- published: 23 Feb 2016
- views: 77940
In constructive mathematics, an apartness relation is a constructive form of inequality, and is often taken to be more basic than equality. It is often written as # to distinguish from the negation of equality (the denial inequality) ≠, which is weaker.
An apartness relation is a symmetric irreflexive binary relation with the additional condition that if two elements are apart, then any other element is apart from at least one of them (this last property is often called co-transitivity or comparison).
That is, a binary relation # is an apartness relation if it satisfies:
The negation of an apartness relation is an equivalence relation, as the above three conditions become reflexivity, symmetry, and transitivity. If this equivalence relation is in fact equality, then the apartness relation is called tight. That is, # is a tight apartness relation if it additionally satisfies:
In classical mathematics, it also follows that every apartness relation is the negation of an equivalence relation, and the only tight apartness relation on a given set is the negation of equality. So in that domain, the concept is not useful. In constructive mathematics, however, this is not the case.
The Cure are an English rock band formed in Crawley, West Sussex, in 1976. The band has experienced several line-up changes, with vocalist, guitarist and principal songwriter Robert Smith being the only constant member. The Cure first began releasing music in the late 1970's with their debut album Three Imaginary Boys; this, along with several early singles, placed the band as part of the post-punk and new wave movements that had sprung up in the wake of the punk rock revolution in the United Kingdom. During the early 1980's, the band's increasingly dark and tormented music was a staple of the emerging gothic rock genre.
After the release of 1982's Pornography, the band's future was uncertain and Smith was keen to move past the gloomy reputation his band had acquired. With the single "Let's Go to Bed" released the same year, Smith began to place a pop sensibility into the band's music and their popularity increased as the decade wore on, with songs like "Just Like Heaven", "Lovesong" and "Friday I'm in Love". The band is estimated to have sold 27 million albums as of 2004 and have released thirteen studio albums, ten EPs and over thirty singles during their career.
Modern Synth Pop anthem on HNF Music www.facebook.com/kasperbjorke Get the track here: www.facebook.com/hfnmusic Art by the American visual artist John Copeland A disco noir track taken from Kasper Bjørke's new album 'After Forever.' Singles 'Rush' and 'Sylvia' were strong but with 'Apart' Kasper's created a modern day dark disco anthem that can proudly sit alongside the likes of Sharon Brown in the hall of fame. The press release describes it as 'commercially friendly'. And it may have charted in 1987. But nowadays the chance of this getting Radio 1 A-listed is slim. It's catchy for sure, but its dark, twisted pop overtones are more akin to French Kiss 'Micheif' - itself a prototype techno anthem from 1979. The drums are 80s and unprocessed. The vocals are female and forlorn. The synth...
Check it out on Apple Music: https://t.co/2gOZM1mqfV
Download on iTunes: http://bit.ly/ApartRmx_iT Listen on Spotify: http://bit.ly/InMyOpinionSP Grab your copy on Beatport: http://bit.ly/ApartRmx_BP Subscribe to Armada TV: http://bit.ly/SubscribeArmada Driving down the freeway slightly too fast... There's a spot inside all of us that cries out for a beautiful radio tune, no matter how much we try to convince our friends that it's "too commercial". Given the backgrounds of both Ørjan Nilsen & Jonathan Mendelsohn, it's clear that these guys have a very "credible" pedigree. The melody, 'Jonathan Mendelsohn' vocals, and the lyrics of 'Apart' are transcendental. No matter what package they're put in, they work wonders. Mike Shiver, and Martin Volt & Quentin State had a field day with their respective mixes, bringing this anthemic gem to the clu...
🔥 Download Link 🔥 ↪︎https://soundcloud.com/krane/fall-apart Trap Nation Spotify: http://spoti.fi/237iVZi 🔊 Trap Nation 🔊 ●http://nations.io ●https://vine.co/thetrapnation ●http://twitter.com/alltrapnation ●http://instagram.com/trapnation ●http://facebook.com/alltrapnation ●http://soundcloud.com/alltrapnation ●https://snapchat.com/add/trapnation ●https://open.spotify.com/user/alltrapnation ●musical.ly: trapnation 📪 Send us stuff! 📭 P.O. Box 341937 3751 Motor Ave. Los Angeles, CA 90034 🎵 KRNE 🎵 ●https://soundcloud.com/krane ●https://www.instagram.com/krnekrne/ ●https://twitter.com/KRNEmusic ●https://www.facebook.com/krne 🎵 Alexander Lewis 🎵 ●https://soundcloud.com/alexanderjlewis ●https://www.facebook.com/officialalexanderlewis/ ●https://twitter.com/_alexanderlewis ●https://www.insta...
Music video by She Wants Revenge performing Tear You Apart. (C) 2005 Flawless / Geffen Records
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Hailing from Denmark, with an appearance that leads you to suspect that he knows his way around the studio (and that's a good thing as far as we're concerned). Kasper Bjørke (Eskimo, Correspondant) is not what one would call a household name. However, over the years he has made a name for himself as a club DJ, radio DJ, producer, remixer, label manager and inbetween all these activities he manages his own career as an artist, as well as that of Trentemøller for instance. He began producing music in the form of the Danish disco house duo named Filur. And even before 2007, when he started his solo career under his real name, the duo managed to release 4 studio albums. But after 2007 things really took off, possible kick started by Bjørke 's cover version of a Rolling Stones track (Heaven) th...
Kasper Bjørke Feat. Sísý Ey - Apart AVAILABLE ON: https://itunes.apple.com/gr/album/apart-feat.-sisy-ey-single/id957869267 http://www.junodownload.com/products/kasper-bjorke-sisy-ey-apart/2686579-02/ https://pro.beatport.com/release/apart/1452019 http://gr.napster.com/artist/kasper-bjorke-electronicadance/album/apart Video credits: Director - Karim Huu Do Producer - Katie Dolan Production co. - Caviar Content Exec Producer - Sorcha Shepherd, Louise Gagen DOP - Andrew Fletcher Colorist - Daniel de Vue / Baconx Camera Assistant - Imogen Forbes 2nd Camera Assistant - Edward Vijayavargiya Steadycam Operator - Andrew Fletcher Production Designer - Oliver Hogan SFX Makeup Artist - Samantha Maxwell Makeup Artist - Florence Teerlinck PM - Aella Jordan-Edge Production Coordinator - Sarah Braimah...
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
Streets apart: Surrey gets significantly less per pupil for children at its schools than London boroughs get for pupils at their schools – even though those schools may be less than a mile apart. LINK TO FULL STORY
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THE SEASON FINALE PT.2 "APART WE FALL"ITS BEEN A LONG ROAD FOR KING AND LOYALTY WITH EVERYTHING THATS BEEN GOING ON BUT LIKE WITH EVERY EMPIRE THERE COMES AN END....WILL KING AND LOYALTY REMAIN TRUE TO THEY UNBREAKABLE BOND OR WILL THIS BE THE END? GET YOUR POPCORN READY BECAUSE THIS IS GONE BE A 2 HOUR RIDE....ITS SO MUCH THATS HAPPENING IN THIS EPISODE.....SO PAY CLOSE ATTENTION SO U WONT MISS ANYTHING...HOPE U ALL ENJOY THE SHOW!!!! THANKS TO ALL OUR FANS FOR THE SUPPORT,WE APPRECIATED ALL THE LUV YALL GIVEN IT HAS BEEN A GREAT 1ST SEASON....STAT TUNED IN TO SEE WHATS NEXT FOR SEASON 2!!!!!!!
A little unintentional Mistake is haunting her for years, who will come to her rescue? Find Out! An Interesting Movie starring Mercy Johnson and many others.
We waited in line to buy a new iPhone 7. And now we're going to tear it apart to show you what's new.
Here is the story of Charles (Tony Umez)and Juliet (Eucheria Anunobi Ekwu); a happy couple facing the issue of childlessness. While the two are still battling to have a child together; Charles incidentally commits a desperate and a secret act in the family which unfortunately throws a once happy family into a big complication. Nollywood movies starring: Eucharia Anunobi Ekwu, Tony Umez, Patience Ozokwor, Ireti isayemi, Ann Ohume, Stan K. Amandi and Geraldine Ekeocha. Director: Michael Jaja Producer: Chibueze Ucheama Company:CHEZ PRODUCTION Click Here To Subscribe To Our Channel::: http://bit.ly/1qV5g8h Like Us On Facebook https://www.facebook.com/nollywood.picturestv/ Follow Us On Twitter https://twitter.com/ Like Us On Instagram https://www.instagram.com/Nollywoodpics/ watc...
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He waits for her to understand
But she won't understand at all
She waits all night for him to call
But he won't call anymore
He waits to hear her say
'Forgive'
But she justs drops her pearl-black eyes
And prays to hear him say
'I love you'
But he tells no more lies
He waits for her to sympathize
But she won't sympathize at all
She waits all night to feel his kiss
But always wakes alone
He waits to hear her say
'Forget'
But she just hangs her head in pain
And prays to hear him say
'No more
I'll never leave again'
How did we get this far apart?
We used to be so close together
How did we get this far apart?
I thought this love would last for ever
He waits for her to understand
But she won't understand at all
She waits all night for him to call
But he won't call
He waits to hear her say
'Forgive'
But she just drops her pearl black eyes
And prays to hear him say
'I love you'
But he tells no more lies
How did we get this far apart?
We used to be so close together
How did we get this far apart?
I thought this love would last for ever