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 ).

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.

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 contrapositive

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.

* 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

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

* " Proof ", a song by Coldplay from " Speed of Sound "

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

* " 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: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Proof by contradiction is used in mathematics to construct proofs.

Proof methods that are not direct include proof by contradiction, including proof by infinite descent.

:: Sketch of proof: Proof by contradiction.

* Proof by contradiction

# REDIRECT Proof by contradiction

* Proof by contradiction

Any proof by contrapositive can also be trivially formulated in terms of a Proof by contradiction: To prove the proposition, we consider the opposite,.

* Proof by contradiction

Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s

Generally this is in a very small detail, such as the number of leaves on the ear of corn on the recent US Wisconsin state quarter: File: 2004 WI Proof. png.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

* Demonstratio evangelica ( Proof of the Gospel ) is closely connected to the Praeparatio and comprised originally twenty books of which ten have been completely preserved as well as a fragment of the fifteenth.

Proof of second property: since a * b and b * b < sup >− 1 </ sup > are defined, so is a * b * b < sup >− 1 </ sup >=

#* Proof: suppose that p is composite, hence can be written with a and Then is prime, but and contradicting statement 1.

#* Proof:, so is a square root of 2 modulo.

* In Hal Clement's short story Proof ( 1942 ), neutronium is the only form of solid matter known to Solarians, the inhabitants of the Sun's interior.

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

( Proof: either 1 is positive or − 1 is positive.

* Proof that R is uncountable

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

Proof: We only give the proof in the simplified case ; the general case is similar.

* Genealogical Proof Standard, also known as Cluster genealogy

Proof: Notice that the nim-sum (⊕) obeys the usual associative and commutative laws of addition (+), and also satisfies an additional property, x ⊕ x = 0 ( technically speaking, the nonnegative integers under ⊕ form an Abelian group of exponent 2 ).

Scotland Yard also guarded Crowe while he was promoting Proof of Life in London in February 2001.

Proof of payment is often in the form of adhesive postage stamps, but postage meters are also used for bulk mailing.

( The state is unspecified, but the county contains a tri-city conglomerate on the Mississippi between Chicago and New Orleans of Proof p. 52 ; compare the " Quad Cities " on the Mississippi, originally Davenport IA, Rock Island IL, Moline IL, and East Moline IL, but now also including Bettendorf IA.

Proof coins were also produced in 1870.

The Maskrafters have also done recent plays including Proof, The Fantasticks, Grease, and Shakespeare's The Tempest.

Most criminal cases within an adversarial system require that the prosecution proves its contentions beyond a reasonable doubt — a doctrine also called the " Burden of 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 ".

Proof by exhaustion, also known as proof by cases, perfect induction, or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases and each case is checked to see if the proposition in question holds.

Other sets, called " Prestige Proof " sets, also contain selected commemorative coins.

Proof also recorded a diss track entitled " Many Men ".

Eminem is the lead actor in 8 Mile and has had cameo appearances in several films and shows, while Proof also appears in 8 Mile as a freestyle rapper called " Lil ' Tic ".

Proof of having insurance or an exemption must also be provided to pay for the motor tax.

A third term, Proof of Mechanism, is closely related and is also described here.

Parker is also the recipient of the 2001 Tony Award for Best Actress for the Broadway play Proof.

Proof that QCD confines at low energy is a mathematical problem of great relevance, and an award has been proposed by the Clay Mathematics Institute for whoever is also able to show that the Yang – Mills theory has a mass gap and its existence.

Proof of this can be found on platform Five of Sheffield railway station, because the Sheaf also runs under that, and it also flooded at the same time.

Newman also wrote Gödel's Proof ( 1958 ) with Ernest Nagel, presenting the main results of Gödel's incompleteness theorem and the mathematical work and philosophies leading up to its discovery in a more accessible manner.

It is also referenced in numerous films, including The Color of Money, National Lampoon's Christmas Vacation, Thelma & Louise, Death Proof, Monster's Ball, Freddy Got Fingered, Out Cold, Crazy Heart, " Cookie's Fortune ", " Frankenhooker ", and Trees Lounge.