* Sanjeev Saxena, " A Simple Proof of Bernoulli's Inequality ", viXra: 1205. 0068, May 2012

Among Moore's most famous works are his book Principia Ethica, and his essays, " The Refutation of Idealism ", " A Defence of Common Sense ", and " A Proof of the External World ".

He famously put the point into dramatic relief with his 1939 essay " Proof of an External World ", in which he gave a common sense argument against scepticism by raising his right hand and saying " Here is one hand ," and then raising his left and saying " And here is another ," then concluding that there are at least two external objects in the world, and therefore that he knows ( by this argument ) that an external world exists.

* A. P. Hazen, " On Gödel's Ontological Proof ", Australasian Journal of Philosophy, Vol.

* ( German ), reprinted in English translation as " Proof that every set can be well-ordered ", van Heijenoort 1976, pp. 139 – 141.

meaning " quod erat demonstrandum " or by one of the tombstone marks "" or "" meaning " End of Proof ", introduced by Paul Halmos following their usage in magazine articles.

In fact, Thurston resolved so many outstanding problems in foliation theory in such a short period of time that, according to Thurston, it led to a kind of exodus from the field, where advisors counselled students against going into foliation theory because Thurston was " cleaning out the subject " ( see " On Proof and Progress in Mathematics ", especially section 6 ).

 He made another major contribution to the field in his 1979 paper, joint with his student Robert A. Reckhow, " The Relative Efficiency of Propositional Proof Systems ", in which they formalized the notions of p-simulation and efficient propositional proof system, which started an area now called propositional proof complexity.

* " Proof ", a 1942 hard SF short story by Hal Clement

* " Proof ", a song by Paul Simon from The Rhythm of the Saints

* " Proof ", a song by Happy Rhodes from Many Worlds Are Born Tonight

* " Proof ", a song by angela

* " Proof ", a song by Mell

* Arora, Sanjeev ; Barak, Boaz, " Complexity Theory: A Modern Approach ", Cambridge University Press, 2009, ISBN 978-0-521-42426-4, section 1. 4, " Machines as strings and the universal Turing machine " and 1. 7, " Proof of theorem 1. 9 "

Shaw sold this story to Analog editor John W. Campbell, who liked it so much Shaw wrote a sequel for him, " Burden of Proof ", in May 1967.

* Hexter, J. H. " The Burden of Proof ", Times Literary Supplement, October 24, 1975.

Under the headline " Orthographical " in James Joyce's novel Ulysses, Leopold Bloom, watching the typesetter foreman Mr. Nannetti read over a " limp galleypage ", thinks " Proof fever ".

The dome is " Water Proof ", because Sandy does not breathe underwater since she is a squirrel.

Mālik ibn Anas ibn Mālik ibn Abī ' Āmir al-Asbahī ( Arabic مالك بن أنس ) ( c. 711 – 795 ) ( 93 AH – 179 AH ) is known as " Imam Malik ," the " Sheikh of Islam ", the " Proof of the Community ," and " Imam of the Abode of Emigration.

In 2002, Bracegirdle co-wrote two songs on Cher's album Living Proof, " You Take It All " and " Alive Again ", the latter which was released as a single in Europe only.

* Roy Bittan – keyboards on " Leap of Faith ", " The Big Muddy " and " Living Proof "

D12, in turn, responded with the song " Instigator ", dissing Natas, while Proof made 2 diss tracks aimed specifically at Esham, " Every Sucker Has A Moment " and " Uh Huh ", though the latter was not released.

* " Proof " ( I Am Kloot song ), a song by I Am Kloot from their eponymous second album

Bikutsi's international renown continued to grow, and the song " Proof " from Paul Simon's Rhythm of the Saints, released to mainstream promotion and success in 1990, gained yet more renown from international audiences.

; Loveline, which Adam hosted ; as well as contributing the song " This Photograph Is Proof ( I Know You Know )" to the soundtrack for Spider-Man 2.

Shortly after his label-mate Proof was shot to death in a Detroit nightclub, a song emerged on the mixtape circuit called " Ride Wit Me ".

The song was dedicated to Proof.

It was also sampled by RJD2 for the song " Weather People Off Cage's Album Weather Proof " and by Army of the Pharaohs in their song " Swords Drawn ".

Intending to record one more song for the album (" Living Proof "), he ended up with ten new songs, which became Lucky Town.

Eminem references Big Daddy Kane in the lyrics to his song ‘ Yellow Brick Road ’ from his Encore album, saying, “ we ( Eminem and Proof ) was on the same shit, that Big Daddy Kane shit, where compound syllables sound combined ” and he quotes the same lines in his book, The Way I Am – this illustrates how Big Daddy Kane had an influence on both Eminem ’ s and Proof ’ s rhyme technique.

The RICANstruction will also feature an unreleased collaboration with D12's Proof and a song with Big Pun.

This is arguably best exemplified by the music on Thrust, particularly on the song " Actual Proof ", Mike Clark has established himself as a true innovator of linear style drumming, incorporating jazz and funk.

Proof, the only group member not to rap in the original song, also utilised the beat in a solo cover version called " Shoot At You " in 2002, available from his website.

Although Proof does not appear in the song, he provides a spoken introduction to the video, and is seen alongside his bandmates.

In Quentin Tarantino's segment of the 2007 Grindhouse, Death Proof, the character Jungle Julia ( Sydney Tamiia Poitier ) calls a contact at the radio station where she works, requesting the group's song " Hold Tight ".

Proof sheets were the means by which syndicates provided newspapers with black-and-white line art for the reproduction of strips ( which they arranged to have colored in the case of Sunday strips ).

* Gödel's Proof ( 2002 revised edition ) by Ernest Nagel and James R. Newman, edited by Hofstadter ( ISBN 0-8147-5816-9 ).

Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).

* Elusive Proof, Elusive Prover: A New Mathematical Mystery, by Dennis Overbye, New York Times, Science, August 15, 2006.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

* Proof by contrapositive

* Proof of Fermat's Last Theorem is discovered by Andrew Wiles.

* Proof by verbosity, sometimes colloquially referred to as argumentum verbosum-a rhetorical technique that tries to persuade by overwhelming those considering an argument with such a volume of material that the argument sounds plausible, superficially appears to be well-researched, and it is so laborious to untangle and check supporting facts that the argument might be allowed to slide by unchallenged.

* Proof, 1980 B / W student film by Black-and-white, expanded to Fandango

* Proof ( 1991 film ), an Australian film by Jocelyn Moorhouse

* Proof ( play ), a play by David Auburn

** Proof ( 2005 film ), a film by John Madden, based on the play