- published: 02 Jun 2015
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In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification.
Uniqueness quantification is often denoted with the symbols "∃!" or ∃=1". For example, the formal statement
may be read aloud as "there is exactly one natural number n such that n - 2 = 4".
Proving uniqueness turns out to be mostly easier than that of existence or expressibility. The most common technique to proving uniqueness is to assume there exists two quantities (say, a and b) that satisfies the condition given, and then logically deducing their equality, i.e. a = b.
As a simple high school example, to show x + 2 = 5 has only one solution, we assume there are two solutions first, namely, a and b, satisfying x + 2 = 5. Thus
By transitivity of equality,
By cancellation,
This simple example shows how a proof of uniqueness is done, the end result being the equality of the two quantities that satisfy the condition. We must say, however, that existence/expressibility must be proven before uniqueness, or else we cannot even assume the existence of those two quantities to begin with.
Barack Hussein Obama II (i/bəˈrɑːk huːˈseɪn oʊˈbɑːmə/; born August 4, 1961) is the 44th and current President of the United States. He is the first African American to hold the office. In January 2005, Obama was sworn in as a U.S. Senator in the state of Illinois. He would hold this office until November 2008, when he resigned following his victory in the 2008 presidential election.
Born in Honolulu, Hawaii, Obama is a graduate of Columbia University and Harvard Law School, where he was the president of the Harvard Law Review. He was a community organizer in Chicago before earning his law degree. He worked as a civil rights attorney in Chicago and taught constitutional law at the University of Chicago Law School from 1992 to 2004. He served three terms representing the 13th District in the Illinois Senate from 1997 to 2004.
Following an unsuccessful bid against the Democratic incumbent for a seat in the United States House of Representatives in 2000, Obama ran for the United States Senate in 2004. Several events brought him to national attention during the campaign, including his victory in the March 2004 Illinois Democratic primary for the Senate election and his keynote address at the Democratic National Convention in July 2004. He won election to the U.S. Senate in Illinois in November 2004. His presidential campaign began in February 2007, and after a close campaign in the 2008 Democratic Party presidential primaries against Hillary Rodham Clinton, he won his party's nomination. In the 2008 presidential election, he defeated Republican nominee John McCain, and was inaugurated as president on January 20, 2009. Nine months later, Obama was named the 2009 Nobel Peace Prize laureate. In April 2011, he announced that he would be running for re-election in 2012.
Actors: Walter Hendrix III (miscellaneous crew), Walter Hendrix III (actor), Wardell Richardson (actor), Shelton Foreman (actor), Senay Jackson (actress), L. Stephanie Ray (actress), Michael Scimeca (actor), DeMarieo James (actor), DeMarieo James (producer), DeMarieo James (editor), DeMarieo James (actor), DeMarieo James (writer), DeMarieo James (director), Terrence V. Walker (actor), Darnell James (actor),
Plot: Humanity is separated by individual situations and personalities. Some people are bound by faith, while others are bound by the blood running through their veins. In the inner city of Atlanta, two brothers cross each other's paths unexpectedly when they both arrive at their mother's house for different reasons...one brother back from college ends up being a product of society turning to drugs as a way to solve his problems, while the other comes back wreaking havoc, murdering, robbing and ultimately making a huge mistake that alters the lives of everyone he loves. With every "Cain" there's an "Abel", but in this game of life and death, who will come out on top in the end?
Genres: Action,Actors: Jamal Hall (director), Jamal Hall (producer), Jamal Hall (writer), Bernard Sherman (actor), Damian Emile (actor), Jonathon Sisco (producer), Ralph F. Goodin (actor), Tyriece Green (actor),
Plot: Inner Reflections is a short film about how your destiny can change at your weakest point of your life. That one moment that can open your eyes to a new life. It takes you a ride from exciting colors to emotional music. This is not your typical Urban Short but more of a spiritual piece within art. Inner Reflections written and directed by Jamal Hall, it stars Damian Emile, Snagg A Puss, Tyriece 'Stepz' Green, and Bernard Sherman.
Genres: Adventure, Drama, Fantasy, Short,Actors: Elaine Hendrix (actress), Debra Wilson (actress), Jason Stuart (actor), Patrick Bristow (actor), Shawn Carter Peterson (producer), Brandon DeShazer (actor), Willie Macc (actor), Camille Carida (actress), Elliot Dal Pra London (producer), Elliot Dal Pra London (actor), Maurice Jamal (producer), Maurice Jamal (actor), Maurice Jamal (writer), Deondray Gossett (miscellaneous crew), Maurice Jamal (director),
Plot: A comedy drama about three very different couples living in Los Angeles trying to make theirs lives complete. Finding love, relationships and struggling to survive in the crazy world of Angelino's. A funny look at how people in the city are and how things just get in the way.
Keywords: african-american, ampersand-in-title, california, digit-in-title, diversity, friend, gay, gay-african-american, gay-couple, gay-interestActors: Richard Cansino (actor), Jesse McCartney (actor), Brian Peck (actor), Ashley Tisdale (actress), Miley Cyrus (actress), Miley Cyrus (actress), Brenda Song (actress), Phill Lewis (actor), Billy Ray Cyrus (actor), Dylan Sprouse (actor), Cole Sprouse (actor), Kyle Massey (actor), Rondell Sheridan (actor), Emily Osment (actress), Emily Osment (actress),
Genres: Comedy, Family,Actors: Roseanne Barr (actress), Kim Cattrall (actress), Malcolm-Jamal Warner (actor), Robert De Niro (actor), Oleg Taktarov (actor), Tygh Runyan (actor), David Alan Grier (actor), Paul Herman (actor), Kelsey Grammer (actor), Edward Burns (actor), Karel Roden (actor), James Handy (actor), Barry Primus (actor), Charlize Theron (actress), Vera Farmiga (actress),
Plot: When Eastern European criminals Oleg and Emil come to New York City to pick up their share of a heist score, Oleg steals a video camera and starts filming their activities, both legal and illegal. When they learn how the American media circus can make a remorseless killer look like the victim and make them rich, they target media-savvy NYPD Homicide Detective Eddie Flemming and media-naive FDNY Fire Marshal Jordy Warsaw, the cops investigating their murder and torching of their former criminal partner, filming everything to sell to the local tabloid TV show "Top Story."
Keywords: acetone, airport, ambulance, american-flag, apartment, arm-sling, arrest, arson, arson-investigator, attempted-murderActors: Bernd Euscher (editor), Clive Gordon (producer), Clive Gordon (director), Graham Shrimpton (editor), Derrick Avery (actor), Tisha Salinas (actress), Tina Dawkins (actress), Shamika Evans (actress), Takela Rogers (actress),
Plot: The movie Pimp Snooky, written with the Pimp Pen Polish of Superfly, The Mack, and Willie Dynamite, definitely transports the viewers along an unrighteous railway, aboard the train of temptation. It is a look into the Jekyll and Hyde metamorphosis of a mannish-boy, overdosed on the thuggish, ghetto power of man-whoring. Pimp Snooky(Derek Avery), reigns over his street sirens with the constant threat of violence, the worst of which, is seen in his piercing soulless eyes. This movie is also a Girls in The Hood field trip to grandmothers house,with Pimp Snooky as the big bad wolf, who devours their womanhood along the journey. The movie Pimp Snooky, is painful to watch and even more disturbing are the horrors that we imagine, as nervous compassion builds inside of us. This movie reminds us of just how cruel the streets of colored town in any city can be, and of the icy, demonic Imps who set he temperature there. This is not a cliché, clownish characterization of the Pimps of 70's movies and television shows. Pimp Snooky is a darkly dramatized film. The supporting characters Tina Dawkins, Shamika Evans, Takela Rogers, Tisa Salinas, all give first rate performances. Their portrayals of these doomed damsel's are executed with a sort of hopeless humanness. And although we know that lives like these can't possibly have a happy ending, these fine actresses proudly pose them under a spotlight of pride. Yet, it is Derek Avery's performance as Pimp Snooky that is ground breaking and ungodly euphoric! We hate the character of Pimp Snooky which Avery portrays, yet we are astonished by his striking screen persona. Idris Elba(The Wire, Daddy's Little Girls) is set to portray Pimp Snooky in Writer, Producer, Malik Jubal's 2011 release "Let Me Pimp or Let Me Die." And with an impressive supporting cast of Oprah Winfrey as Snooky's mother Pearl Marjhani, Tisha Cambell(Martin, My Wife and Kids), Janet Jackson(Poetic Justice, Why Did I Get Married), the movie threatens to be a formidable offering.
Genres: ,Actors: John Wardlaw (editor), John Wardlaw (actor), John Wardlaw (producer), John Wardlaw (producer), John Wardlaw (writer), John Wardlaw (composer), John Wardlaw (director), Michael Wilcox (actor), Michael Wilcox (producer), Philip Haynes (actor), John N. Dickson (actor), Ruston Slager (actor), Mark Rumer (actor), Shannon Perry (actress), Karen Lowery (actress),
Plot: In this James Bond Spoof, Blofelch industries has created the impotence inducing virus "Scrotitis" and plans to use the cure for global domination. Lames Blond, agent Double O Zero must join forces with Felix Heavier to fight the evil Mr. Cowabunga (the Man with the Foaming hand) and the seductive Shirly Bilt.
Keywords: james-bond-spoof, parody, secret-agent, secret-service, spoof, spy, spy-spoof, spyingI wear my hat down low so the world can't see my eyes, I wera my shades and go, so nobody can see me cry cus everybody and they momma wanna know why. why we ain't 2getha now I ain't going lie, I messed up with her now I'm getting what I deserved. Acting all slick dipping n Double trying to keep a secret (oh No) She is on the line the world see's what I'm winning like,
Yes I'm the star tonight and all eyes are on me but the spotlights been on me know this is my time cus there ain't no no moneys be the ones go into me, I'm the worlds biggest Jerk tonight! I'm the worlds biggest Jerk tonight!
Ready to leave this show, don't even cares who knows my namewhat am I smiling for? cus the smile couldn't mass the pain Everybody and they momma saying I'm dumb cus I let the baddest girl in the world run I really played myseld hate to see her with somebody else. Acting all slick dipping n Double trying to keep a secret (oh No) She is on the line the world see's what I'm winning like,
Yes I'm the star tonight and all eyes are on me but the spotlights been on me know this is my time cus there ain't no no moneys be the ones go into me, I'm the worlds biggest Jerk tonight! I'm the worlds biggest Jerk tonight!
I know I ain't the only one that messed up with a girl so all my felloas out there in the world, stand up if you know your a jerk didn't know how much I missed her now I understand. So all my ladies with a jerk for a man come on give em one more chance
Yes I'm the star tonight and all eyes are on me but the spotlights been on me know this is my time cus there ain't no no moneys be the ones go into me, I'm the worlds biggest Jerk tonight!