- published: 12 Sep 2014
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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.
Sarah Terenzi (born as Sarah Marianne Corina Lewe on June 13, 1980), better known by her stage name Sarah Connor, is a German singer, songwriter, and television personality. Connor debuted in 2001 under the guidance of artist manager George Glueck and became the first solo act to ever have four consecutive chart-topping hits on the German Singles Chart. Following success in mainland Europe with her single "From Sarah with Love" and her debut album Green Eyed Soul, a series of hit records established her position as the most successful German pop female vocalists to emerge in the 2000s with sales in excess of over 15 million copies worldwide. Her seventh studio album Real Love, was released in October 2010, amid her engagement as judge on the German reality television show X Factor. Her first German album Muttersprache released on May 22, 2015 debuted on the top of the German and Swiss Albums Chart.
Awarded with several prizes and accolades, Connor has received four Comets, a Top of the Pops Award, a Goldene Kamera, a Goldene Europa, a World Music Award, and two Echos. She married the American pop-rock musician Marc Terenzi in 2004, with whom she appeared in two reality shows, Sarah & Marc in Love (2007) and Sarah & Marc Crazy in Love (2008). They ended their relationship with divorce in 2008.
Austin Post (born July 4, 1995), better known by his stage name Post Malone, is an American recording artist and songwriter from Dallas, Texas. He first gained major recognition for his single "White Iverson" after releasing it on SoundCloud in February 2015. He is currently signed with Republic Records.
Austin Post was born on July 4, 1995, in Syracuse, New York. When he was 10-years old, he and his family moved to Dallas, Texas. He enjoyed playing basketball and watching sports. His father was the Dallas Cowboys' assistant director of food and beverage, and this meant that he was able to get free food and tickets to Dallas Cowboy games.
Post then taught himself on how to play the saxophone, and then he became a member of the heavy metal band in high school. He credited his initial interest in learning guitar to the popular video game Guitar Hero. He first learned how to produce music through FL Studio. When he was 16-years old, he's been started working on his first mixtape. He showed it to some of his classmates and it gained some popularity at his school. He credits his love for music to his father, who exposed him to many genres, including country music, while growing up and also his cousin Raj who exposed him to rap music at a young age. He often mentions his cousin who he used to watch basketball with from a young age but has lost touch with because of his new found fame.
"Never Tear Us Apart" is a single released by Australian rock group INXS in August 1988. It was also included on the band's sixth studio album, Kick. The music was written by keyboardist Andrew Farriss, who recorded a blues-style demo and gave it to vocalist Michael Hutchence who wrote the lyrics.
"Never Tear Us Apart" is a sensuous ballad, written in the tempo of a modern Viennese waltz, layered with synthesizers and containing dramatic pauses before the instrumental breaks. Kirk Pengilly lends a cathartic saxophone solo near the end. According to the liner notes of Shine Like It Does: The Anthology (1979–1997), the song was originally composed on piano as a bluesy number in the style of Fats Domino. Producer Chris Thomas suggested a synth-based arrangement instead.
The video for the song, featuring an extended intro, was filmed in various locations in Prague along with "Guns in the Sky" and "New Sensation", all directed by Richard Lowenstein.
The single reached #24 in the UK, and stayed on the charts for seven weeks. In the U.S., it reached #7 on the Billboard Hot 100.
Jonathan Neil Mendelsohn, Baron Mendelsohn (born 30 December 1966) is a British lobbyist and Labour political organiser. He was appointed the Director of General Election Resources for the party in 2007.
With Neal Lawson and Ben Lucas, he founded LLM Communications in 1997, a lobbying firm with notable access to the new Labour Government. He has been a spokesman and lobbyist for the gambling company PartyGaming.
He had written to controversial Labour donor David Abrahams claiming he was one of Labour's "strongest supporters". In 1998 he was caught on tape along with Derek Draper boasting to Greg Palast, an undercover reporter posing as a businessman, about how they could sell access to government ministers and create tax breaks for their clients in a scandal that was dubbed "Lobbygate". Draper denied the allegations.
In the same incident Mendelsohn was approached by an undercover journalist posing as a representative of American energy companies who were seeking to ignore environmental laws. Despite LLM's claim that "we believe that there will be a new breed of 'ethical winners' who will demonstrate that businesses no longer operate in a moral vacuum", Mendelsohn went on to advise the reporter to rephrase their plans into language that sounded "Earth-Friendly" going on to say "Tony [Blair] is very anxious to be seen as green. Everything has to be couched in environmental language – even if it's slightly Orwellian."
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...
Music video by Ricky Blaze performing Apart. (C) 2016 FME Recordings, LLC, under exclusive licence to Island Records, a division of Universal Music Operations Limited http://vevo.ly/MjgiR7
Check it out on Apple Music: https://t.co/2gOZM1mqfV
During their heated debate on #PMQs Jeremy Corbyn hits out Conservatives, Theresa May hit back saying "everyone pays price for Labour". Like what you see? Please subscribe http://youtube.com/RTUKnews FOLLOW ON TWITTER: http://twitter.com/RTUKnews FOLLOW ON FACEBOOK: http://fb.com/RTUKnews READ MORE http://rt.com/uk/ WATCH LIVE: http://rt.com/on-air/rt-uk-air/
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...
Post Malone - I Fall Apart Post Malone - I Fall Apart Post Malone - I Fall Apart Post Malone - I Fall Apart *New Song* Stoney Album
INXS are celebrating the 25th Anniversary of 'KICK' by releasing special Deluxe, Super Deluxe and Digital versions of this landmark album. Order Now: Super Deluxe www.smarturl.it/kicksuperphys Standard Deluxe www.smarturl.it/kickstandardphys 1987's KICK lifted INXS to an new level and firmly established the band as a force to be reckoned with, sending 4 singles--"New Sensation", "Devil Inside", "Need You Tonight" and the timeless ballad "Never Tear Us Apart"—straight to the charts. The rest of KICK, especially "Guns in the Sky" and the groove filled "Wild Life" remain ever popular with fans. Music video by INXS performing Never Tear Us Apart. (C) 1987 Mercury Records Limited
I finally receive my front skinny's for my 2011 mustang. I also show you how to tell different injectors apart. Id1000 DW95's LU47 Mu52 Injectors Injector dynamics Fuel injector clinig Coyote mustang Alejandro Flores Yolodouchebag #Yolodouchebag
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