document_title: Transformers: Age of Extinction

question_text: who did the voices in transformers age of extinction

text: Transformers: Age of Extinction

text: Plot[edit]

text: Sixty five million years ago, an alien race known as the "Creators" used devices called Seeds to terraform planet Earth, effectively wiping out the dinosaurs and covering it with an alloy called Transformium. In the present day, geologist Darcy Tirrel excavates the Transformium for K.S.I. Industries, which uses it to build man-made artificial Transformer drones.

text: Five years after The Battle of Chicago, the humans have begun to view the Transformers as a threat, leading the U.S government to terminate all human-Autobot joint programs. Although the public believes that the Autobots have been granted sanctuary, they are being hunted by a rogue, vengeful and xenophobic CIA black ops division known as Cemetery Wind, led by opportunistic government official Harold Attinger, who believes that all Transformers should be exterminated regardless of their faction. They are aided by Lockdown, a Cybertronian bounty hunter working for the Creators, promising to give Attinger a Seed if his division manages to capture Optimus Prime. Cemetery Wind locates Ratchet in Mexico City and Lockdown kills him when he refuses to give up the whereabouts of Optimus Prime.

text: Optimus, damaged in Mexico City and disguised as a rundown semi-truck, is discovered in an abandoned theater by Cade Yeager, a financially struggling Texan inventor, and brings him back to the farm. While his teenage daughter Tessa and business partner Lucas Flannery encourage him to turn Optimus over to the authorities after realizing what he really is, Cade instead fixes Optimus, hoping to understand his technology and unexpectedly revives him. Still skeptical of Optimus and worried about Cade's safety, Lucas calls Cemetery Wind, who attacks and destroys the farm, but Optimus and Tessa's boyfriend, Irish rally car driver Shane Dyson, come to the family's aid. While on the run from Cemetery Wind and Lockdown, Lucas is killed by one of Lockdown's grenades. After escaping from their attackers, they take refuge in an abandoned gas station. Later, Optimus scans a passing truck and turns into a Western Star 5700 Phantom Custom truck with the original red and blue paint with flames. Afterwards, Optimus summons the surviving Autobots – Bumblebee, who has assumed an alternate form, Hound, Drift, and Crosshairs – who have come to distrust humans due to Cemetery Wind constantly hunting them down. Using a CIA drone which he stole during the home invasion, Cade discovers K.S.I.'s involvement in the attacks on the Autobots. Optimus vows to personally kill Attinger for his actions against his brethren.

text: Infiltrating K.S.I.'s headquarters in Chicago, Cade discovers the remains of Autobots and Decepticons are being melted down to make the drones. Joshua Joyce, the ambitious company CEO, is in league with Attinger to revolutionize global defenses and improve human society using the Seed. He has captured Brains and is using him and Megatron's head to create prototype Transformer soldiers Galvatron and Stinger. In a fit of rage, the Autobots storm the building, during which Bumblebee regains his original form by scanning a passing car, where they rescue Brains and destroy the laboratory, but they soon leave after Joshua announces that they are no longer needed. Attinger forces Joshua to deploy Galvatron and Stinger to attack the Autobots. During the battle, Galvatron's behavior becomes slightly erratic when he starts destroying vehicles. As Galvatron battles Optimus, it frees itself from control and speaks to Optimus. Lockdown then arrives and abducts Optimus while Galvatron and Stinger retreat; Tessa is inadvertently captured alongside Optimus in the midst of the chaos, leaving Cade and Shane devastated.

text: While Lockdown's large prison spacecraft hovers over Chicago to hand over the Seed, Cade, Shane, and the Autobots use this opportunity to sneak on board and rescue Optimus and Tessa. They hijack a smaller ship, containing a number of other Autobots called the Dinobots, just before Lockdown leaves Earth. The Autobots reveal to Cade that "Galvatron" is in fact Megatron, who had transferred his consciousness into the Galvatron drone after K.S.I. officials had accidentally revived him. They realize that Galvatron is plotting to use the Seed and the K.S.I. drones to conquer the world, by detonating the Seed in Hong Kong, as K.S.I. has brought it there to use it in the remote Mongolian desert to create vast amounts of usable Transformium. Cade informs Joshua of Megatron's presence, causing him to have a change of heart and agreeing to hand over the Seed with help from Darcy and his Chinese business associate Su Yueming. Meanwhile, Lockdown discovers that Optimus has escaped and stole a part of his ship, forcing him to return to Earth to retrieve them. Optimus decides for the Autobots to no longer help the humans because of how they revived Megatron, but Cade explains to Optimus why something unintentional is not a reason for him to lose faith in them. Back at the facility, Joshua gets into a disagreement with Attinger over the Seed, threatening to expose Attinger's nefarious activities, whilst Attinger deduces Joshua's plot to betray him. Galvatron unexpectedly reactivates himself and promptly takes control of the K.S.I. drones, and a battle follows in Hong Kong's streets between Cade's group, the Autobots, Cemetery Wind, Galvatron, and his drones. During the fight, Optimus gains the alliance of the Dinobots, who become essential to the Autobots' victory while Bumblebee kills Stinger.

text: Lockdown returns to capture Optimus and the Dinobots, using a large magnet in his ship that picks up and drops metal objects, causing destruction to the city. After disabling the magnet, Optimus fights Lockdown at an abandoned factory. In the ensuing duel, Optimus kills Attinger (who still angrily deems all Cybertronians aside from Lockdown as a threat) to save Cade, and avenging the deaths of his fellow Autobots. However, this allows Lockdown to pin Optimus down by impaling his chest with his own sword, damaging his spark. Cade, Bumblebee, Tessa, and Shane fight Lockdown, with Cade ending up fighting him one-on-one while Tessa and Shane use a tow truck to free Optimus, who kills Lockdown before using one of his grenades to finish off the remaining drones. Galvatron retreats, vowing to return. As Lockdown's ship leaves Earth, Optimus tells the Autobots to protect the Yeagers (with Joshua offering to help the Yeagers build a new home) and lets the Dinobots go, before flying away into space with the Seed to hide it away, sending a message to the Creators that he is coming for them.

text: Cast[edit]

text:
Mark Wahlberg as Cade Yeager
A single father and struggling inventor.[7]
Stanley Tucci as Joshua Joyce
The ambitiously arrogant head of KSI who wants to build his own Transformers.[8][9]
Kelsey Grammer as Harold Attinger
A paranoid CIA operative and government official who created the CIA black-ops unit, Cemetery Wind to eliminate all Transformers, Autobot or Decepticon, from Earth.[10]
Nicola Peltz as Tessa Yeager
Cade's daughter who is secretly dating Shane.
Jack Reynor as Shane Dyson
Tessa's boyfriend and an Irish rally car driver.[11][12]
Titus Welliver as James Savoy
A ruthless CIA Agent and second-in command of the Cemetery Wind working for Attinger.[13]
Sophia Myles as Darcy Tirrel
Joshua's geologist assistant and ex-girlfriend.[14][15]
Li Bingbing as Su Yueming (苏月明 Sū Yuèmíng)
The owner of the Chinese factory used by KSI to build their artificial Transformers.[16]
T. J. Miller as Lucas Flannery
Cade's best friend and a mechanic.[17]
James Bachman as Gill Wembley
A scientist working with Joshua Joyce at KSI.
Thomas Lennon as the Chief of Staff.

text: Greg Anderson, Melanie Specht and Victoria Summer play Joshua's assistants.[18][19] Han Geng portrays himself, playing the guitar and singing in a parked car that is magnetized by Lockdown's ship.[20] Edward T. Welburn plays a KSI executive.[21] Kevin Covais plays a motorist.[22]

text: Voices[edit]

text:
Peter Cullen as Optimus Prime
The leader of the Autobots who transforms into a rusty Marmon 97 semi truck and later, a blue and red Western Star 5700 XE semi-trailer truck with flame decals.[23][24][25][26][27]
Frank Welker as Galvatron
A human-made KSI Transformer drone intended to be modeled after Optimus Prime, but ultimately using data downloaded from the remains of Megatron. It is later revealed that the Galvatron drone has become possessed by the Decepticon leader, who molecularly transforms into a black and grey 2014 Freightliner Argosy cab over trailer truck.[26][27][28][29]
John Goodman as Hound
An Autobot commando unit who transforms into an Oshkosh Defense Medium Tactical Vehicle.[30][31][32]
Ken Watanabe as Drift
A Samurai-motif Autobot, tactician and a former Decepticon assassin who transforms into a black and blue 2013 Bugatti Veyron 16.4 Grand Sport Vitesse and a Sikorsky S-97 Raider Helicopter.
Robert Foxworth as Ratchet
The Autobot medical officer who transforms into a white and green 2004 Search and rescue Hummer H2 ambulance.
John DiMaggio as Crosshairs
An Autobot paratrooper and elite sniper who transforms into a black and green 2014 Chevrolet Corvette C7 Stingray.[24]
Mark Ryan as Lockdown
An extremely powerful, relentless, heavily enhanced, ruthless Cybertronian bounty hunter who transforms into a grey 2013 Lamborghini Aventador LP 700–4 Coupe and is hired by the mysterious Creators to bring Optimus Prime back to them.[24][26]
Reno Wilson voices Brains
A former Decepticon drone turned Autobot who has lost his right leg.[27]

text: Non-speaking characters[edit]

text:
Bumblebee
An Autobot scout and Optimus Primes' new second in command, who communicates through voice clips and sound bites via his radio who transforms into a modified 1967 Chevrolet Camaro and later, a 2016 Chevrolet Camaro concept.
Grimlock, the leader of the vicious Dinobots who transforms into a mechanical horned, fire-breathing Tyrannosaurus.[24][26]
Strafe
A Dinobot who specializes in assault infantry and transforms into a mechanical two-headed, two-tailed Pteranodon.[26][28]
Slug
The Dinobots' destroyer who transforms into a mechanical spiked and bestial Triceratops.[26][28]
Scorn
The Dinobots' demolition specialist who transforms into a mechanical three-sailed Spinosaurus.[26][28]
Stinger
a human-made KSI Transformer modeled after Bumblebee who later becomes a Decepticon and molecularly transforms into a red and black 2013 Pagani Huayra.[24][25][26][27]
Junkheap
A human-made KSI Transformer who has a three-man splitting technique and later becomes a Decepticon under Galvatron's control. It molecularly transforms into a Mack garbage truck of Waste Management, Inc.[33]
"Traxes"
A human-made KSI Transformers modeled after Roadbuster who later become Decepticons under Galvatron's control and molecularly transform into red, blue, black or white Chevrolet Traxes.[34]
"Two-Heads"
A two-headed human-made KSI Transformers modeled from the remains of Shockwave who later become Decepticons under Galvatron's control.
"KSI Bosses"
A human-made KSI Transformers modeled after Soundwave who later become Decepticons under Galvatron's control.
Steeljaws
the savage techno-organic wolf-like minions of Lockdown.

text: Cameos[edit]

text: Ironhide, Arcee, Wheeljack Loader and Starscream make cameos, depicted on cards stamped with an X to indicate their deaths. The leader of the Wreckers, Leadfoot, makes a cameo voiced by Robert Foxworth in video footage shown after Cade steals the KSI spy drone, shown being killed by humans from Cemetery Wind. Sentinel Prime and Megatron's heads ares seen in the KSI labs, where they download data from the dead Transformers' remains. Barricade and some Decepticon Protoforms make cameos in footage from the Battle of Chicago. The Insecticons make a cameo, transferring data from Megatron's mind, infecting the Galvatron drone.

text: Production[edit]

text: Development[edit]

text: During production for Dark of the Moon, Shia LaBeouf and Bay confirmed that they would not return for a fourth installment of the franchise.[35] Roland Emmerich, Joe Johnston, Jon Turteltaub, Stephen Sommers, Louis Leterrier and David Yates were rumored to replace Bay.[36] Jason Statham was rumored to star in the fourth installment. Hasbro CEO Brian Goldner revealed that he was able to announce the film as he was talking with Steven Spielberg, Bay and Paramount.[37] There were rumors that the fourth and fifth installment would be shot back-to-back with Statham as the lead role, which he and Bay denied.[38] Spielberg hoped Bay would return for a fourth installment.[39]

text: After final negotiations with Bay to direct the film,[40] producer Lorenzo di Bonaventura confirmed that there would be a fourth film in the franchise.[41] In February 2012, Paramount Pictures and Michael Bay announced that Bay would be producing and directing a fourth Transformers film, scheduled for a June 27, 2014 release.[42][43] The film will not be a reboot but a sequel to Dark of the Moon,[12] taking place four years later.[44] Ehren Kruger and Steve Jablonsky returned to write the script and the score, respectively.[45] In April 2013, it was announced that China Movie Channel and Jiaflix Enterprises would co-produce the film with Paramount.[46][47]

text: On September 1, 2013, Fusible revealed three possible subtitles for the film, which were Last Stand, Future Cast, and Apocalypse. On September 2, TFW 2005 revealed one last possible title, Age of Extinction.[48][49] On September 3, 2013, Paramount released an official teaser poster for the film, revealing the title to be Transformers: Age of Extinction.[50]

text: Casting[edit]

text: In November 2012, Mark Wahlberg was cast in the film.[7] Also in November 2012, The Hollywood Reporter reported that casting had begun for two additional leads: the daughter to Wahlberg's character and her boyfriend, a race car driver. Isabelle Cornish, Nicola Peltz, Gabriella Wilde, and Margaret Qualley were all considered for the role of the daughter, while Luke Grimes, Landon Liboiron, Brenton Thwaites, Jack Reynor, and Hunter Parrish were all considered for the boyfriend. The leads are contracted for three films.[51] In January 2013, Reynor was cast as the boyfriend,[12] and in March 2013, Nicola Peltz was cast as Wahlberg's daughter.[52]

text: Peter Cullen reprises his role as the voice of Optimus Prime.[23] Glenn Morshower stated in September 2012 that he would appear in the next two films, reprising his role of General Morshower, but Morshower announced in May 2013 that he would not be able to appear in the new films due to a scheduling conflict.[53] In April 2013, Bay revealed that actor Stanley Tucci had joined the cast.[54] On May 1, 2013, actor Kelsey Grammer was cast as the lead human villain named Harold Attinger.[55] On May 6, 2013, actress Sophia Myles was cast in a major role.[14] That same month, Chinese actress Li Bingbing and comedian T. J. Miller joined the cast.[56] On July 14, 2013, Bay announced that Han Geng had joined the cast.[20] That same month, Titus Welliver also joined the cast.[13]

text: Filming[edit]

text: Bay announced that filming had begun on May 28, 2013, in Monument Valley, Utah. Detroit, Michigan, was used as a stand-in for Hong Kong[57] while McCormick Place in Chicago, Illinois, was re-dressed to portray a city in China.[58] The movie was the first feature film to be shot using smaller digital IMAX 3D cameras.[54] It also was shot in various other formats, including IMAX 70mm film cameras, digital stereo 3D, and anamorphic and spherical 35mm film.[59] From May 28 to June 24, 2013, Michael Bay uploaded photographs of several cars featured in the film, all apparently Autobots, to social networks including Facebook and Flickr. The film featured two unknown Autobots that transformed into a black and blue 2013 Bugatti Veyron Grand Sport Vitesse (going by production name "Drift"), and a green 2014 C7 Corvette Stingray concept (going by production name "Slingshot"). Also revealed was a truck from Western Star Trucks as Optimus Prime's new alternate mode. The Dinobots and Lockdown were confirmed to appear. On October 29, Michael Bay's Official Twitter Account tweeted that principal photography of Transformers 4 had been completed in Hong Kong, China and the cast and crew were heading to the Chinese mainland. (According to previous reports, they would be filming there for one week.)[60] Additional filming in Detroit began in early 2014; a pair of steamships (Columbia and Ste. Clair) which had once traveled between Detroit and Bois Blanc Island's amusement park were partially restored and used as props for the film.[61]

text: Incidents[edit]

text: On October 17, 2013, while filming in Hong Kong, Bay was assaulted by two brothers surnamed Mak, who demanded a payment of HK$100,000 (US$12,900). The elder brother also assaulted three police officers during the incident. Both brothers and a third man surnamed Chan were arrested on suspicion of assault, with the younger Mak also charged on suspicion of blackmail.[62] The Mak brothers pleaded guilty to both charges in February 2014 and were incarcerated, with the prosecutor noting that the case had attracted a great deal of media attention and affected Hong Kong's image.[63]

text: Post-production[edit]

text: Industrial Light & Magic's VFX supervisor Scott Farrar, who had also supervised the three prior films in the Transformers franchise, rendered the visual effects. He said the film contains about ninety minutes of visual effects (out of the movie's 165-minute length).[64] Farrer said it was the biggest project, using the largest crew, of his career, and noted that over five hundred crews had worked on it, using various facilities.[65]

text: The nine different formats used in the film included IMAX film, IMAX digital, single-frame anamorphic film, GoPros, crashcams, Red cameras on 3Ality stereo 3D gigs, and red cameras for 2D.[65]

text: Music[edit]

text: Like its predecessors, Steve Jablonsky composed the film's score, marking his sixth film collaboration with director Michael Bay, four of which are Transformers films. The film's score was praised by critics and fans. The soundtrack album sold more than 15,000 units worldwide. It is also the first Transformers film not to feature a Linkin Park song.

text: Skrillex worked on sound design for the film, having said that he was creating "the craziest Skrillex sounds I could ever make" and mentioned working on sounds for the Dinobots.[66][67]

text: Imagine Dragons wrote a single specifically for the film itself, titled "Battle Cry". The track "Leave Planet Earth Alone" samples the drum beat of Battle Cry so that the former serves as an intro to the latter as the credits start, though this version is only present in the film; Battle Cry isn't featured on the soundtrack album, and Leave Planet Earth Alone has a unique outro. No mashup version or otherwise is available for purchase. Imagine Dragons also worked with Steve Jablonsky and Hans Zimmer to contribute additional music to the film's score.[68]

text: Linkin Park's new single "Until It's Gone" is included in the video game soundtrack of the movie.[69]

text: On June 30, 2014, an extended play was digitally released on iTunes, featuring four tracks as a teaser for the full official score, which features variations of the four themes.[70] On July 4, 2014, the long play was released digitally on iTunes containing the full score of the film.[71] The soundtrack album was released on CD by record label La-La Land Records on October 7, 2014.

text: On November 20, 2014, Steve Jablonsky released a statement via Facebook saying that the score would no longer be available on iTunes and other digital music stores after it had reached its limit of 15,000 units before re-use fees would have to be paid. Jablonsky personally expressed his own disappointment in the turn of events, hoping there would be a way to eventually re-release the score, along with the score to Transformers: Dark of the Moon, which had also been removed from iTunes and other digital music stores several months prior when it too reached the 15,000 unit limit.[72]

text: Release[edit]

text: The film had its world premiere in Hong Kong on June 19, with a live concert by Imagine Dragons.[73]

text: Marketing[edit]

text: The first televised advertisement for Transformers: Age of Extinction aired during Super Bowl XLVIII. In a poll by Fandango, the spot was determined to be the most anticipated film trailer to be shown, receiving 48% of the vote in the poll.[74] The first official teaser trailer was released on March 4, 2014.[75] A viral marketing campaign was started for the film upon the teaser trailer's release.[76] On March 30, 2014, a shortened version of the teaser trailer was aired during the season 4 finale of The Walking Dead. Another shortened version of the teaser trailer was aired during the 2014 MTV Movie Awards.

text: Chevrolet aired a commercial at the New York International Auto Show featuring General Motors vehicles with clips from the film, along with putting them on display.[77]

text: Hasbro released an app on May 8 surrounding the film available for iOS and Android devices, allowing users to access exclusive material such as character biographies, images, and interviews with the stars, among other things.[78] A clip featuring never-before-seen scenes from the film and an interview with Imagine Dragons aired during The Voice on May 12, 2014.

text: DeNA and Hasbro teamed up to construct an official mobile video game for the film. The game was first announced on May 13, 2014, though, the title is still in active development.[79] Also on this date, Oreo launched a marketing campaign to promote the film.[80] This included a television commercial where a boy gives a wounded Optimus Prime an Oreo cookie to continue the fight.[81]

text: An exclusive theatrical trailer debuted on May 15 on iTunes Movie Trailers at 12:01 AM Pacific Standard Time.[82] On May 21, 2014, two television spots appeared online, both containing new footage from the film.[83] The film's viral campaign updated on May 22, showcasing all-new posters and realistic news reports of the damage done to Chicago from the third film.[84] Three more television spots, all sporting new footage, appeared online on May 30, 2014.[85][86][87]

text: Imagine Dragons's single for the film officially released online on June 2, 2014.[88]

text: Jack Reynor and Nicola Peltz made multiple appearances in the Twin Cities on June 8, 2014. During an appearance on the Canadian version of The Morning Show, both Reynor and Peltz promised big things that would please fans.[89] Kelsey Grammer made an appearance on The Late Show with David Letterman on June 9, 2014. During his visit, the very first clip from the film debuted, showcasing Grammer's character and Wahlberg's in a heated argument. During the first commercial break for the show, a brand new television spot aired.[90] On June 10, 2014, two television spots appeared online, both containing extensive new footage from the film.[citation needed]

text: At the Nickelodeon Kids' Choice Awards on March 29, 2014, Mark Wahlberg, who stars in the film, hosted the event. There was also a transmission from Peter Cullen as Optimus Prime, and Nicola Peltz and Jack Reynor assembled with Wahlberg to take out cannons that fired slime.

text: Three more television spots appeared online on June 14, 2014, containing new footage of the Dinobots transforming and of Lockdown speaking.[91] On June 17, a brand-new television spot aired on Comedy Central containing new footage.[citation needed] Another television spot appeared online on June 18, sporting new footage as well.[citation needed]

text: The film's unusual marketing strategy of letting people video the shooting of the film in select locations was the subject of film critic Kevin B. Lee's critical video essay Transformers: The Premake.[92]

text: Video games[edit]

text: In February 2014, Transformers: Rise of the Dark Spark, developed by Edge of Reality, published by Activision was announced as a companion to the film. It was released in June 2014 for Microsoft Windows, Nintendo 3DS, PlayStation 3, PlayStation 4, Wii U, Xbox 360, and Xbox One.[93]

text: In summer 2014, Rovio and Hasbro announced Angry Birds Transformers. The game has Transformers movie designs on two of the characters.

text: Reception[edit]

text: Box office[edit]

text: Worldwide[edit]

text: Transformers: Age of Extinction grossed $245.4 million in the United States and Canada and $858.6 million in other countries for a worldwide total of $1.104 billion, against a budget of $210 million.[4] It was the only film of 2014 to earn over $1 billion at the box office worldwide.[94] Deadline.com calculated the net profit of the film to be $250.2 million, when factoring together all expenses and revenues for the film, making it the most profitable film of 2014.[94] Worldwide, in its opening weekend, the film earned $302.1 million, which is the 14th-highest ever, the highest in 2014, and the second-largest for Paramount behind Transformers: Dark of the Moon ($382.4 million).[95] It was the 17th-highest-grossing film worldwide, the highest-grossing film of 2014, the second-highest-grossing film in the Transformers film series, and the 11th-highest-grossing film of Paramount (domestically).[96] It is the second film in the Transformers installment to earn over $1 billion following Dark of the Moon[97] and the 19th film overall. Despite being a box office hit, it was considered by several box office experts to have fallen well below expectations.

text: North America[edit]

text: Transformers: Age of Extinction is the fifth-highest-grossing film of 2014 in the U.S. and Canada.[98] It was released on June 27, 2014 in across 4,233 theaters in North America. It earned $8.75 million from Thursday late-night run, which was the fifth-biggest of 2014.[99] On Friday, the film grossed an additional $31.25 million bringing its total day gross to $41.6 million, including $10.7 million from IMAX theaters. In its opening weekend, the film earned $100,038,390[nb 1] setting an opening record of 2014 (overtaken by The Hunger Games: Mockingjay – Part 1 with $121.9 million),[102] which is the fourth-highest opening for Paramount,[103] and the fifth-highest for a film released in June.[104] The opening-weekend audience was evenly split among those under and over the age of 25 (with 58%), male (64%), and under 18 (27%).[105] The film remained at the summit for two consecutive weekends before being overtaken by Dawn of the Planet of the Apes in its third weekend. It also crossed the $200 million mark in its third weekend, becoming the fifth film of 2014 to do so.[106][107] The film closed down its theatrical run on October 9, 2014[108] and earned a total of $245,439,076, making it the fifth-highest-grossing film of 2014 in the U.S.[108][109]

text: Outside North America[edit]

text: Outside North America, it is the highest-grossing film of 2014,[110] and the sixth-highest-grossing film.[111] Transformers: Age of Extinction earned $202.1 million in its opening weekend from 37 countries in 10,152 screens, which is 35% bigger than Dark of the Moon and marking the biggest overseas opening of 2014 (breaking X-Men: Days of Future Past's record set one month prior).[112] It scored the biggest IMAX overseas opening weekend with $16.6 million from 266 theaters (overtaken by Jurassic World).[112][113] The film topped the box office outside North America for four consecutive weekends despite coinciding with the 2014 FIFA World Cup before being overtaken by Dawn of the Planet of the Apes in its fifth weekend.[114]

text: International openings of over $5 million occurred in South Korea ($21.7 million), Brazil ($16.5 million), Germany ($11.2 million), Australia ($9.6 million), France ($8.8 million), Taiwan ($8.1 million), Malaysia ($6.7 million), Japan ($6.4 million), the Philippines ($5.7 million), India ($5.35 million), Hong Kong ($5.1 million), and Italy ($5 million).[112] In Russia, the film opened to number one with $21.7 million from 1,100 screens, which is the second-largest in the territory for which 3D accounted for 80% of the total gross. IMAX comprised $2.6 million of the total gross from 34 IMAX screens.[112] Its biggest opener outside the U.S. was in China, where it scored one of the biggest non-North American openings of all time with $91.2 million from 4,400 screens, which was once the second-biggest opening of all time there.[112][115] The film set an all-time IMAX opening record with $9.7 million.[112][116] After five days of its release, Age of Extinction surpassed its North American run with $134.5 million.[117][118] In China, the film earned an additional $50.9 million in its second weekend for a total of $212.8 million. In only 10 days of its release, it became the highest-grossing film in China with $222.74 million, thus overtaking Avatar's previous record.[119][120][121] Adding to the film's revenue and popularity were product placements of Chinese brands edited into the movie specifically for Chinese audiences.[122]

text: It became the highest-grossing film in China, with $301–$320 million[nb 2] in revenue surpassing 2009's record set by Avatar ($204 million),[124][129][130] until it was surpassed by Furious 7 in 2015 over $390 million.[131] It is also the first movie in China to gross more than $300 million at the box office.[132] A large part of the success in China has been attributed to the large fan base there and because of its accompanying animated TV series—which ran during the 1980s and 1990—was one of the highest-quality TV programs at that time which resulted in many children getting attached to it. Transformers toy merchandising was one of the first successful cases by a foreign company in China at its time, its line of transforming robot toys was highly sought-after, especially by boys.[133]

text: At the end of its theatrical run outside North America, the film earned $858,600,000 which is 77.8% of its total gross. In total earnings, the highest revenue came from China ($301 million), Russia ($45.2 million), South Korea ($43.3 million), Germany ($38.2 million), Mexico ($33.5 million), and the UK ($33.1 million).[134]

text: Authenticity over North American box office opening[edit]

text: The $100 million opening announced for Transformers: Age of Extinction is disputed within the industry. According to Rentrak—which has a direct line into the vast majority of theatres in the United States and Canada to track actual ticket sales—about 4,100 of the 4,233 theatres playing the film generated $95.9 million. The projected total from the Rentrak sales data would put the opening three-day weekend gross at around $97.5 million. For Transformers to have crossed the $100 million threshold, it would have needed to gross more than the nationwide average in the theatres not tracked by Rentrak. Some media outlets have elected to go with the Rentrak figure.[100][101]

text: Critical response[edit]

text: On review aggregation website Rotten Tomatoes the film has an approval rating of 18% based on 188 reviews, with an average rating of 3.9/10. The site's critical consensus reads, "With the fourth installment in Michael Bay's blockbuster Transformers franchise, nothing is in disguise: Fans of loud, effects-driven action will find satisfaction, and all others need not apply."[135] On Metacritic, the film has a score of 32 out of 100, based on 38 critics, indicating "generally unfavorable reviews".[136] Audiences polled by CinemaScore gave the film an average grade of "A–" on an A+ to F scale.[137]

text: Richard Roeper gave the film a "D", saying that "the longer the movie goes on, the less interesting it becomes; it just wears you down. As we were finally reaching the 165-minute mark, all that noise and fury was about as exciting as the special effects in an Ed Wood movie."[138] Peter Travers of Rolling Stone gave the film zero out of four stars, calling it "the worst and most worthless Transformers movie yet."[139] Kyle Smith of the New York Post gave the film one-and-a-half out of four stars, commenting that "This series was never good, but it was once fun, or at least flashy. Now that its gears have gone rusty, it’s time for an Alien vs. Predator-style rethink."[140] A. O. Scott of The New York Times said in his review that "The story is scaffolding for the action and like every other standing structure, it is wrecked in a thunderous shower of metal, glass, masonry, and earth."[141]

text: Clarence Tsui of The Hollywood Reporter commented on his review that it "barely skirts the idea that humankind and planet Earth are about to be totally annihilated. What is extinguished is the audience's consciousness after being bombarded for nearly three hours with overwrought emotions ('There's a missile in the living room!' Tessa hollers — twice), bad one-liners, and battles that rarely rise above the banal. A trio of editors make a technical marvel out of the fight scenes, but can do little to link the story's multiple threads into something coherent."[142] Roth Cornet of IGN gave the film a score of 6.3 out of 10, praising the "slightly darker/surprising tone and Lockdown and his ship while criticizing the logic/script issues and long running time."[143] Joe Neumaier of the New York Daily News gave the film 1 out of five stars, commenting that "If the 'human scenes' all reek of adolescent dialogue and dopey snark masquerading as character development, it's a toss-up if that's better or worse than seeing clattering collections of caliginous junk."[144]

text: Home media[edit]

text: Transformers: Age of Extinction was released on Blu-ray, DVD, and Blu-ray 3D formats on September 30, 2014, in North America. The film was also released on digital download through iTunes and Google Play on September 16, 2014.

text: Accolades[edit]

text: This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (June 2015) (Learn how and when to remove this template message)

text:
Award
Category
Recipients
Result

2014 Teen Choice Awards
Choice Movie: Villain
Kelsey Grammer
Nominated

Choice Movie: Breakout Star
Nicola Peltz
Nominated

Choice Summer Movie
Transformers: Age of Extinction
Nominated

Choice Summer Movie Star
Mark Wahlberg
Nominated

2014 Golden Trailer Awards
Best Summer 2014 Blockbuster Trailer
Paramount Pictures and Creative Buzz Industries
Nominated

2014 Hollywood Film Awards
Best Visual Effects of the Year
Scott Farrar
Won

2014 Houston Film Critics Society Awards
Worst Film
Transformers: Age of Extinction
Nominated

2015 Annie Awards
Outstanding Achievement, Animated Effects in a Live Action Production
Michael Balog, Jim Van Allen, Rick Hankins, and John Hansen
Nominated

2015 Satellite Awards
Best Visual Effects
John Frazier, Patrick Tubach, Scott Benza, and Scott Farrar
Nominated

Best Sound (Editing & Mixing)
Erik Aadahl, Ethan Van Der Ryn, and Peter J. Devlin
Nominated

2015 Golden Raspberry Awards
Worst Picture
Transformers: Age of Extinction
Nominated

Worst Director
Michael Bay
Won

Worst Supporting Actor
Kelsey Grammer (also for The Expendables 3, Legends of Oz: Dorothy's Return, and Think Like a Man Too)
Won

Worst Supporting Actress
Nicola Peltz
Nominated

Worst Screenplay
Ehren Kruger
Nominated

Worst Prequel, Remake, Rip-off or Sequel
Transformers: Age of Extinction
Nominated

Worst Screen Combo
Transformers: Age of Extinction
Nominated

text: Sequels[edit]

text: A fifth Transformers film, titled The Last Knight, was released on June 21, 2017 to poor reviews, with both Bay and Wahlberg stating it was their final entry of the series.

text: A spin-off film, Bumblebee, is scheduled for a December 21, 2018 release, while a sixth installment, Transformers 6, is scheduled for release for June 28, 2019.[145]


document_title: There's a Ghost in My House

question_text: who sang there's a ghost in my house

question_tokens: who sang there 's a ghost in my house

root

text: There's a Ghost in My House

text:
"There's a Ghost in My House"

Single by R. Dean Taylor

B-side
"Don't Fool Around"
UK: "Let's Go Somewhere"

Released
April 1967
UK: 1974

Format
7"

Genre
R&B, pop

Label
V.I.P. 25042
UK: Tamla Motown TMG 896

Songwriter(s)
Brian Holland, Lamont Dozier, Eddie Holland, R. Dean Taylor

Producer(s)
Brian Holland, Lamont Dozier

tag: table

text: "There's a Ghost in My House" is a song written by Brian Holland, Lamont Dozier, and Eddie Holland of Motown Records, together with R. Dean Taylor. It was originally recorded by Taylor in 1966.

tag: p

text: Produced by Brian Holland and Lamont Dozier, it was released as a single on the Motown subsidiary V.I.P. label in April 1967,[1] but was not a hit. However, after it had become a popular dance song in Northern soul clubs in Britain, such as the Blackpool Mecca and Wigan Casino, R. Dean Taylor's record was reissued on EMI's Tamla Motown label with a B-side of "Let's Go Somewhere",[2] and reached no. 3 on the UK Singles Chart in 1974.[3]

text: Versions of the song were later recorded by British bands Yachts (1980), B.E.F. (British Electric Foundation) featuring Paul Jones (1982), and The Very Things (1987).[4][5] A version recorded by The Fall in 1987 became their first single to reach the top 50 in the UK, peaking at no. 30,[6] and was included on their album The Frenz Experiment.[7] A version was included by Graham Parker in 2000 on Loose Monkeys, an album of out-takes.[8]


document_title: Coming to America

question_text: who did eddie murphy play in coming to america

text: Coming to America

text: Plot

text: This section's plot summary may be too long or excessively detailed. Please help improve it by removing unnecessary details and making it more concise. (August 2017) (Learn how and when to remove this template message)

text: Heir to Zamunda's (a fictional African kingdom) throne Akeem Joffer lives a pampered lifestyle with every daily task performed by servants. On his 21st birthday, Akeem has become fed up with this and wishes to do more for himself. The final straw comes when his parents, King Jaffe and Queen Aeoleon, present him with an arranged bride-to-be named Imani Izzi, whom he has never met and who has been trained to obey Akeem's every command. Akeem concocts a plan to travel to the United States to find an intelligent, independent-minded woman he can both love and respect, and who will love Akeem for who he is and not for his wealth and social status as a prince. Akeem and his best friend/personal aide, Semmi, flip a coin to decide between going to either Los Angeles or New York City, and end up going to New York City. They end up in the borough of Queens and rent a run-down apartment in the neighborhood of Long Island City under the guise of poor foreign students. They begin working at a local fast food restaurant called McDowell's—an obvious ripoff of McDonald's—owned by widower Cleo McDowell and his two daughters, Lisa and Patrice.

text: Akeem soon falls in love with Lisa, who possesses all the qualities that the prince is looking for in a woman, as first seen by Akeem at a rally where she makes a strong plea to renovate a playground. The rest of the film centers on Akeem's attempts to win Lisa's hand in marriage, which is complicated by Lisa's lazy and obnoxious boyfriend, Darryl Jenks (Eriq La Salle), whose father owns "Soul Glo" (a Jheri curl–like hairstyling aid). Lisa eventually breaks up with Darryl after he announces their engagement (without Lisa having given her consent) to their families, and starts dating Akeem. Although Akeem thrives on hard work and learning how commoners live, Semmi is not comfortable with living the life of a poor man. After a dinner date with Lisa is thwarted since Semmi has furnished their apartment with jacuzzi and other luxuries, Akeem confiscates their travel money and donates it to two homeless men. Semmi wires a telegraph to King Jaffe for financial help. This causes Akeem's parents to travel to Queens and expose Akeem's identity as a prince to the McDowells.

text: Mr. McDowell, initially disapproving of the match as he did not want to see his daughter with a man of poor means, is ecstatic that she has in fact attracted the interest of an extremely wealthy prince. Lisa, however, becomes angry and confused as to why Akeem lied to her about his identity, as he had told her before that he was actually a goat herder. Still hurt and angry that Akeem lied to her, she refuses to marry him, even after he offers to renounce his throne. He returns home with a broken heart, resigned to marry the woman chosen for him by his parents. On the way to the airport, King Jaffe remarks that Akeem can't marry Lisa anyway because of "tradition," and tries defending himself by saying "Who am I to change it?", with Queen Aeoleon curtly responding, "I thought you were the King".

text: At the final scene's wedding procession, a still heartbroken Akeem waits dejectedly at the altar as his soon-to-be consort makes her way down the aisle. However, when Akeem lifts the veil to kiss her, he finds Lisa instead of Imani. Akeem and Lisa are married, and they ride happily in a carriage after the ceremony to the cheers of Zamundans. Witnessing such splendor, Lisa is both surprised and touched by the fact that Akeem would have given it up just for her. Akeem offers to formally abdicate if she doesn't want a life like this, but Lisa playfully declines and decides to become royalty instead.

text: Cast

text:
Eddie Murphy as Prince Akeem Joffer, the prince of Zamunda; Randy Watson, a soul singer with the fictional band Sexual Chocolate.[3] Eddie Murphy also plays Saul, the Jewish barbershop customer, as well as Clarence, the owner of the barber shop.[4][5]
Arsenio Hall as Semmi, Akeem's friend; Reverend Brown;[6] Morris the barber; and an ugly barfly.[7][8]
James Earl Jones as King Jaffe Joffer, Akeem's father and King of Zamunda.[9]
John Amos as Cleo McDowell, Akeem's employer and Lisa's father.
Madge Sinclair as Queen Aeoleon, Akeem's mother and the Queen of Zamunda.
Shari Headley as Lisa McDowell, Cleo's oldest daughter and Akeem's love interest.
Paul Bates as Oha, a royal servant.
Eriq La Salle as Darryl Jenks, Lisa's boyfriend whom she eventually breaks up with.

tag: ul

text: The cast also includes: Frankie Faison[10] as Mr. Townsend, Akeem and Semmi's landlord in Queens; Vanessa Bell as Imani Izzi, Akeem's arranged wife, and Calvin Lockhart as Colonel Izzi, her father; Louie Anderson as Maurice, a McDowell's employee; Allison Dean as Patrice McDowell, Cleo's youngest daughter and Lisa's sister; Samuel L. Jackson as a robber; Vondie Curtis-Hall as the Basketball game vendor; Garcelle Beauvais as a rose bearer; Victoria Dillard as one of Akeem's Zamundan attendants, and Clint Smith as Sweets. Cuba Gooding Jr. made his film debut as a barber shop customer (he was credited as Boy Getting Haircut). Don Ameche and Ralph Bellamy reprise their roles as, respectively, Mortimer and Randolph Duke from Landis' 1983 Murphy-starring comedy film Trading Places.[11] A segment of the Trading Places score can be heard during their scene. The Dukes' limo driver from that film also cameos as the driver of Akeem and Semmi's limo.[citation needed]

text: Coming to America features Murphy and Hall in several different roles, which, following the success of this film, became a Murphy staple.[12] Hall plays Reverend Brown, who introduces Randy Watson (Murphy).[13] Murphy and Hall play elderly barbers Clarence and Morris respectively, who engage in debate with Saul, the old Jewish man (Murphy). Hall also plays a woman (credited as Extremely Ugly Girl) who flirts with Akeem and Semmi.

text: James Earl Jones and Madge Sinclair would again play a royal couple in The Lion King, voicing the characters of King Mufasa and Queen Sarabi. Additionally, Sinclair also previously co-starred with John Amos in the miniseries Roots.

text: Production

text: Coming to America reunited star Eddie Murphy with director John Landis. The two had previously worked together on the comedy hit Trading Places (1983); however, Landis later recalled the differences in working with Murphy on the two movies: "The guy on Trading Places was young and full of energy and curious and funny and fresh and great. The guy on Coming to America was the pig of the world... But I still think he's wonderful in the movie."[14]

text: "We had a tussling confrontation… We didn't come to blows. Personalities didn't mesh. I grabbed him, and he thought I was playing. So he tried to grab my balls and I pushed him away. But I wasn't kidding. He was doing some silly shit that made me mad. He directed me in Trading Places when I was just starting out as a kid, but he was still treating me like a kid five years later during Coming to America. And I hired him to direct the movie! I was gonna direct Coming to America myself, but I knew that Landis had just done three fucked-up pictures in a row and that his career was hanging by a thread after the Twilight Zone trial. I figured the guy was nice to me when I did Trading Places, so I'd give him a shot… I was going out of my way to help this guy, and he fucked me over. Now he's got a hit picture on his resumé, a movie that made over $200 million, as opposed to him coming off a couple of fucked-up movies – which is where I'd rather see him be right now (laughs)." – Eddie Murphy[15]

text: Despite the experience, Landis and Murphy collaborated again six years later on Beverly Hills Cop III.

text: South African chorus Ladysmith Black Mambazo sings Mbube during the opening sequence (the song also known as The Lion Sleeps Tonight). The group has gone on to record several different versions of Mbube; however, the version heard in Coming to America had not been released on its soundtrack or on CD as of 2006.

text: Landis' calling card/easter egg, "See You Next Wednesday", appears on a science-fiction movie poster in the subway station after Lisa storms off the train.

text: A promotional song for the film, also titled "Coming to America", was written and performed by The System.

text: Release

text: Paramount cancelled press screenings of the film, after initial negative reactions to a press screening in New York.[16]

text: Box office

text: Released on June 29, 1988, by Paramount Pictures in the United States, it was a commercial box-office success, both domestically and worldwide.[17][18] The film debuted at number one with $21,404,420 from 2,064 screens, for a five-day total of $28,409,497. The film made $128,152,301 in the United States and ended up with a worldwide total of $288,752,301.[19] It was the highest earning film that year for the studio and the third-highest-grossing film at the United States box office.[20]

text: It opened a month later in the UK and earned $7,712,622 during its seven-week run. It opened on September 2 in West Germany, where it debuted at number one with $3,715,791 from 297 screens. It ended its run after 13 weeks with $15,743,447.

text: Reception

text: Review-aggregation website Rotten Tomatoes gives the film a score of 68%, based on reviews from 37 critics.[21]

text: Sheila Benson in the Los Angeles Times called it a "hollow and wearying Eddie Murphy fairy tale" and bemoans, "That an Eddie Murphy movie would come to this."[22] Vincent Canby in The New York Times was also critical of the writing, calling it a "possibly funny idea" but suggesting the screenplay had escaped before it was ready. Canby viewed the film as essentially a romantic comedy but said the romantic elements fell flat, and the film instead goes for broad slapstick.[23] Siskel & Ebert had mixed opinions on the film. Siskel enjoyed the acting from Murphy and Hall but Ebert was disappointed that Murphy did not bring his usual more lively performance, and Ebert was also critical of the unoriginal script.[24]

text: Awards

text: The film was nominated for two Oscars: Best Costume Design by Deborah Nadoolman Landis and Best Makeup by Rick Baker, who designed the makeup effects for both Murphy's and Arsenio Hall's multiple supporting characters.[citation needed]

text: Lawsuit

text: The film was the subject of the Buchwald v. Paramount civil suit, which the humorist Art Buchwald filed in 1990 against the film's producers on the grounds that the film's idea was stolen from his 1982 script treatment about a rich, despotic African potentate who comes to America for a state visit. Paramount had optioned the treatment from Buchwald, and John Landis was attached as director and Eddie Murphy as the lead, but after two years of development hell Paramount abandoned the project in March 1985. In 1987, Paramount began working on Coming to America based on a story by Eddie Murphy.[25][26] Buchwald won the breach of contract action and the court ordered monetary damages. The parties later settled the case out-of-court prior to an appeal going to trial.[27]

text: Soundtrack

text:
Coming to America: Original Motion Picture Soundtrack

Soundtrack album by Various artists

Released
July 1988

Genre
Pop

Length
40:16

Label
Atco Records

Singles from Coming to America

"Coming to America"
"Come into My Life"
"That's the Way It Is"
"Better Late Than Never"

text: The soundtrack to the film was released on LP, cassette and CD. The songs "Coming to America" by The System, "Better Late Than Never" by The Cover Girls and "Come into My Life" by Laura Branigan and Joe Esposito were released as singles from the album. "That's The Way It Is" by Mel & Kim had been released as a single in the UK, prior to the film's release, in February 1988, and became a top ten hit. It was released as a single in the USA at the time of the film's release.

text:
"Coming to America" — The System (3:49)
"Better Late Than Never" — The Cover Girls (4:02)
"All Dressed Up (Ready to Hit the Town)" — Chico DeBarge (4:50)
"I Like It Like That" — Michael Rodgers (4:01)
"That's the Way It Is" — Mel and Kim (3:25)

tag: ol

text:
"Addicted to You" — LeVert (3:54)
"Comin' Correct" — J.J. Fad (3:56)
"Livin' the Good Life" — Sister Sledge (3:46)
"Transparent" — Nona Hendryx (3:50)
"Come into My Life" — Laura Branigan and Joe Esposito (4:39)

text: Legacy

text: Television pilot

text: A television pilot of a weekly sitcom version of the film was produced for CBS, following the film's success, starring Tommy Davidson as Prince Tariq, and Paul Bates reprising his role as Oha. The pilot went unsold, but was televised on July 4, 1989 as part of the CBS Summer Playhouse pilot anthology series.[28][2]

text: Movie adaptation

text: A Tamil movie, My Dear Marthandan, was produced based on the plot of Coming to America. A Hong Kong movie, The Fun, the Luck & the Tycoon, also has the same plot.

text: Influences in music

text: The melody heard in the bathroom scene, where Prince Akeem is being washed by female servants, was sampled in Snoop Dogg's 2006 song "That's That" featuring R. Kelly; a remix of the song featuring rapper Nas includes a woman's voice saying "the royal penis is clean your highness", a line taken from the same scene. Also, the music video for Busta Rhymes' 1997 single "Put Your Hands Where My Eyes Could See" is loosely based on the film.

text: Planned sequel

text: In early 2017, an announcement was publicized which addressed the impending production of a sequel to the film. Kevin Misher was named as producer, and Sheffield and Blaustein, the original screenwriters, were also attached to the project. However, a possible participation of lead actors Eddie Murphy and Arsenio Hall was left undefined.[29][30] According to several public accounts, Murphy himself apparently posted an announcement regarding the film project a month prior on Facebook, but later claimed that his account had been hacked and completely deleted it.[29]


document_title: Cardinality

question_text: how to write the number of elements in a set

text: Cardinality

text: Comparing sets[edit]

text: While the cardinality of a finite set is just the number of its elements, extending the notion to infinite sets usually starts with defining the notion of comparison of arbitrary (in particular infinite) sets.

text: Definition 1: |A| = |B|[edit]

text: Definition 2: |A| ≤ |B|[edit]

text: Definition 3: |A| < |B|[edit]

text: If |A| ≤ |B| and |B| ≤ |A| then |A| = |B| (Schröder–Bernstein theorem). The axiom of choice is equivalent to the statement that |A| ≤ |B| or |B| ≤ |A| for every A, B.[3][4]

text: Cardinal numbers[edit]

text: Above, "cardinality" was defined functionally. That is, the "cardinality" of a set was not defined as a specific object itself. However, such an object can be defined as follows.

text: The relation of having the same cardinality is called equinumerosity, and this is an equivalence relation on the class of all sets. The equivalence class of a set A under this relation then consists of all those sets which have the same cardinality as A. There are two ways to define the "cardinality of a set":

text:
The cardinality of a set A is defined as its equivalence class under equinumerosity.
A representative set is designated for each equivalence class. The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.

text: Assuming AC, the cardinalities of the infinite sets are denoted

text:
For each ordinal

α

{\displaystyle \alpha }

,

ℵ

α
+
1

{\displaystyle \aleph _{\alpha +1}}

 is the least cardinal number greater than

ℵ

α

{\displaystyle \aleph _{\alpha }}

.

text:
The cardinality of the natural numbers is denoted aleph-null (

ℵ

0

{\displaystyle \aleph _{0}}

), while the cardinality of the real numbers is denoted by "

c

{\displaystyle {\mathfrak {c}}}

" (a lowercase fraktur script "c"), and is also referred to as the cardinality of the continuum. Cantor showed, using the diagonal argument, that

c

>

ℵ

0

{\displaystyle {\mathfrak {c}}>\aleph _{0}}

. We can show that

c

=

2

ℵ

0

{\displaystyle {\mathfrak {c}}=2^{\aleph _{0}}}

, this also being the cardinality of the set of all subsets of the natural numbers. The continuum hypothesis says that

ℵ

1

=

2

ℵ

0

{\displaystyle \aleph _{1}=2^{\aleph _{0}}}

, i.e.

2

ℵ

0

{\displaystyle 2^{\aleph _{0}}}

 is the smallest cardinal number bigger than

ℵ

0

{\displaystyle \aleph _{0}}

, i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers.
The continuum hypothesis is independent of ZFC, a standard axiomatization of set theory; that is, it is impossible to prove the continuum hypothesis or its negation from ZFC (provided ZFC is consistent). See below for more details on the cardinality of the continuum.[5][6][7]

text: Finite, countable and uncountable sets[edit]

text: If the axiom of choice holds, the law of trichotomy holds for cardinality. Thus we can make the following definitions:

text:
Any set X with cardinality less than that of the natural numbers, or | X | < | N |, is said to be a finite set.
Any set X that has the same cardinality as the set of the natural numbers, or | X | = | N | =

ℵ

0

{\displaystyle \aleph _{0}}

, is said to be a countably infinite set.
Any set X with cardinality greater than that of the natural numbers, or | X | > | N |, for example | R | =

c

{\displaystyle {\mathfrak {c}}}

 > | N |, is said to be  uncountable.

text: Infinite sets[edit]

text:
Our intuition gained from finite sets breaks down when dealing with infinite sets. In the late nineteenth century Georg Cantor, Gottlob Frege, Richard Dedekind and others rejected the view that the whole cannot be the same size as the part. One example of this is Hilbert's paradox of the Grand Hotel.
Indeed, Dedekind defined an infinite set as one that can be placed into a one-to-one correspondence with a strict subset (that is, having the same size in Cantor's sense); this notion of infinity is called Dedekind infinite. Cantor introduced the cardinal numbers, and showed that (according to his bijection-based definition of size) some infinite sets are greater than others. The smallest infinite cardinality is that of the natural numbers (

ℵ

0

{\displaystyle \aleph _{0}}

).

text: Cardinality of the continuum[edit]

text:
One of Cantor's most important results was that the cardinality of the continuum (

c

{\displaystyle {\mathfrak {c}}}

) is greater than that of the natural numbers (

ℵ

0

{\displaystyle \aleph _{0}}

); that is, there are more real numbers R than whole numbers N. Namely, Cantor showed that

c

=

2

ℵ

0

=

ℶ

1

{\displaystyle {\mathfrak {c}}=2^{\aleph _{0}}=\beth _{1}}

 (see Beth one) satisfies:

text: The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers, that is,

text: However, this hypothesis can neither be proved nor disproved within the widely accepted ZFC axiomatic set theory, if ZFC is consistent.

text: Cardinal arithmetic can be used to show not only that the number of points in a real number line is equal to the number of points in any segment of that line, but that this is equal to the number of points on a plane and, indeed, in any finite-dimensional space. These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it.

text: The first of these results is apparent by considering, for instance, the tangent function, which provides a one-to-one correspondence between the interval (−½π, ½π) and R (see also Hilbert's paradox of the Grand Hotel).

text: The second result was first demonstrated by Cantor in 1878, but it became more apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves are not a direct proof that a line has the same number of points as a finite-dimensional space, but they can be used to obtain such a proof.

text:
Cantor also showed that sets with cardinality strictly greater than

c

{\displaystyle {\mathfrak {c}}}

 exist (see his generalized diagonal argument and theorem). They include, for instance:

text:
the set of all subsets of R, i.e., the power set of R, written P(R) or 2R
the set RR of all functions from R to R

text: Both have cardinality

text:
The cardinal equalities

c

2

=

c

,

{\displaystyle {\mathfrak {c}}^{2}={\mathfrak {c}},}

c

ℵ

0

=

c

,

{\displaystyle {\mathfrak {c}}^{\aleph _{0}}={\mathfrak {c}},}

 and

c

c

=

2

c

{\displaystyle {\mathfrak {c}}^{\mathfrak {c}}=2^{\mathfrak {c}}}

 can be demonstrated using cardinal arithmetic:

text: Examples and properties[edit]

text:
If X = {a, b, c} and Y = {apples, oranges, peaches}, then | X | = | Y | because { (a, apples), (b, oranges), (c, peaches)} is a bijection between the sets X and Y. The cardinality of each of X and Y is 3.
If | X | < | Y |, then there exists Z such that | X | = | Z | and Z ⊆ Y.
If | X | ≤ | Y | and | Y | ≤ | X |, then | X | = | Y |. This holds even for infinite cardinals, and is known as Cantor–Bernstein–Schroeder theorem.
Sets with cardinality of the continuum

text: Union and intersection[edit]

text: If A and B are disjoint sets, then

text: From this, one can show that in general the cardinalities of unions and  intersections are related by[8]