Look up completeness in Wiktionary, the free dictionary.

In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields.

Logical completeness[link]

In logic, semantic completeness is the converse of soundness for formal systems. A formal system is "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system that is consistent with the rules of the system). Kurt Gödel, Leon Henkin, and Emil Post all published proofs of completeness. (See History of the Church–Turing thesis.) A formal system is consistent if for all formulas φ of the system, the formulas φ and ¬φ (the negation of φ) are not both theorems of the system (that is, they cannot be both proved with the rules of the system).

• A formal system S is semantically complete or simply complete, if and only if every tautology of S is a theorem of S. That is, Failed to parse (Missing texvc executable; please see math/README to configure.): \models_{\mathcal S} \varphi\ \to\ \vdash_{\mathcal S} \varphi

.^[1]

• A formal system S is strongly complete or complete in the strong sense if and only if for every set of premises Γ, any formula which semantically follows from Γ is derivable from Γ. That is, Failed to parse (Missing texvc executable; please see math/README to configure.): \Gamma\models_{\mathcal S} \varphi \ \to\ \Gamma \vdash_{\mathcal S} \varphi

.

• A formal system S is syntactically complete or deductively complete or maximally complete or simply complete if and only if for each formula φ of the language of the system either φ or ¬φ is a theorem of S. This is also called negation completeness. In another sense, a formal system is syntactically complete if and only if no unprovable axiom can be added to it as an axiom without introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement consisting of a single variable "a" is not a theorem, and neither is its negation, but these are not tautologies). Gödel's incompleteness theorem shows that any recursive system that is sufficiently powerful, such as Peano arithmetic, cannot be both consistent and complete.

• A formal system is inconsistent if and only if every sentence is a theorem.^[2]

• A system of logical connectives is functionally complete if and only if it can express all propositional functions.

• A language is expressively complete if it can express the subject matter for which it is intended.^{[citation needed]}

• A formal system is complete with respect to a property if and only if every sentence that has the property is a theorem.^{[citation needed]}

Mathematical completeness[link]

In mathematics, "complete" is a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion". See, for example, algebraically closed field or compactification.

• The completeness of the real numbers is one of the defining properties of the real number system. It may be described equivalently as either the completeness of R as metric space or as a partially ordered set (see below).

• A metric space is complete if every Cauchy sequence in it converges. See Complete metric space.

• A uniform space is complete if every Cauchy net in it converges (or equivalently every Cauchy filter in it converges).

• In functional analysis, a subset S of a topological vector space V is complete if its span is dense in V. In the particular case of Hilbert spaces (or more generally, inner product spaces), an orthonormal basis is a set that is both complete and orthonormal.

• A measure space is complete if every subset of every null set is measurable. See complete measure.

• In commutative algebra, a commutative ring can be completed at an ideal (in the topology defined by the powers of the ideal). See Completion (ring theory).

• More generally, any topological group can be completed at a decreasing sequence of open subgroups.

• In statistics, a statistic is called complete if it does not allow an unbiased estimator of zero. See completeness (statistics).

• In graph theory, a complete graph is an undirected graph in which every pair of vertices has exactly one edge connecting them.

• In category theory, a category C is complete if every diagram from a small category to C has a limit; it is cocomplete if every such functor has a colimit.

• In order theory and related fields such as lattice and domain theory, completeness generally refers to the existence of certain suprema or infima of some partially ordered set. Notable special usages of the term include the concepts of complete Boolean algebra, complete lattice, and complete partial order (cpo). Furthermore, an ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field, which should be compared to the (slightly different) order-theoretical notion of bounded completeness. Up to isomorphism there is only one complete ordered field: the field of real numbers (but note that this complete ordered field, which is also a lattice, is not a complete lattice).

• In algebraic geometry, an algebraic variety is complete if it satisfies an analog of compactness. See complete algebraic variety.

• In quantum mechanics, a complete set of commuting operators (or CSCO) is one whose eigenvalues are sufficient to specify the physical state of a system.

Computing[link]

• In algorithms, the notion of completeness refers to the ability of the algorithm to find a solution if one exists, and if not, to report that no solution is possible.
• In computational complexity theory, a problem P is complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction.
  For example, each problem in the class NP-complete is complete for the class NP, under polynomial-time, many-one reduction.
• In computing, a data-entry field can autocomplete the entered data based on the prefix typed into the field; that capability is known as autocompletion.
• In software testing, completeness has for goal the functional verification of call graph (between software item) and control graph (inside each software item).
• The concept of completeness is found in knowledge base theory.

Economics, finance, and industry[link]

• Complete markets versus incomplete markets
• In auditing, completeness is one of the financial statement assertions that have to be ensured. For example, auditing classes of transactions. Rental expense which includes 12-month or 52-week payments should be all booked according to the terms agreed in the tenancy agreement.
• Oil or gas well completion, the process of making a well ready for production.

Botany[link]

• A complete flower is a flower with both male and female reproductive structures as well as petals and sepals. See Sexual reproduction in plants.

References[link]

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 2008)

Minnie Jean Riperton (November 8, 1947 – July 12, 1979) was an American singer-songwriter best known for her vocal range of five-and-a-half octaves, and her 1975 single "Lovin' You". She was married to songwriter and music producer Richard Rudolph from 1972 until her death in the summer of 1979. They had two children—music engineer Marc Rudolph and actress/comedienne Maya Rudolph.^[1]

Riperton grew up on Chicago's South Side. As a child, she studied music, drama, and dance at Chicago's Lincoln Center. In her teen years, she sang lead vocals for the Chicago-based girl group, The Gems. Her early affiliation with the legendary Chicago-based Chess Records afforded her the opportunity to sing backup for various established artists such as Etta James, Fontella Bass, Ramsey Lewis, Bo Diddley, Chuck Berry, and Muddy Waters. While at Chess, Riperton also sang lead for the experimental rock/soul group Rotary Connection, from 1967 to 1971. In 1969 Riperton, along with Rotary Connection, played in the first Catholic Rock Mass at the Liturgical Conference National Convention, Milwaukee Arena, Milwaukee, WI, produced by James F. Colaianni. Riperton reached the apex of her career with her number-one hit single, "Lovin' You," on April 4, 1975. The single was the last release from her 1974 gold album entitled Perfect Angel.

In January 1976, Riperton was diagnosed with breast cancer and underwent a radical mastectomy.^[2] By the time of diagnosis, the cancer had metastasized and she was given about six months to live. Despite the grim prognosis, she continued recording and touring. Riperton was one of the first celebrities to go public with her breast cancer diagnosis, but did not disclose she was terminally ill. In 1977, she became a spokesperson for the American Cancer Society. In 1978, Riperton also received the American Cancer Society's Courage Award which was presented to her at the White House by President Jimmy Carter. She died at age 31 on July 12, 1979.^[2][3]

Early life[link]

Riperton was born in Chicago to Thelma and Daniel Riperton, a Pullman porter.^[4] The youngest of eight children in a musical family, Riperton embraced the arts early on. Although she began with ballet and modern dance, Riperton's parents recognized her vocal and musical abilities and encouraged her to pursue music and voice.

At Chicago's Lincoln Center, Riperton received operatic vocal training from Marion Jeffery. She practiced breathing and phrasing, with particular emphasis on diction. Jeffery also trained Riperton to use her full range.

While studying under Jeffery, Riperton sang operettas and show tunes, in preparation for a career in opera. Jeffery was so convinced of her pupil's abilities that she strongly pushed her to further study the classics at Chicago's Junior Lyric Opera. The young Riperton was, however, becoming very interested in soul, rhythm and blues, and rock. After graduating from Hyde Park High School, now Hyde Park Career Academy, she enrolled at Loop College and became a member of the prestigious Zeta Phi Beta. She dropped out of college to pursue her music career. In 1967, Riperton met songwriter Richard Rudolph, whom she married five years later. They have a son named Marc, and their daughter is Maya Rudolph, a successful television and film actress/comedienne.

Career[link]

Early career[link]

Riperton's first professional singing engagement was with The Gems, when she was fifteen. Raynard Miner, a blind pianist, heard Riperton singing during her stint with Hyde Park's A Capella Choir and became her musical patron. The Gems had relatively limited commercial success, but proved to be a good outlet for Riperton's talent. Eventually the group became a session group known as Studio Three and it was during this period that they provided the backing vocals on the classic 1965 Fontella Bass hit "Rescue Me".^[5]

In 1964, The Gems released a local hit, I Can't Help Myself, and their last single, He Makes Me Feel So Good, was released in 1965. After that, the group released records under numerous names—most notably 1966's Baby I Want You by the Girls Three and 1967's My Baby's Real by the Starlets. The latter has achieved cult status with northern soul fans and remains a favorite. It also was a Motown-style song reminiscent of Tammi Terrell. In 1968, Watered Down was released as a follow-up, under the name The Starlets. It was the last release of Riperton's former girl group.

Andrea Davis[link]

While a part of Studio Three, Riperton met her mentor, producer Billy Davis. He would write her first local hit, "Lonely Girl", and also "You Gave Me Soul". In honor of Davis, she used the pseudonym Andrea Davis for the release of those two singles.

Rotary Connection[link]

Some months after her Andrea Davis singles hit the radio, Riperton joined Rotary Connection, a funky rock-soul group creation of Marshall Chess, the son of Chess Records' founder Leonard Chess.

Rotary Connection consisted of Riperton, Chess, Judy Hauff, Sidney Barnes and Charles Stepney. The group released their debut in 1967 and, eventually, five more albums: 1968's Aladdin; the Christmas album Peace; Songs; and finally 1970's Dinner Music and Hey Love.

[edit] Come to My Garden

Riperton's first solo album, Come to My Garden, produced, arranged, and orchestrated by Charles Stepney, was released in 1970 by GRT Records. She was presented as a solo artist by Ramsey Lewis on Saturday, December 26, 1970 at Chicago's famed London House. She performed several numbers from the album accompanied by Charles Stepney, the album's producer. Although commercially unsuccessful, Come to My Garden is now considered a masterpiece by music critics and many others in the music industry.^[2]

[edit] Perfect Angel and "Lovin' You"

In 1973, a college intern for Epic Records found Riperton in semiretirement. She had become a housewife and a mother of two in Gainesville, Florida. After he heard a demo of the song "Seeing You This Way," the rep took the tape to Don Ellis, VP of A&R for Epic. Riperton signed with Epic Records, and the family moved to Los Angeles, California. The subsequent record, Perfect Angel, turned out to be one of Riperton's best-selling albums. Included were the rock-soul anthem "Reasons", the second single, "Take a Little Trip" (written by Stevie Wonder, who also coproduced the album), and the third single, "Seeing You This Way".

Sales of the album started out slow. Epic was ready to move on to the next record, but Rudolph convinced them to release another single. With the fourth single, "Lovin' You", the album caught on, and in April 1975, the song went to the top of the charts in the U.S. and 24 other countries. The song reached number two in the UK, and number three on the U.S. R&B charts. It sold more than one million copies, and was awarded a gold disc by the RIAA in April 1975.^[6] Perfect Angel went gold, and Riperton was finally revered as the "lady with the high voice and flowers in her hair." The album also featured the song "Every Time He Comes Around," with Deniece Williams singing the background vocals.

Riperton's daughter is Saturday Night Live actress Maya Rudolph, who was a child when "Lovin' You" was recorded. According to the liner notes from Riperton's Petals compilation CD, the melody to "Lovin' You" was created as a distraction for Maya when she was a baby, so Riperton and Richard Rudolph could spend time together.^[2] Near the end of the unedited "Lovin' You", Riperton sings "Maya, Maya, Maya"; in concert, near her death, she changed this to "Maya, Maya, Ringo, Maya." Ringo was her nickname for her son, Marc. Maya Rudolph can also be heard in discussion with Teena Marie on the final track Too Many Colors (Tee's Interlude) of Teena's 1980 album Lady T.

Later career[link]

After Perfect Angel, Riperton and Richard Rudolph started on Riperton's third album, Adventures in Paradise (1975). Joe Sample of The Crusaders cowrote the title song, "Adventures in Paradise", and Crusaders' producer Stewart Levine, coproduced the album. While shooting a promotional clip for the album, she was attacked by a lion, but was not seriously injured. During an appearance on The Sammy Davis, Jr. Show, she played the footage of the incident for Sammy and her fellow guests, including Richard Pryor. The album was a modest success. Despite the R&B hit "Inside My Love" (a number five U.S. R&B hit, later covered by Trina Broussard and Chanté Moore), the album did not match the success of Perfect Angel. Some radio stations refused to play "Inside My Love" due to the lyrics: "Will you come inside me?" Her fourth album for Epic Records entitled Stay in Love featured another collaboration with Stevie Wonder in the funky disco tune "Stick Together". She also sang backup on Wonder's songs "Creepin'" from 1974's "Fullfillingness' First Finale" and "Ordinary Pain" from 1976's Songs in the Key of Life and was mentioned prominently in his song "Positivity" on A Time to Love.

In 1978, Riperton's attorney Mike Rosenfeld and her husband, Richard Rudolph, orchestrated a move to Capitol Records for Riperton and her CBS Records catalogue. In April 1979, Riperton released her fifth and final album, Minnie. During the recording of the album, her cancer progressed to the point that she was in a great deal of pain.^[2] "Memory Lane" was a hit from the album, and was arguably Riperton's greatest work. Riperton incorporated the sadness of the ending of a relationship while suddenly shifting to cries of "I don't want to go," "save me," "now I'm slippin' fast," "thought it was over; here I go again," and "travelin' down, faster than the speed of sound." It is thought that "Memory Lane" was her farewell to her family and to the world. Her last televised performance was on an episode of The Merv Griffin Show (aired July 6, 1979), during which she performed Memory Lane and Lover and Friend.

Illness and death[link]

On August 24, 1976, Riperton told Flip Wilson, who was guest-hosting for Johnny Carson on The Tonight Show, that she had undergone a mastectomy due to breast cancer.^[2] At the time of her diagnosis, Riperton found out her cancer had already spread to the lymphatic system, and was given about six months to live.^[2] She continued touring in 1977 and 1978, and became the national spokeswoman for the American Cancer Society 1978–79 campaign.^[2]

Extreme lymphedema immobilized her right arm in early 1979. In her final singing appearances on television (most notably on the Mike Douglas Show), her right arm would remain in a fixed position during her performances.^[2] By mid-June, she was confined to bed. She entered Cedars-Sinai Medical Center in Los Angeles on July 10. On Thursday, July 12 at 10am, while lying in her husband's arms, Riperton died while listening to a recording Stevie Wonder had made for her.^[2] That Sunday, following a funeral service attended by more than five hundred mourners, Riperton was interred in the Westwood Village Memorial Park Cemetery in Los Angeles. Her epitaph is the opening line of her most famous song, "Lovin' you is easy cause you're beautiful".

Riperton's grave at Westwood Village Memorial Park Cemetery

Posthumous recordings[link]

After Riperton died, several artists contributed vocals to tracks she had recorded before her death, to help compile Richard Rudolph's final tribute to his wife, Love Lives Forever. Included, among others, were Peabo Bryson, Michael Jackson and Stevie Wonder.

Riperton's last single, "Give Me Time", was released in 1980. Richard Rudolph wrote the song, "Now That I Have You" for Riperton, but she never got the chance to record it; he gave the song to Teena Marie, who recorded it (and coproduced it with Rudolph) on Marie's second LP, Lady T. Finally, in 1981, Capitol Records released The Best of Minnie Riperton, a greatest hits collection. The "new" song on the album was a remake of Joni Mitchell's "A Woman of Heart and Mind", which was a holdover from the Minnie sessions. Also included were an alternate mix of "Memory Lane", live versions of "Can You Feel What I'm Saying", "Lover And Friend", "Young, Willing and Able" and two "Moments with Minnie". It also included the hits "Perfect Angel", "Lovin' You", "Inside My Love", "Adventures In Paradise", and two tracks from Love Lives Forever: the singles "Here We Go" and "You Take My Breath Away". During the 1990s, Riperton's music was sampled by many rap and hip-hop artists, including Tupac Shakur, Dr. Dre, A Tribe Called Quest, Blumentopf, and Tragedy Khadafi.^[2]

Vocal ability[link]

Aside from her various hits, Riperton is perhaps best remembered today for her ability to sing in the whistle register, in which she had rare facility.^[7] Riperton possessed a five-octave vocal range (the liner notes to her Petals legacy album ascribe five-and-a-half octaves to her). Riperton's ability to enunciate in the high registers set her apart from most other whistle-register singers. This feature is most notably heard in the song Here We Go, where she sings "here we go" in the whistle register. Whistle-register enunciation can also be heard in songs such as "Inside My Love", "Adventures in Paradise", "Expecting", "Only When I'm Dreaming", and also in "Teach Me How to Fly" and "Like a Rolling Stone" with the Rotary Connection. Riperton was also noted for her ability to sound almost mechanical or instrumental in the whistle register. In "You Take My Breath Away", she sang a portamento ending two octaves above the staff. She has also been credited for her ability to sustain notes in the sixth and seventh octave for long periods of time, as in "Reasons", "Could It Be I'm in Love", "Adventures in Paradise", and "Inside My Love" and also "Love Me Now" with the Rotary Connection. Having an innate ability to imitate many instruments helped lead to Riperton's discovery while she was a secretary at Chess Records. In her recordings. Riperton's highest recorded note reached in the whistle register was F7 on the third scale of "You Take My Breath Away". Minnie reached this extremely high note before on an early recording of "Teach Me How to Fly" and "Could It Be I'm in Love". Also in a live performance of the song "Ruby Tuesday" from Rotary Connection, she sang an F#7. In a 1998 interview for Vibe magazine, Mariah Carey cited Riperton as an influence on her.

Documentary[link]

On June 7, 2009, TV One (US TV network's) Unsung series premièred a one-hour documentary on Riperton's career and life. It included interviews with her husband Richard, son Marc, daughter Maya (Maya Rudolph), sister Sandra Riperton, and many others who worked with Riperton.^[2]

Discography[link]

Studio albums[link]

Compilation albums[link]

Singles[link]

References[link]

External links[link]

• Minnie Riperton at Allmusic
• Minnie Riperton at Find a Grave
• 1968 photo: backstage at Washington University in St. Louis, performing with the band Rotary Connection

Itamar Moses (born 1977) is an American playwright, author, and television writer.

Moses grew up in Berkeley, California, earned his bachelor's degree at Yale University, and his Master of Fine Arts degree in dramatic writing from New York University. He has taught playwriting at both Yale and New York University, and he has written for Men of a Certain Age and Boardwalk Empire.

Works[link]

• Nobody Loves You, co-written with Gaby Alter, at San Diego Old Globe Theatre, May 24, 2012^[1]
• Completeness, world premiere at South Coast Repertory Theatre, April 17, 2011
• Yellowjackets, world premiere at Berkeley Repertory Theatre, September 2008
• Back Back Back, world premiere at the San Diego Old Globe Theatre, September 2008
• Bach at Leipzig
• Outrage, world premiere at Portland Center Stage, 2003. Workshop at Just Add Water: A Playwright's Festival in 2001.^[2][3]
• Celebrity Row, world premiere at Portland Center Stage, March 2006
• The Four of Us
• Authorial Intent
• Idea
• Dorothy and Alice

Bibliography[link]

• Bach at Leipzig. New York: Faber and Faber, 2005.
• The Four of Us. New York: Faber and Faber, 2008.

External links[link]

• Outrage at Google Books
• Review of Outrage at curtainup.com

References[link]

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