Uniqueness quantification
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
The most common technique to proving uniqueness is to first prove existence of entity with the desired condition; then, to assume there exist two entities (say, a and b) that should both satisfy the condition, and logically deduce 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. However, that existence/expressibility must be proven before uniqueness, or else we cannot even assume the existence of those two quantities to begin with our current knowledge to date.
Unique (DJ Encore album)
Unique is the second album by the Danish eurodance producer DJ Encore, with vocals by Swedish singer Johanna Elkesdotter, whereas the first album featured the vocals of Danish singer Engelina. It was released on May 8, 2007 on US label Koch Records.
The song "You Can Walk on Water" is a cover version of the 2002 song "Walk on Water (Baby U Can)" by Danish dance act Catch. "Out There" was originally released on DJ Encore's first album, Intuition, with vocals by Engelina.
Track listing
References
External links
Unique (band)
Unique was a short-lived post-disco studio act from New York, best known for their crossover number "What I Got Is What You Need" released in 1983 for a well-established dance label, Prelude Records. The group was formed by producer/songwriter Deems J. Smith in 1982 and consists of Smith and Darryl K. Henry. The said hit song somewhat established itself on the Billboard Dance Singles and Black Singles charts and even scored over the atlantic reaching No. 27 on UK Singles Chart.
History
Around 1982, record producer Deems J. Smith hired studio musicians to appear in a project he named Unique. He was signed to dance record label Prelude and under this name released two singles: "What I Got Is What You Need" in 1983 and "You Make Me Feel So Good" in 1984. Other people involved in the group were Mona Maria Norris and Darryl K. Henry who co-wrote "What I Got Is What You Need." Smith wrote the second song alone and it was mixed by an aspiring dance-pop producer Shep Pettibone.
Chart performance
Podcasts:
Unique
ALBUMS
- Más Világ released: 2006
- Mozaik nagykoncert (2004-11-04: Budapest, PeCsa) released: 2005
- Mozaik released: 2003
- Úttalan utakon released: 2001
Unique
ALBUMS
- Mixmag Presents: Destination: Future (Lost in Translation) released: 2010
Mixmag Presents: Destination: Future (Lost in Translation)
Released 2010- Remember Me
- Art & Cash (SBTRKT remix)
- Unique Morning
- Aundy (James Zabiela's Mad for Marky's mix mash-up)
- Premonition (feat. Kelly Dean)
- The Ubiquity Incident
- VI
- Cruise Control
- Fall Short
- History (Tom Budden's ALIVE remix)
- Our Time Our Chance (feat. Ian Whitelaw)
- Dream Runner (Funk D'Void remix)
- Jamelia (R3volve remix)
- Coastal Brake (Manual remix)
- Þú ert sólin
Unique
ALBUMS
- My Way released: 2008
Unique
ALBUMS
- Dance Classics, Volume 47 & 48 released: 2012
- All Star Selection 3 released: 2010
- Floorfillers 80s Club Classics released: 2009
- Best Of Funk released: 2008
- 100% Disco released: 2008
- Disco released: 2008
- Ferry Maat's Soulshow: Saturday Night Grooves released: 2005
- Disco Classics: The Greatest Disco Themes released: 2004
- Boogie Nights: Classic Disco Anthems released: 2003
- Rare Preludes, Volume 1 released: 2003
- Mega Funk released: 2002
- Pure Groove: The Classics released: 2002
- À l'ancienne released: 2001
- Total Prelude released: 2001
- Funky People, Volume 2 released: 1998
- Soul Weekender released: 1998
- Get Down Tonight: Disco Classics released: 1996
- 80s Dance Groove released: 1996
- Dance Floor Classics, Volume 3 released: 1996
- Dance Classics released: 1995
- Culture Dance Collector released: 1995
- Mega Dance Classics released: 1994
- Golden Dance Grooves, Volume 2: 11:" Original" Full Length Dance Classics released: 1990
- The History of Prelude Records released: 1989
- What I Got Is What You Need released: 1983
- Mastermix Classic Cuts 49: Disco/Funk released:
- Royal Funk, Volume 2 released:
- Les Années Mia: Greatest Hits released:
Dance Classics, Volume 47 & 48
Released 2012- Swept Away (long version)
- You're All Played Out (club mix)
- I've Been Watching You (extended)
- 1 Touch 2 Much (extended dance mix by Ben Liebrand)
- Hot Summer Nights (extended)
- Call Me (12 inch mix)
- What I Got Is What You Need (extended)
- Right on Target (12" version)
- Love Attack (12 inch version)
- Round and Around (extended version)
- Jody (dance hall version)
- Love Fever (extended)
All Star Selection 3
Released 2010- Intro
- C'est hella (DJ Nab remix)
- Célébration (DJ Nab remix)
- Hiya (DJ Nab remix)
- Khalata (DJ Nab remix)
- Freestyl
- L'ambiance du Bled
- Bienvenur (DJ Nab remix)
- L'Mebliya (DJ Nab remix)
- Freestyl (DJ Nab remix)
- Outstanding
- High Come Down
- Grande classe (DJ Nab remix)
- Shine
- It's A Party
- Love 1st Sight
- All My Love
- Pitch On A Party
- Patate (Prod DJ Nab)
- Freestyl Algeria (Prod DJ Nab)
- Son de l'eté (Prod DJ nab)
- Jamais trop tard (DJ Nab remix)
- Mama (DJ Nab remix)
- I Can't Make You Dance
- Can Make You Dance
- J'etais comme eux (DJ Nab remix)
- Nobody Else
- Même style (DJ Nab remix)
- Halla style (DJ Nab remix)
- Lover Boy
- What's You Need
- She Can't Love You
- Outro
Best Of Funk
Released 2008- And the Beat Goes On
- A Night to Remenber
- Last Night a DJ Saved My Life
- Why Did You Do It?
- She Can't Love You
- Act Like You Know
- Aimer D'Amour
- I Hear Music in the Streets
- Going Back to My Roots
- Cola Battle Baby
- Long Train Runnin'
- Keep On
- Get on Up
- What I Got Is What You Need
- Keep on Movin' and Groovin'
- Fantastic Voyage
- Call Me
- Saddle Up
- Body Music
- Wot
100% Disco
Released 2008- Play That Funky Music
- Blame It on the Boogie
- That's the Way (I Like It)
- Upside Down
- Let's Groove
- Spank
- Relight My Fire
- Heart of Glass
- Sing It Back (Boris radio edit)
- I'm So Excited
- It's Raining Men
- It's Just Begun
- Movin'
- Feels Like I'm in Love
- Hot Stuff
- Ladies Night
- Change of Heart
- Last Night a DJ Saved My Life
- Just an Illusion
- Elle et moi
Disco
Released 2008- Born to Be Alive
- D.I.S.C.O.
- Let's All Chant
- Just an Illusion
- And the Beat Goes On
- Cuba
- I Will Survive
- Saddle Up
- Move on Up
- Can You Feel the Force
- Free Your Mind
- Love Really Hurt Without You
- Black Soul Music
- Moment of My Life
- Suspicious Minds
- Mr. Blindman
- The Bottle
- Love Sensation
- Dancing Queen
- Darlin'
Disco Classics: The Greatest Disco Themes
Released 2004- Upside Down
- Relight My Fire
- Hot Stuff
- You See the Trouble With Me
- Ain't Nobody
- I Will Survive
- Love Sensation
- Let the Music Play
- The Hustle
- Going Back to My Roots
- And the Beat Goes On
- Ain't No Mountain High Enough
- If I Can't Have You
- Dance to the Music
- I Like It (What You're Doing to Me)
- Don't Leave Me This Way
- Love Machine
- Dr. Love
- I'm Caught Up (in a One Night Affair)
- Windy City Theme
Mega Funk
Released 2002- And the Beat Goes On
- Just an Illusion
- Last Night a DJ Saved My Life
- A Night to Remember
- Somebody Else's Guy
- You & I
- Midas Touch
- She's a Groovy Freak
- Keep On
- Saddle Up
- Can't Fake the Feeling
- Move On Up
- The Message
- One Nation Under a Groove
- Rock Your Baby
- Do It
- Use Me
- Across 110th Street
- Gimme the Funk
- The Message
Pure Groove: The Classics
Released 2002- Ain't Nobody
- I Want Your Love
- September
- Give It Up
- Dancing Tight
- Just an Illusion
- Let's Go Dancin' (Ooh, La, La, La)
- Thinking of You
- Somebody Else's Guy
- What I Got Is What You Need
- Going Back to My Roots
- Let's Go Round Again, Part 1
- Disco Nights (Rock Freak)
- Stomp
- Spanish Hustle
- Get Down Saturday Night
- Got to Be Real
- Brighter Tomorrow
- Walking in Rhythm
- Dancing in the Key of Life
À l'ancienne
Released 2001- Intro
- Let the Music...
- Ain't No Stoppin' Us Now (Ain't No Way version)
- What I Got Is What You Need
- It Should Have Been You
- Music
- Must Be the Music
- Darlin' (I Think About You)
- Love's Comin' at Ya
- Stomp!
- The Throwdown Mix
- Shine On
- A Lovers Holiday
- Reach out
- Joy and Pain
- Act Like You Know
- Somebody Else's Guy
- Ain't Nobody
- Mary Jane
- Only Thing I Need (Say You'll Be version)
Funky People, Volume 2
Released 1998- Just an Illusion (version longue)
- Gimme the Funk
- What I Got Is What You Need (version longue)
- Act Like You Know (version longue)
- The Message
- You're the One for Me (version longue)
- Midas Touch
- The Lover in You
- You to Me Are Everything
- Love Come Down (version longue)
- It's a Love Thing (version longue)
- I Want Your Love
- He's the Greatest Dancer (version longue)
- Darlin' (I Think About You)
- You Got the Power (version longue)
Soul Weekender
Released 1998- Somebody Else's Guy
- Check Out the Groove
- Take That to the Bank
- It's a Love Thing
- Shame
- One Nation Under the Groove
- Funkin' for Jamaica
- Pick Up the Pieces
- Let the Music Play
- You Know How to Love Me
- Turn Up the Music
- You're the One for Me
- Last Night a DJ Saved My Life
- What I Got Is What You Need
- Southern Freeez
- Walking on Sunshine
- Midas Touch
- Can You Handle It
- I Found Lovin
Get Down Tonight: Disco Classics
Released 1996- More More More
- You To Me Are Everything
- Get Down Tonight
- Sad Sweet Dreamer
- Uptown Festival (single edit)
- What I Got Is What You Need
- This Is It
- Dancing on a Saturday Night
- Go Deh Yaka (Go To The Top)
- Dolly My Love
- Zing! Went the Strings of My Heart
- Zoom
- Girls
- Isn't She Lovely
- Swing Your Daddy
- A Night to Remember
- Headlines
- Do You Wanna Dance
- Shame, Shame, Shame
- Galaxy of Love
- Come Back and Finish What You Started
Dance Floor Classics, Volume 3
Released 1996- Pump Up the Jam
- Let the Music Play
- White Lines (Don't Do It)
- Rapper's Delight
- What I Got Is What You Need
- You Gave Me Love
- I Don't Want to Be a Freak (But I Can't Help Myself)
- Do It Again medley with Billie Jean
- Walking on Sunshine
- Sunshine Day
- Take That to the Bank
- I'm Your Boogie Man
- Go Deh Yaka (Go to the Top)
- Headlines
- (Sending Out an) S.O.S.
- Walk On By
Mega Dance Classics
Released 1994- Somebody Else's Guy
- And the Beat Goes On
- Hot Shot
- Let's All Chant
- On the Beat
- Doctor Love
- The Second Time Around
- Rappers Delight
- Ring My Bell
- My Turn to Love
- Can You Handle It
- That's the Way (I Like It)
- Why Did You Do It
- What I Got Is What You Need
- You to Me Are Everything
- Pick Up the Pieces
- Get Down
- See You When I Get There
Mastermix Classic Cuts 49: Disco/Funk
- She's Strange
- She's a Bad Mama Jama
- Searching
- Just an Illusion
- Ai No Corrida
- Get Down Tonight
- Ooh La La La
- Juicy Fruit
- Going Back to My Roots
- We Got the Funk
- Can You Handle It
- Forget Me Nots
- There It Is
- He's the Greatest Dancer
- Takes a Little Time
- What I Got Is What You Need
- I Shoulda Loved Ya
- Don't Stop the Music
Les Années Mia: Greatest Hits
- Somebody Else's Guy
- Act Like You Know
- Help Yourself to My Love
- Going Back to My Roots
- Last Night a DJ Saved My Life
- Funn
- So Different
- Gimme the Funk
- Keepin' My Lover Satisfied
- Show Me the Way
- What I Got Is What You Need
- Love Come Down
- Get Down Saturday Night
- Forget Me Nots
- Got to Find My Way Back to You
- Still Got the Magic (Sweet Delight)
Unique
ALBUMS
- Hook Off released: 2014
- Fast *Rap. released: 2001
- Pure Dynamite / Axe Maniac released: 1989
Fast *Rap.
Released 2001- Raw
- Freestyle
- Prisoners of War
- Welcome to the Terrordome (instrumental)
- Axe-Maniac
- Mission Accomplished
- Something for the Bassline
- Back to Back Rhyming
- The Creator
- Warm It Up Kane
- At the Drop of a Dime (instrumental)
- Small Time Hustler
- Black & Proud
- Stop the World
- Reflection of Perfection
- He Got So Much Soul
- Now Ya Know
- Kool Is Back
- Lung Collapsing Lyrics
- A Chorus Line
- Real Solo Please Stand Up
- Rampage (remix)
- Jokes on You Jack (instrumental)
- Strobelite Honey (remix)
- It's That Simple
- I'm the Peacemaker
- Know the Ledge
- Patterson Projects Battle 1989
Unique
ALBUMS
- Slow, Loud and Bangin', Volume 4 released: 2004
- Slow, Loud and Bangin', Volume 3 released: 2003
- The Greatest Knockouts: Beat Box Mix CD, Volume 1 released: 2003
Slow, Loud and Bangin', Volume 4
Released 2004- D-Bo (S.L.A.B.ed)
- Pimpin' (S.L.A.B.ed)
- Ride on Our Enemies (S.L.A.B.ed)
- Slow, Loud and Bangin' (S.L.A.B.ed)
- Charlie Berry (S.L.A.B.ed)
- All I Have (S.L.A.B.ed)
- What I Represent (S.L.A.B.ed)
- Trae (S.L.A.B.ed)
- In a Slab (S.L.A.B.ed)
- Niggas in tha Game (S.L.A.B.ed)
- Better Way (S.L.A.B.ed)
- Got Mine (S.L.A.B.ed)
- Wreckin' (S.L.A.B.ed)
- We Represent H-Town (S.L.A.B.ed)
- Remix (S.L.A.B.ed)
- What You Gon' Do
The Greatest Knockouts: Beat Box Mix CD, Volume 1
Released 2003- Let's Get Ready to Rumble
- Essentials (JS-1 Remix)
- Live in London
- Rahstrumental Breaks 1
- Nuthin to Fuck Wit
- The Four Elements
- Freestyle 1 (Tim Westwood Show)
- It's a Must (feat. Rakim)
- Rahstrumental Breaks 2
- Childrens Story
- Rahstrumental Breaks 3 (Deep Cover)
- Hot 97.1 Interlude (LIVE with Funkmaster Flex)
- Used to be Perfect (Beat Box Remix)
- Southern Girl
- The Lesson Part 1
- Rahzel vs. DJ JS-1
- Live from Atlanta (Radio)
- Live from Philadelphia
- Time to Get Live!
- Night Rider (JS-1 Remix)
- The Undisputed (Interlude)
- Rahstrumental Breaks 4
- Freestyle 2 (Tim Westwood Show)
- U.N.I.T.Y.
- Tribute to Aaliyah ('One in a Million' - Live in London)
- Guess (U Never Knew)
Unique
ALBUMS
- Hardy Boyz Present Nasty Noise released: 2004
- Derek the Bandit's World of Dance 5 released: 2003
Derek the Bandit's World of Dance 5
Released 2003- The Race (Tomcraft remix)
- Just Crusin' (Beachballin' Again) (Steve Murano mix)
- Radioloxy (techno mix)
- Big.Bass.Drum (Alex Butcher remix)
- Serene Spaces
- Connected (PvD's Moto mix)
- The Prayer (Survivors mix)
- Summer Sun (DJ 4 Strings mix)
- Time of Our Lives (PvD vocal club mix)
- Timeless (Ron Van Den Beuken mix)
- Nobody Scream (Graham Gold mix)
- ''O'' Class
- Tribal Shock
- Fate & Fortune
- Deep Blue (DJ Dizzy remix)
- Rush (Hardy Boys remix)
- The Rainmaker
- The Vision
- Pitch Bender
Unique
ALBUMS
- Jerry 4 W.A released: 2002
Jerry 4 W.A
Released 2002- Intro, Part 1
- Intro, Part 2
- Definition of Real
- Make It Shine (interlude)
- A.K Heavy Weights (feat. Mareko and Savage)
- What Goes
- The Plateau (interlude)
- Who Want It
- Who Got It Like This (feat. Kalista and Jessone)
- What It Is (interlude)
- Outspoken
- Showing You How
- Jerry 4 W.A
- Unique Will Get Ill
- Sprayed Out Linguistics (feat. Blayzedone)
- Niceness
- Outro
U'nique
ALBUMS
- Disco Funk released: 2008
- Motivation Songs for Make-Up released:
Disco Funk
Released 2008- Ring My Bell
- Let's All Chant
- And the Beat Goes On
- Fame
- Act Like You Know
- Dancing Queen
- High Energy
- I Am What I Am
- Cuba
- Baby I Need Your Loving
- Dance Dance Dance
- I Know You I Live You
- Hit n' Run
- Car Wash
- Hit 'n' Run Lover
- Mr Blindman
- Electric Boggie Break Dance
- Let No Man Put Asunder
- Keep On
- She Can't Love You
Motivation Songs for Make-Up
- Hold It Down (album mix)
- Dance to the Music (Knee Deep remix) (feat. One)
- Reach (club mix)
- Happy House (D.Funked remixed by Dexter)
- Move Me (Fatback mix)
- Libre (Axwell vocal mix)
- Pom Pop (DJ Cam A.K.A. Cam remix)
- What Is Love (edit)
- Take U Home (Besides mix)
- Piano Things
- So Right (Axwell vocal mix)
- Choices (Tweek Freekz Vox) (feat. Lynnette Curtis)
U-nique
ALBUMS
- Ballermann 6 Balneario: Pole Position 2007 released: 2007
Ballermann 6 Balneario: Pole Position 2007
Released 2007- Rock This Party (Everybody dance Now) (radio edit)
- Let's Go (Original mix)
- Put Your Hands Up for Detroit (radio edit)
- Ein Freund, ein guter Freund
- Tu mi piaci (radio edit)
- Mein letztes Gebet (Das 4. Gebet)
- Summerlove (radio version)
- El Temperamento (Spanish single version)
- Eye of the Tiger (Sunset Crew radio edit)
- Ich hab' das Gras flüstern hör'n (Moskau-Abtanz-Mix)
- Aloha Heja He
- Dieser Flug (radio version)
- Wenn Du denkst Du denkst, dann denkst Du nur Du denkst
- Der Schunkelsong
- Nur mit dir
- Seemann 2006 (radio version)
- Mief (Apestaro Mixo)
- Amigo Charly Brown 2007 (Party version)
- Zorba (Gyros edit)
- Ich weiss nicht zu wem ich gehöre (radio version)
Unique
ALBUMS
- t:me 1010 released: 1994
Unique
ALBUMS
- Get Your Kicks on MODEified 6 released: 2005
- MODEified V - Songs From the So-Called Space Age released: 2000
- MODEified IV - Things We Said released: 1998
Unique
ALBUMS
- Hardcore Nation 2 released: 2005
Hardcore Nation 2
Released 2005- We're Rockin' This Place
- A Feeling
- Drop It
- Walk Away (feat. Lou Lou)
- Kick That Bass
- Take Me Higher
- Cross the Fader
- Just Gotta Dance (feat. Charm)
- That's How I Roll
- All About You (feat. Cat Knight)
- The Devil
- Taking My Time
- Twilight
- Everynight
- Something Like This
- Touch the Sky
- Enjoy the Silence
- Open Your Eyes (feat. Lisa Marie)
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Tonight
by: UniqueI 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!
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