finishing as their top scorer.


title: Salomón Rondón

text: Rondón started 2011–12 on the substitutes bench. He eventually beat competition from ageing Ruud van Nistelrooy, again finishing as Málaga's best scorer – this included goals in narrow home wins against RCD Espanyol (2–1) and Levante UD (1–0), and a brace against Rayo Vallecano (4–2 success, also at La Rosaleda Stadium).


title: Salomón Rondón

text: In August 2012, Rondón signed for Russian Premier League team FC Rubin Kazan, for a reported fee of €10 million which made him the most expensive Venezuelan player in history. He made his league debut on the 12th in a 2–0 home win over FC Dynamo Moscow, and he scored his first goal against FC Terek Grozny on 1 September, albeit in a 1–2 home defeat.


title: Salomón Rondón

text: Rondón made his first appearance in the UEFA Europa League against Inter Milan, and he scored once in a 2–2 group stage away draw, also playing the entire match. In the second match between the two sides he netted a brace in the final three minutes, helping his team to a 3–0 win.


title: Salomón Rondón

text: On 10 March 2013, following the winter break in the Russian Premier League, Rondón scored the only goal of the match as Rubin claimed a home victory over reigning champions FC Zenit Saint Petersburg. In continental competition, he opened up the scoring in the 100th minute of the round-of-16 clash against Levante, latching on to a cross from Bibras Natcho as the hosts won it 2–0 in that leg and on aggregate.


title: Salomón Rondón

text: On 19 April 2013, Rondón opened the scoring for Rubin, who could only manage a 1–1 draw at relegation-threatened FC Amkar Perm. In the club's next league match, against PFC CSKA Moscow, he netted the first goal in a 2–0 victory over the league leaders and eventual champions.


title: Salomón Rondón

text: On 1 September 2013, Rondón scored a hat-trick in a 3–0 win against recently promoted FC Ural Sverdlovsk Oblast.


title: Salomón Rondón

text: On 31 January 2014, Rondón underwent a medical and joined fellow league club Zenit Saint Petersburg, signing a five-year contract for a fee in the region of £15.8 million. He played his first game for his new team on 25 February, scoring in an eventual 2–1 away win against Borussia Dortmund in the UEFA Champions League's round of 16-second-leg (4–5 aggregate defeat).


title: Salomón Rondón

text: On 6 April 2014, again as a second-half substitute, Rondón scored a rare second-half hat-trick in a 6–2 home routing of former team Rubin. On 20 September he added another three, in a 5–0 win at FC Rostov.


title: Salomón Rondón

text: On 26 February 2015, Rondón scored a brace at home against PSV Eindhoven, being essential in a 3–0 home victory for the Europa League round of 32 and a 4–0 aggregate triumph.


title: Salomón Rondón

text: On 10 August 2015, Rondón joined English club West Bromwich Albion on a four-year-deal for a club-record fee of £12 million. He made his debut in the Premier League five days later, replacing Craig Gardner in the 62nd minute of an eventual 0–0 away draw against Watford. On 23 August, he made his first start, at the expense of Tottenham Hotspur-linked Saido Berahino, in a 2–3 home defeat to Chelsea, assisting James Morrison in his first goal and later being brought down by John Terry who received a straight red card.


title: Salomón Rondón

text: Rondón scored his first goal for the Baggies on 29 August 2015, netting the game's only in stoppage time of the first half of the away fixture against nine-man Stoke City. On 19 December, he was sent off at the end of a 1–2 home loss to AFC Bournemouth for thrusting his head at Dan Gosling, with teammate James McClean also dismissed in the first half; he finished his first season in English football with ten goals.


title: Salomón Rondón

text: Rondón began the 2016–17 campaign strongly, scoring the winner in the opening match win over Crystal Palace, then continued his impressive form in September with goals in consecutive matches against West Ham United and Stoke. On 21 November he netted once and provided an assist in a 4–0 victory over Burnley, and on 14 December, against Swansea City, he scored his first Premier League hat-trick after netting three headers in a 3–1 win, which was only the second time this feat was achieved in the history of the competition, the first being Everton's Duncan Ferguson in 1997.


title: Salomón Rondón

text: Rondón's goal in a 1–1 draw with Tottenham, on 25 November 2017, made him the first Venezuelan to score at either the rebuilt Wembley Stadium or the original facilities, as well as the first Albion player to score at the new ground. The following 20 January, early into the second half of the away fixture against Everton, he accidentally broke James McCarthy's leg, and was reduced to tears upon realising the extent of McCarthy's injury; recalling the incident in an interview some months later also caused him to become upset.


title: Salomón Rondón

text: On 6 August 2018, Rondón joined Newcastle United on a one-year loan swap, with Dwight Gayle heading in the opposite direction. He made his debut five days later, in a 2–1 home loss against Tottenham on the opening day of the season. He scored his first goal in a 3–1 EFL Cup defeat at Nottingham Forest on 29 August.


title: Salomón Rondón

text: Rondón opened his league account on 10 November 2018, scoring twice to help the hosts defeat Bournemouth 2–1. In the second half of the season, his partnership up front with Ayoze Pérez began to take shape and the Venezuelan often assisted the Spaniard with his goals. He also maintained a steady record in terms of goalscoring and was neck-and-neck with Pérez until the latter stages of the campaign, finishing with eleven league goals—just one behind his teammate.


title: Salomón Rondón

text: In May 2019, Rondón was named Newcastle's player of the year, becoming the first forward to win the award since Alan Shearer in 2003.


title: Salomón Rondón

text: On 19 July 2019, Rondón signed with Dalian Yifang of the Chinese Super League, reuniting with manager Rafael Benítez who had joined the club two weeks before and reportedly activated the player's release clause of £16.5 million.


title: Salomón Rondón

text: On 15 February 2021, Rondón joined Russian Premier League side CSKA Moscow on loan. In his first match at Arena CSKA, Rondón scored his first goal for the Moscow team and also gave an assist, merits that led him to be named the best player of the match. Furthermore, he was voted the best CSKA player of the month of March. Rondón ended his time at CSKA becoming one of the most valuable players in the Russian competition after participating in 37.5% of the team's goals since his arrival with four goals and two assists of the team's 16 goals in that time.


title: Salomón Rondón

text: On 31 August 2021 Rondón joined Everton on a free transfer, reuniting with his former Newcastle and Dalian Pro manager Rafael Benítez. He signed a two-year contract with the option for a third season. He scored his first goal for the club in December 2021 against Crystal Palace in a 3–1 loss at Selhurst Park. In March 2022, he scored both goals in a 2–0 victory over National League side Boreham Wood at Goodison Park in the fifth round of the FA Cup. On 16 December 2022, Everton announced that Rondon had left "with immediate effect after reaching an agreement with the club to terminate his contract".


title: Salomón Rondón

text: Rondón appeared for the Venezuela under-20 side in the 2009 FIFA World Cup in Egypt. He scored four times during the competition – as teammate Yonathan del Valle, with both netting hat-tricks in the 8–0 group stage routing of Tahiti – as the former managed to qualify for the last-16 stage.


title: Salomón Rondón

text: Previously, on 3 February 2008, 18-year-old Rondón made his debut for the senior team in a friendly with Haiti, scoring his first goal on 23 March against El Salvador (another exhibition match, another 1–0 win). In 2011, he took 4th place at Copa America. For this, the team received copper medals.


title: Salomón Rondón

text: Selected by manager Noel Sanvicente to the 2015 Copa América, he scored in "La Vinotinto"'s first game of the tournament to help defeat Colombia 1–0; later that year, he was among 15 national players who threatened to quit the team after the president of the Venezuelan Football Federation accused them of conspiring to get the manager sacked.


title: Salomón Rondón

text: On 5 June 2016, during the Copa América Centenario, Rondón earned his 50th cap, starting in a 1–0 group stage win against Jamaica in Chicago. He scored the only goal of the following game against Uruguay to become the first Venezuelan player to find the net at three tournaments, and repeated the feat in the quarter-finals, a 1–4 defeat to Argentina.


title: Salomón Rondón

text: On 9 June 2019, after his brace in a 3–0 friendly victory over the United States in Cincinnati, Rondón surpassed former holder Juan Arango to become Venezuela's all-time top scorer at 24 goals.


title: Addition

text: Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or "sum" of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression (that is, "3 "plus" 2 is equal to 5").


title: Addition

text: Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.


title: Addition

text: Addition has several important properties. It is commutative, meaning that the order of the operands does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see "Summation"). Repeated addition of is the same as counting (see "Successor function"). Addition of does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.


title: Addition

text: Performing addition is one of the simplest numerical tasks to do. Addition of very small numbers is accessible to toddlers; the most basic task, , can be performed by infants as young as five months, and even some members of other animal species. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.


title: Addition

text: Addition is written using the plus sign "+" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,


title: Addition

text: The sum of a series of related numbers can be expressed through capital sigma notation, which compactly denotes iteration. For example,


title: Addition

text: The numbers or the objects to be added in general addition are collectively referred to as the terms, the addends or the summands;


title: Addition

text: Some authors call the first addend the "augend". In fact, during the Renaissance, many authors did not consider the first addend an "addend" at all. Today, due to the commutative property of addition, "augend" is rarely used, and both terms are generally called addends.


title: Addition

text: All of the above terminology derives from Latin. "Addition" and "add" are English words derived from the Latin verb "addere", which is in turn a compound of "ad" "to" and "dare" "to give", from the Proto-Indo-European root "to give"; thus to "add" is to "give to". Using the gerundive suffix "-nd" results in "addend", "thing to be added". Likewise from "augere" "to increase", one gets "augend", "thing to be increased".


title: Addition

text: "Sum" and "summand" derive from the Latin noun "summa" "the highest, the top" and associated verb "summare". This is appropriate not only because the sum of two positive numbers is greater than either, but because it was common for the ancient Greeks and Romans to add upward, contrary to the modern practice of adding downward, so that a sum was literally higher than the addends.


title: Addition

text: "Addere" and "summare" date back at least to Boethius, if not to earlier Roman writers such as Vitruvius and Frontinus; Boethius also used several other terms for the addition operation. The later Middle English terms "adden" and "adding" were popularized by Chaucer.


title: Addition

text: The plus sign "+" (Unicode:U+002B; ASCII: codice_1) is an abbreviation of the Latin word "et", meaning "and". It appears in mathematical works dating back to at least 1489.


title: Addition

text: Addition is used to model many physical processes. Even for the simple case of adding natural numbers, there are many possible interpretations and even more visual representations.


title: Addition

text: This interpretation is easy to visualize, with little danger of ambiguity. It is also useful in higher mathematics (for the rigorous definition it inspires, see below). However, it is not obvious how one should extend this version of addition to include fractional numbers or negative numbers.


title: Addition

text: One possible fix is to consider collections of objects that can be easily divided, such as pies or, still better, segmented rods. Rather than solely combining collections of segments, rods can be joined end-to-end, which illustrates another conception of addition: adding not the rods but the lengths of the rods.


title: Addition

text: The sum "a" + "b" can be interpreted as a binary operation that combines "a" and "b", in an algebraic sense, or it can be interpreted as the addition of "b" more units to "a". Under the latter interpretation, the parts of a sum play asymmetric roles, and the operation is viewed as applying the unary operation +"b" to "a". Instead of calling both "a" and "b" addends, it is more appropriate to call "a" the augend in this case, since "a" plays a passive role. The unary view is also useful when discussing subtraction, because each unary addition operation has an inverse unary subtraction operation, and "vice versa".


title: Addition

text: Addition is commutative, meaning that one can change the order of the terms in a sum, but still get the same result. Symbolically, if "a" and "b" are any two numbers, then


title: Addition

text: The fact that addition is commutative is known as the "commutative law of addition" or "commutative property of addition". Some other binary operations are commutative, such as multiplication, but many others are not, such as subtraction and division.


title: Addition

text: Addition is associative, which means that when three or more numbers are added together, the order of operations does not change the result.


title: Addition

text: As an example, should the expression "a" + "b" + "c" be defined to mean ("a" + "b") + "c" or "a" + ("b" + "c")? Given that addition is associative, the choice of definition is irrelevant. For any three numbers "a", "b", and "c", it is true that . For example, .


title: Addition

text: When addition is used together with other operations, the order of operations becomes important. In the standard order of operations, addition is a lower priority than exponentiation, nth roots, multiplication and division, but is given equal priority to subtraction.


title: Addition

text: Adding zero to any number, does not change the number; this means that zero is the identity element for addition, and is also known as the additive identity. In symbols, for every , one has


title: Addition

text: This law was first identified in Brahmagupta's "Brahmasphutasiddhanta" in 628 AD, although he wrote it as three separate laws, depending on whether "a" is negative, positive, or zero itself, and he used words rather than algebraic symbols. Later Indian mathematicians refined the concept; around the year 830, Mahavira wrote, "zero becomes the same as what is added to it", corresponding to the unary statement . In the 12th century, Bhaskara wrote, "In the addition of cipher, or subtraction of it, the quantity, positive or negative, remains the same", corresponding to the unary statement .


title: Addition

text: Within the context of integers, addition of one also plays a special role: for any integer "a", the integer is the least integer greater than "a", also known as the successor of "a". For instance, 3 is the successor of 2 and 7 is the successor of 6. Because of this succession, the value of can also be seen as the "b"th successor of "a", making addition iterated succession. For example, is 8, because 8 is the successor of 7, which is the successor of 6, making 8 the 2nd successor of 6.


title: Addition

text: To numerically add physical quantities with units, they must be expressed with common units. For example, adding 50 milliliters to 150 milliliters gives 200 milliliters. However, if a measure of 5 feet is extended by 2 inches, the sum is 62 inches, since 60 inches is synonymous with 5 feet. On the other hand, it is usually meaningless to try to add 3 meters and 4 square meters, since those units are incomparable; this sort of consideration is fundamental in dimensional analysis.


title: Addition

text: Studies on mathematical development starting around the 1980s have exploited the phenomenon of habituation: infants look longer at situations that are unexpected. A seminal experiment by Karen Wynn in 1992 involving Mickey Mouse dolls manipulated behind a screen demonstrated that five-month-old infants "expect" to be 2, and they are comparatively surprised when a physical situation seems to imply that is either 1 or 3. This finding has since been affirmed by a variety of laboratories using different methodologies. Another 1992 experiment with older toddlers, between 18 and 35 months, exploited their development of motor control by allowing them to retrieve ping-pong balls from a box; the youngest responded well for small numbers, while older subjects were able to compute sums up to 5.


title: Addition

text: Even some nonhuman animals show a limited ability to add, particularly primates. In a 1995 experiment imitating Wynn's 1992 result (but using eggplants instead of dolls), rhesus macaque and cottontop tamarin monkeys performed similarly to human infants. More dramatically, after being taught the meanings of the Arabic numerals 0 through 4, one chimpanzee was able to compute the sum of two numerals without further training. More recently, Asian elephants have demonstrated an ability to perform basic arithmetic.


title: Addition

text: Typically, children first master counting. When given a problem that requires that two items and three items be combined, young children model the situation with physical objects, often fingers or a drawing, and then count the total. As they gain experience, they learn or discover the strategy of "counting-on": asked to find two plus three, children count three past two, saying "three, four, "five"" (usually ticking off fingers), and arriving at five. This strategy seems almost universal; children can easily pick it up from peers or teachers. Most discover it independently. With additional experience, children learn to add more quickly by exploiting the commutativity of addition by counting up from the larger number, in this case, starting with three and counting "four, "five"." Eventually children begin to recall certain addition facts ("number bonds"), either through experience or rote memorization. Once some facts are committed to memory, children begin to derive unknown facts from known ones. For example, a child asked to add six and seven may know that and then reason that is one more, or 13. Such derived facts can be found very quickly and most elementary school students eventually rely on a mixture of memorized and derived facts to add fluently.


title: Addition

text: Different nations introduce whole numbers and arithmetic at different ages, with many countries teaching addition in pre-school. However, throughout the world, addition is taught by the end of the first year of elementary school.


title: Addition

text: Children are often presented with the addition table of pairs of numbers from 0 to 9 to memorize. Knowing this, children can perform any addition.


title: Addition

text: The prerequisite to addition in the decimal system is the fluent recall or derivation of the 100 single-digit "addition facts". One could memorize all the facts by rote, but pattern-based strategies are more enlightening and, for most people, more efficient:


title: Addition

text: As students grow older, they commit more facts to memory, and learn to derive other facts rapidly and fluently. Many students never commit all the facts to memory, but can still find any basic fact quickly.


title: Addition

text: The standard algorithm for adding multidigit numbers is to align the addends vertically and add the columns, starting from the ones column on the right. If a column exceeds nine, the extra digit is "carried" into the next column. For example, in the addition


title: Addition

text: 7 + 9 = 16, and the digit 1 is the carry. An alternate strategy starts adding from the most significant digit on the left; this route makes carrying a little clumsier, but it is faster at getting a rough estimate of the sum. There are many alternative methods.


title: Addition

text: Since the end of the 20th century, some US programs, including TERC, decided to remove the traditional transfer method from their curriculum. This decision was criticized, which is why some states and counties didn't support this experiment.


title: Addition

text: Decimal fractions can be added by a simple modification of the above process. One aligns two decimal fractions above each other, with the decimal point in the same location. If necessary, one can add trailing zeros to a shorter decimal to make it the same length as the longer decimal. Finally, one performs the same addition process as above, except the decimal point is placed in the answer, exactly where it was placed in the summands.


title: Addition

text: In scientific notation, numbers are written in the form formula_8, where formula_9 is the significand and formula_10 is the exponential part. Addition requires two numbers in scientific notation to be represented using the same exponential part, so that the two significands can simply be added.


title: Addition

text: Addition in other bases is very similar to decimal addition. As an example, one can consider addition in binary. Adding two single-digit binary numbers is relatively simple, using a form of carrying:


title: Addition

text: Adding two "1" digits produces a digit "0", while 1 must be added to the next column. This is similar to what happens in decimal when certain single-digit numbers are added together; if the result equals or exceeds the value of the radix (10), the digit to the left is incremented:


title: Addition

text: This is known as "carrying". When the result of an addition exceeds the value of a digit, the procedure is to "carry" the excess amount divided by the radix (that is, 10/10) to the left, adding it to the next positional value. This is correct since the next position has a weight that is higher by a factor equal to the radix. Carrying works the same way in binary:


title: Addition

text: In this example, two numerals are being added together: 01101 (13) and 10111 (23). The top row shows the carry bits used. Starting in the rightmost column, . The 1 is carried to the left, and the 0 is written at the bottom of the rightmost column. The second column from the right is added: again; the 1 is carried, and 0 is written at the bottom. The third column: . This time, a 1 is carried, and a 1 is written in the bottom row. Proceeding like this gives the final answer 100100 (36).


title: Addition

text: Analog computers work directly with physical quantities, so their addition mechanisms depend on the form of the addends. A mechanical adder might represent two addends as the positions of sliding blocks, in which case they can be added with an averaging lever. If the addends are the rotation speeds of two shafts, they can be added with a differential. A hydraulic adder can add the pressures in two chambers by exploiting Newton's second law to balance forces on an assembly of pistons. The most common situation for a general-purpose analog computer is to add two voltages (referenced to ground); this can be accomplished roughly with a resistor network, but a better design exploits an operational amplifier.


title: Addition

text: Addition is also fundamental to the operation of digital computers, where the efficiency of addition, in particular the carry mechanism, is an important limitation to overall performance.


title: Addition

text: The abacus, also called a counting frame, is a calculating tool that was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere; it dates back to at least 2700–2300 BC, when it was used in Sumer.


title: Addition

text: Blaise Pascal invented the mechanical calculator in 1642; it was the first operational adding machine. It made use of a gravity-assisted carry mechanism. It was the only operational mechanical calculator in the 17th century and the earliest automatic, digital computer. Pascal's calculator was limited by its carry mechanism, which forced its wheels to only turn one way so it could add. To subtract, the operator had to use the Pascal's calculator's complement, which required as many steps as an addition. Giovanni Poleni followed Pascal, building the second functional mechanical calculator in 1709, a calculating clock made of wood that, once setup, could multiply two numbers automatically.


title: Addition

text: Adders execute integer addition in electronic digital computers, usually using binary arithmetic. The simplest architecture is the ripple carry adder, which follows the standard multi-digit algorithm. One slight improvement is the carry skip design, again following human intuition; one does not perform all the carries in computing , but one bypasses the group of 9s and skips to the answer.


title: Addition

text: In practice, computational addition may be achieved via XOR and AND bitwise logical operations in conjunction with bitshift operations as shown in the pseudocode below. Both XOR and AND gates are straightforward to realize in digital logic allowing the realization of full adder circuits which in turn may be combined into more complex logical operations. In modern digital computers, integer addition is typically the fastest arithmetic instruction, yet it has the largest impact on performance, since it underlies all floating-point operations as well as such basic tasks as address generation during memory access and fetching instructions during branching. To increase speed, modern designs calculate digits in parallel; these schemes go by such names as carry select, carry lookahead, and the Ling pseudocarry. Many implementations are, in fact, hybrids of these last three designs. Unlike addition on paper, addition on a computer often changes the addends. On the ancient abacus and adding board, both addends are destroyed, leaving only the sum. The influence of the abacus on mathematical thinking was strong enough that early Latin texts often claimed that in the process of adding "a number to a number", both numbers vanish. In modern times, the ADD instruction of a microprocessor often replaces the augend with the sum but preserves the addend. In a high-level programming language, evaluating does not change either "a" or "b"; if the goal is to replace "a" with the sum this must be explicitly requested, typically with the statement . Some languages such as C or C++ allow this to be abbreviated as .


title: Addition

text: On a computer, if the result of an addition is too large to store, an arithmetic overflow occurs, resulting in an incorrect answer. Unanticipated arithmetic overflow is a fairly common cause of program errors. Such overflow bugs may be hard to discover and diagnose because they may manifest themselves only for very large input data sets, which are less likely to be used in validation tests. The Year 2000 problem was a series of bugs where overflow errors occurred due to use of a 2-digit format for years.


title: Addition

text: To prove the usual properties of addition, one must first define addition for the context in question. Addition is first defined on the natural numbers. In set theory, addition is then extended to progressively larger sets that include the natural numbers: the integers, the rational numbers, and the real numbers. (In mathematics education, positive fractions are added before negative numbers are even considered; this is also the historical route.)


title: Addition

text: There are two popular ways to define the sum of two natural numbers "a" and "b". If one defines natural numbers to be the cardinalities of finite sets, (the cardinality of a set is the number of elements in the set), then it is appropriate to define their sum as follows:


title: Addition

text: Here, is the union of "A" and "B". An alternate version of this definition allows "A" and "B" to possibly overlap and then takes their disjoint union, a mechanism that allows common elements to be separated out and therefore counted twice.


title: Addition

text: Again, there are minor variations upon this definition in the literature. Taken literally, the above definition is an application of the recursion theorem on the partially ordered set N. On the other hand, some sources prefer to use a restricted recursion theorem that applies only to the set of natural numbers. One then considers "a" to be temporarily "fixed", applies recursion on "b" to define a function ""a" +", and pastes these unary operations for all "a" together to form the full binary operation.


title: Addition

text: This recursive formulation of addition was developed by Dedekind as early as 1854, and he would expand upon it in the following decades. He proved the associative and commutative properties, among others, through mathematical induction.


title: Addition

text: The simplest conception of an integer is that it consists of an absolute value (which is a natural number) and a sign (generally either positive or negative). The integer zero is a special third case, being neither positive nor negative. The corresponding definition of addition must proceed by cases:


title: Addition

text: Although this definition can be useful for concrete problems, the number of cases to consider complicates proofs unnecessarily. So the following method is commonly used for defining integers. It is based on the remark that every integer is the difference of two natural integers and that two such differences, and are equal if and only if .


title: Addition

text: So, one can define formally the integers as the equivalence classes of ordered pairs of natural numbers under the equivalence relation


title: Addition

text: The equivalence class of contains either if , or otherwise. If is a natural number, one can denote the equivalence class of , and by the equivalence class of . This allows identifying the natural number with the equivalence class .


title: Addition

text: A straightforward computation shows that the equivalence class of the result depends only on the equivalences classes of the summands, and thus that this defines an addition of equivalence classes, that is integers. Another straightforward computation shows that this addition is the same as the above case definition.


title: Addition

text: This way of defining integers as equivalence classes of pairs of natural numbers, can be used to embed into a group any commutative semigroup with cancellation property. Here, the semigroup is formed by the natural numbers and the group is the additive group of integers. The rational numbers are constructed similarly, by taking as semigroup the nonzero integers with multiplication.


title: Addition

text: This construction has been also generalized under the name of Grothendieck group to the case of any commutative semigroup. Without the cancellation property the semigroup homomorphism from the semigroup into the group may be non-injective. Originally, the "Grothendieck group" was, more specifically, the result of this construction applied to the equivalences classes under isomorphisms of the objects of an abelian category, with the direct sum as semigroup operation.


title: Addition

text: Addition of rational numbers can be computed using the least common denominator, but a conceptually simpler definition involves only integer addition and multiplication:


title: Addition

text: Addition of fractions is much simpler when the denominators are the same; in this case, one can simply add the numerators while leaving the denominator the same: formula_16, so formula_17.


title: Addition

text: The commutativity and associativity of rational addition is an easy consequence of the laws of integer arithmetic. For a more rigorous and general discussion, see "field of fractions".


title: Addition

text: A common construction of the set of real numbers is the Dedekind completion of the set of rational numbers. A real number is defined to be a Dedekind cut of rationals: a non-empty set of rationals that is closed downward and has no greatest element. The sum of real numbers "a" and "b" is defined element by element:


title: Addition

text: The commutativity and associativity of real addition are immediate; defining the real number 0 to be the set of negative rationals, it is easily seen to be the additive identity. Probably the trickiest part of this construction pertaining to addition is the definition of additive inverses.


title: Addition

text: Unfortunately, dealing with multiplication of Dedekind cuts is a time-consuming case-by-case process similar to the addition of signed integers. Another approach is the metric completion of the rational numbers. A real number is essentially defined to be the limit of a Cauchy sequence of rationals, lim "a". Addition is defined term by term:


title: Addition

text: This definition was first published by Georg Cantor, also in 1872, although his formalism was slightly different.


title: Addition

text: One must prove that this operation is well-defined, dealing with co-Cauchy sequences. Once that task is done, all the properties of real addition follow immediately from the properties of rational numbers. Furthermore, the other arithmetic operations, including multiplication, have straightforward, analogous definitions.


title: Addition

text: Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers "A" and "B", interpreted as points of the complex plane, is the point "X" obtained by building a parallelogram three of whose vertices are "O", "A" and "B". Equivalently, "X" is the point such that the triangles with vertices "O", "A", "B", and "X", "B", "A", are congruent.


title: Addition

text: There are many binary operations that can be viewed as generalizations of the addition operation on the real numbers. The field of abstract algebra is centrally concerned with such generalized operations, and they also appear in set theory and category theory.


title: Addition

text: In linear algebra, a vector space is an algebraic structure that allows for adding any two vectors and for scaling vectors. A familiar vector space is the set of all ordered pairs of real numbers; the ordered pair ("a","b") is interpreted as a vector from the origin in the Euclidean plane to the point ("a","b") in the plane. The sum of two vectors is obtained by adding their individual coordinates:


title: Addition

text: This addition operation is central to classical mechanics, in which velocities, accelerations and forces are all represented by vectors.


title: Addition

text: Matrix addition is defined for two matrices of the same dimensions. The sum of two "m" × "n" (pronounced "m by n") matrices A and B, denoted by , is again an matrix computed by adding corresponding elements:


title: Addition

text: In modular arithmetic, the set of available numbers is restricted to a finite subset of the integers, and addition "wraps around" when reaching a certain value, called the modulus. For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function. A similar "wrap around" operation arises in geometry, where the sum of two angle measures is often taken to be their sum as real numbers modulo 2π. This amounts to an addition operation on the circle, which in turn generalizes to addition operations on many-dimensional tori.


title: Addition

text: The general theory of abstract algebra allows an "addition" operation to be any associative and commutative operation on a set. Basic algebraic structures with such an addition operation include commutative monoids and abelian groups.


title: Addition

text: A far-reaching generalization of addition of natural numbers is the addition of ordinal numbers and cardinal numbers in set theory. These give two different generalizations of addition of natural numbers to the transfinite. Unlike most addition operations, addition of ordinal numbers is not commutative. Addition of cardinal numbers, however, is a commutative operation closely related to the disjoint union operation.


title: Addition

text: In category theory, disjoint union is seen as a particular case of the coproduct operation, and general coproducts are perhaps the most abstract of all the generalizations of addition. Some coproducts, such as direct sum and wedge sum, are named to evoke their connection with addition.


title: Addition

text: Addition, along with subtraction, multiplication and division, is considered one of the basic operations and is used in elementary arithmetic.


title: Addition

text: Subtraction can be thought of as a kind of addition—that is, the addition of an additive inverse. Subtraction is itself a sort of inverse to addition, in that adding and subtracting are inverse functions.


title: Addition

text: Given a set with an addition operation, one cannot always define a corresponding subtraction operation on that set; the set of natural numbers is a simple example. On the other hand, a subtraction operation uniquely determines an addition operation, an additive inverse operation, and an additive identity; for this reason, an additive group can be described as a set that is closed under subtraction.


title: Addition

text: Multiplication can be thought of as repeated addition. If a single term appears in a sum "n" times, then the sum is the product of "n" and . If "n" is not a natural number, the product may still make sense; for example, multiplication by yields the additive inverse of a number.


title: Addition

text: In the real and complex numbers, addition and multiplication can be interchanged by the exponential function:


title: Addition

text: This identity allows multiplication to be carried out by consulting a table of logarithms and computing addition by hand; it also enables multiplication on a slide rule. The formula is still a good first-order approximation in the broad context of Lie groups, where it relates multiplication of infinitesimal group elements with addition of vectors in the associated Lie algebra.


title: Addition

text: There are even more generalizations of multiplication than addition. In general, multiplication operations always distribute over addition; this requirement is formalized in the definition of a ring. In some contexts, such as the integers, distributivity over addition and the existence of a multiplicative identity is enough to uniquely determine the multiplication operation. The distributive property also provides information about addition; by expanding the product in both ways, one concludes that addition is forced to be commutative. For this reason, ring addition is commutative in general.


title: Addition

text: Division is an arithmetic operation remotely related to addition. Since , division is right distributive over addition: . However, division is not left distributive over addition; is not the same as .


title: Addition

text: The maximum operation "max ("a", "b")" is a binary operation similar to addition. In fact, if two nonnegative numbers "a" and "b" are of different orders of magnitude, then their sum is approximately equal to their maximum. This approximation is extremely useful in the applications of mathematics, for example in truncating Taylor series. However, it presents a perpetual difficulty in numerical analysis, essentially since "max" is not invertible. If "b" is much greater than "a", then a straightforward calculation of can accumulate an unacceptable round-off error, perhaps even returning zero. See also "Loss of significance".


title: Addition

text: The approximation becomes exact in a kind of infinite limit; if either "a" or "b" is an infinite cardinal number, their cardinal sum is exactly equal to the greater of the two. Accordingly, there is no subtraction operation for infinite cardinals.


title: Addition

text: Maximization is commutative and associative, like addition. Furthermore, since addition preserves the ordering of real numbers, addition distributes over "max" in the same way that multiplication distributes over addition:


title: Addition

text: For these reasons, in tropical geometry one replaces multiplication with addition and addition with maximization. In this context, addition is called "tropical multiplication", maximization is called "tropical addition", and the tropical "additive identity" is negative infinity. Some authors prefer to replace addition with minimization; then the additive identity is positive infinity.


title: Addition

text: Tying these observations together, tropical addition is approximately related to regular addition through the logarithm:


title: Addition

text: which becomes more accurate as the base of the logarithm increases. The approximation can be made exact by extracting a constant "h", named by analogy with Planck's constant from quantum mechanics, and taking the "classical limit" as "h" tends to zero:


title: Addition

text: Summation describes the addition of arbitrarily many numbers, usually more than just two. It includes the idea of the sum of a single number, which is itself, and the empty sum, which is zero. An infinite summation is a delicate procedure known as a series.


title: Addition

text: Integration is a kind of "summation" over a continuum, or more precisely and generally, over a differentiable manifold. Integration over a zero-dimensional manifold reduces to summation.


title: Addition

text: Linear combinations combine multiplication and summation; they are sums in which each term has a multiplier, usually a real or complex number. Linear combinations are especially useful in contexts where straightforward addition would violate some normalization rule, such as mixing of strategies in game theory or superposition of states in quantum mechanics.


title: Addition

text: Convolution is used to add two independent random variables defined by distribution functions. Its usual definition combines integration, subtraction, and multiplication. In general, convolution is useful as a kind of domain-side addition; by contrast, vector addition is a kind of range-side addition.


title: Addition

text: Addition is also used in the musical set theory. George Perle gives the following example: “do-mi, re-fa♯, mi♭-sol are different requirements of one interval... or other type of equality... and are connected with the axis of symmetry. Do-mi belongs to the family of symmetrically connected dyads as it is shown further:”


title: Addition

text: A tonal range of Alban Berg’s Lyric Suite {0,11,7,4,2,9,3,8,10,1,5,6} is a series of six dyads with their total number being 11. If the line is turned and inverted, then it is {0,6,5,1...} with all dyads in total being 6.


title: Radix

text: In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9.


title: Radix

text: In any standard positional numeral system, a number is conventionally written as with "x" as the string of digits and "y" as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (100) is equivalent to 100 (the decimal system is implied in the latter) and represents the number one hundred, while (100) (in the binary system with base 2) represents the number four.


title: Radix

text: "Radix" is a Latin word for "root". "Root" can be considered a synonym for "base," in the arithmetical sense.


title: Radix

text: In the system with radix 13, for example, a string of digits such as 398 denotes the (decimal) number = 632.


title: Radix

text: More generally, in a system with radix "b" (), a string of digits denotes the number , where . In contrast to decimal, or radix 10, which has a ones' place, tens' place, hundreds' place, and so on, radix "b" would have a ones' place, then a "b"s' place, a "b"s' place, etc.


title: Radix

text: The octal and hexadecimal systems are often used in computing because of their ease as shorthand for binary. Every hexadecimal digit corresponds to a sequence of four binary digits, since sixteen is the fourth power of two; for example, hexadecimal 78 is binary . Similarly, every octal digit corresponds to a unique sequence of three binary digits, since eight is the cube of two.


title: Radix

text: This representation is unique. Let "b" be a positive integer greater than 1. Then every positive integer "a" can be expressed uniquely in the form


title: Radix

text: Radices are usually natural numbers. However, other positional systems are possible, for example, golden ratio base (whose radix is a non-integer algebraic number), and negative base (whose radix is negative).


title: Radix

text: A negative base allows the representation of negative numbers without the use of a minus sign. For example, let "b" = −10. Then a string of digits such as 19 denotes the (decimal) number = −1.


title: Ron Cephas Jones

text: Ron Cephas Jones (born January 8, 1957) is an American actor. He is best known for his role in the drama series "This Is Us" (2016–2022), which earned him four consecutive Primetime Emmy Award nominations, winning twice for Outstanding Guest Actor in a Drama Series in 2018 and 2020.


title: Ron Cephas Jones

text: Jones appeared in television series such as "Mr. Robot" (2015–2016), "The Get Down" (2016–2017), "Luke Cage" (2016–2018), and "Truth Be Told" (2019-present). He also appeared in a number of films, including "Half Nelson" (2006), "Across the Universe" (2007), "Glass Chin" (2014), "The Holiday Calendar" (2018), "Dog Days" (2018), and "Dolemite Is My Name" (2019).


title: Ron Cephas Jones

text: Jones was born on January 8, 1957, in Paterson, New Jersey. He attended John F. Kennedy High School and graduated from Ramapo College. While at Ramapo, Jones had originally intended to study jazz under director Arnold Jones (no relation), but changed majors to theater after getting the lead in a production of "Cinderella Ever After" his sophomore year.


title: Ron Cephas Jones

text: Jones graduated from Ramapo in 1978, after which he moved to Los Angeles, California and drove a bus for the Southern California Rapid Transit District for the next four years. During that time, Jones stated he "fell in love, had a child, got separated". He then "traveled around", living in San Francisco, Arizona, and New Orleans before returning to New York City in 1985.


title: Ron Cephas Jones

text: After returning to New York in 1985, Jones began spending time at the Nuyorican Poets Café in Manhattan's East Village. During that time, he performed in a play based on the Billie Holiday song "Don't Explain". His performance caught the attention of a casting director, which led to Jones being offered the lead role in the Tazewell Thompson production of the Cheryl West play "Holiday Heart" in 1994. Jones has performed in several theatrical productions with the Steppenwolf Theatre Company in Chicago, Illinois; appeared as the title character of Shakespeare's "Richard III" with The Public Theater in New York City, New York, as well as other Off Broadway productions. Jones has served as an understudy or standby in several Broadway theatre productions. In 2014 Jones starred as Prometheus in Prometheus Bound directed by Travis Preston through the CalArts Center for New Performance.


title: Ron Cephas Jones

text: His film credits include "He Got Game" (1998), "Sweet and Lowdown" (1999), "Half Nelson" (2006), and "Across The Universe" (2007). In television, he appeared as Reverend Lowdown in the episode "The Goat Rodeo" of the 2013 television series "Low Winter Sun" and he played Romero, a member of "fsociety" in the 2015 television series "Mr. Robot". He also appeared on season 3 of the show "Banshee" as Philadelphia kingpin, Mr. Frasier. He played Harlem chess master Bobby Fish in season 1 of Marvel's "Luke Cage". Since 2016, Jones stars on the NBC drama series "This Is Us" as William Hill, the biological father of Randall Pearson (Sterling K. Brown). Jones received critical acclaim for his performance on "This Is Us" and received a Primetime Emmy Award for Outstanding Guest Actor in a Drama Series in 2018 and 2020 for his performance.


title: Ron Cephas Jones

text: Currently, Jones appears in the Hulu teen drama series "Looking for Alaska", as well as the Apple TV+ crime drama series "Truth Be Told", opposite Octavia Spencer, Lizzy Caplan and Aaron Paul.


title: Ron Cephas Jones

text: Jones and British-born jazz singer Kim Lesley have a daughter, American stage and screen actress Jasmine Cephas Jones.


title: Aposematism

text: Aposematism is the advertising by an animal to potential predators that it is not worth attacking or eating. This unprofitability may consist of any defences which make the prey difficult to kill and eat, such as toxicity, venom, foul taste or smell, sharp spines, or aggressive nature. These advertising signals may take the form of conspicuous coloration, sounds, odours, or other perceivable characteristics. Aposematic signals are beneficial for both predator and prey, since both avoid potential harm.


title: Aposematism

text: The term was coined in 1877 by Edward Bagnall Poulton for Alfred Russel Wallace's concept of warning coloration. Aposematism is exploited in Müllerian mimicry, where species with strong defences evolve to resemble one another. By mimicking similarly coloured species, the warning signal to predators is shared, causing them to learn more quickly at less of a cost.


title: Aposematism

text: A genuine aposematic signal that a species actually possesses chemical or physical defences is not the only way to deter predators. In Batesian mimicry, a mimicking species resembles an aposematic model closely enough to share the protection, while many species have bluffing deimatic displays which may startle a predator long enough to enable an otherwise undefended prey to escape.


title: Aposematism

text: There is good evidence for aposematism in terrestrial animals; its existence in marine animals is possible but disputed.


title: Aposematism

text: The term aposematism was coined by the English zoologist Edward Bagnall Poulton in his 1890 book "The Colours of Animals". He based the term on the Ancient Greek words ἀπό "apo" 'away' and σῆμα "sēma" 'sign', referring to signs that warn other animals away.


title: Aposematism

text: The function of aposematism is to prevent attack, by warning potential predators that the prey animal has defences such as being unpalatable or poisonous. The easily detected warning is a primary defence mechanism, and the non-visible defences are secondary. Aposematic signals are primarily visual, using bright colours and high-contrast patterns such as stripes. Warning signals are honest indications of noxious prey, because conspicuousness evolves in tandem with noxiousness. Thus, the brighter and more conspicuous the organism, the more toxic it usually is. This is in contrast to deimatic displays, which attempt to startle a predator with a threatening appearance but which are bluffing, unsupported by any strong defences.


title: Aposematism

text: The most common and effective colours are red, yellow, black, and white. These colours provide strong contrast with green foliage, resist changes in shadow and lighting, are highly chromatic, and provide distance dependent camouflage. Some forms of warning coloration provide this distance dependent camouflage by having an effective pattern and colour combination that do not allow for easy detection by a predator from a distance, but are warning-like from a close proximity, allowing for an advantageous balance between camouflage and aposematism. Warning coloration evolves in response to background, light conditions, and predator vision. Visible signals may be accompanied by odours, sounds or behaviour to provide a multi-modal signal which is more effectively detected by predators.


title: Aposematism

text: Unpalatability, broadly understood, can be created in a variety of ways. Some insects such as the ladybird or tiger moth contain bitter-tasting chemicals, while the skunk produces a noxious odour, and the poison glands of the poison dart frog, the sting of a velvet ant or neurotoxin in a black widow spider make them dangerous or painful to attack. Tiger moths advertise their unpalatability by either producing ultrasonic noises which warn bats to avoid them, or by warning postures which expose brightly coloured body parts (see Unkenreflex), or exposing eyespots. Velvet ants (actually parasitic wasps) such as "Dasymutilla occidentalis" both have bright colours and produce audible noises when grabbed (via stridulation), which serve to reinforce the warning. Among mammals, predators can be dissuaded when a smaller animal is aggressive and able to defend itself, as for example in honey badgers.


title: Aposematism

text: Aposematism is widespread in insects, but less so in vertebrates, being mostly confined to a smaller number of reptile, amphibian, and fish species, and some foul-smelling or aggressive mammals. Pitohuis, red and black birds whose toxic feathers and skin apparently comes from the poisonous beetles they ingest, could be included. It has been proposed that aposematism played a role in human evolution, body odour carrying a warning to predators of large hominins able to defend themselves with weapons.


title: Aposematism

text: Perhaps the most numerous aposematic vertebrates are the poison dart frogs (family: Dendrobatidae). These neotropical anuran amphibians exhibit a wide spectrum of coloration and toxicity. Some species in this poison frog family (particularly "Dendrobates", "Epipedobates", and "Phyllobates") are conspicuously coloured and sequester one of the most toxic alkaloids among all living species. Within the same family, there are also cryptic frogs (such as "Colostethus" and "Mannophryne") that lack these toxic alkaloids. Although these frogs display an extensive array of coloration and toxicity, there is very little genetic difference between the species. Evolution of their conspicuous coloration is correlated to traits such as chemical defense, dietary specialization, acoustic diversification, and increased body mass.


title: Aposematism

text: Some plants are thought to employ aposematism to warn herbivores of unpalatable chemicals or physical defences such as prickled leaves or thorns. Many insects, such as cinnabar moth caterpillars, acquire toxic chemicals from their host plants. Among mammals, skunks and zorillas advertise their foul-smelling chemical defences with sharply contrasting black-and-white patterns on their fur, while the similarly-patterned badger and honey badger advertise their sharp claws, powerful jaws, and aggressive natures. Some brightly coloured birds such as passerines with contrasting patterns may also be aposematic, at least in females; but since male birds are often brightly coloured through sexual selection, and their coloration is not correlated with edibility, it is unclear whether aposematism is significant.


title: Aposematism

text: The sound-producing rattle of rattlesnakes is an acoustic form of aposematism. Sound production by the caterpillar of the Polyphemus moth, "Antheraea polyphemus", may similarly be acoustic aposematism, connected to and preceded by chemical defences. Similar acoustic defences exist in a range of Bombycoidea caterpillars.


title: Aposematism

text: The existence of aposematism in marine ecosystems is controversial. Many marine organisms, particularly those on coral reefs, are brightly coloured or patterned, including sponges, corals, molluscs and fish, with little or no connection to chemical or physical defenses. Caribbean reef sponges are brightly coloured, and many species are full of toxic chemicals, but there is no statistical relationship between the two factors.


title: Aposematism

text: Nudibranch molluscs are the most commonly cited examples of aposematism in marine ecosystems, but the evidence for this has been contested, mostly because (1) there are few examples of mimicry among species, (2) many species are nocturnal or cryptic, and (3) bright colours at the red end of the colour spectrum are rapidly attenuated as a function of water depth. For example, the Spanish Dancer nudibranch (genus "Hexabranchus"), among the largest of tropical marine slugs, potently chemically defended, and brilliantly red and white, is nocturnal and has no known mimics. Mimicry is to be expected as Batesian mimics with weak defences can gain a measure of protection from their resemblance to aposematic species. Other studies have concluded that nudibranchs such as the slugs of the family Phyllidiidae from Indo-Pacific coral reefs are aposematically coloured. Müllerian mimicry has been implicated in the coloration of some Mediterranean nudibranchs, all of which derive defensive chemicals from their sponge diet.


title: Aposematism

text: The crown-of-thorns starfish, like other starfish such as "Metrodira subulata", has conspicuous coloration and conspicuous long, sharp spines, as well as cytolytic saponins, chemicals which could function as an effective defence; this evidence is argued to be sufficient for such species to be considered aposematic.


title: Aposematism

text: It has been proposed that aposematism and mimicry is less evident in marine invertebrates than terrestrial insects because predation is a more intense selective force for many insects, which disperse as adults rather than as larvae and have much shorter generation times. Further, there is evidence that fish predators such as blueheads may adapt to visual cues more rapidly than do birds, making aposematism less effective.


title: Aposematism

text: Blue-ringed octopuses are venomous. They spend much of their time hiding in crevices whilst displaying effective camouflage patterns with their dermal chromatophore cells. However, if they are provoked, they quickly change colour, becoming bright yellow with each of the 50-60 rings flashing bright iridescent blue within a third of a second. It is often stated this is an aposematic warning display, but the hypothesis has rarely if ever been tested.


title: Aposematism

text: The mechanism of defence relies on the memory of the would-be predator; a bird that has once experienced a foul-tasting grasshopper will endeavour to avoid a repetition of the experience. As a consequence, aposematic species are often gregarious. Before the memory of a bad experience attenuates, the predator may have the experience reinforced through repetition. Aposematic organisms often move in a languid fashion, as they have little need for speed and agility. Instead, their morphology is frequently tough and resistant to injury, thereby allowing them to escape once the predator is warned off.


title: Aposematism

text: Aposematic species do not need to hide or stay still as cryptic organisms do, so aposematic individuals benefit from more freedom in exposed areas and can spend more time foraging, allowing them to find more and better quality food. They may also be able to make use of conspicuous mating displays, including vocal signals, which may then develop through sexual selection.


title: Aposematism

text: In a letter to Alfred Russel Wallace dated 23 February 1867, Charles Darwin wrote, "On Monday evening I called on Bates & put a difficulty before him, which he could not answer, & as on some former similar occasion, his first suggestion was, 'you had better ask Wallace'. My difficulty is, why are caterpillars sometimes so beautifully & artistically coloured?" Darwin was puzzled because his theory of sexual selection (where females choose their mates based on how attractive they are) could not apply to caterpillars since they are immature and hence not sexually active.