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

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 ).

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.

A more successful effort was the Standard Proof for Pythagoras ' Theorem, that replaced the more than 100 incompatible existing proofs.

Lessing outlined the concept of the religious " Proof of Power ": How can miracles continue to be used as a base for Christianity when we have no proof of miracles?

For the role, Crowe won an Australian Film Institute ( AFI ) award for Best Actor, following up from his Best Supporting Actor award for Proof in 1991.

The U. S. Mint began producing silver quarters again in 1992 for inclusion in the annual Silver Proof set.

*** Washington Bicentennial 1975 – 1976 ( all were dated 1776 – 1976 ) ( 40 % Silver-clad Proof, not intended for circulation )

Proposed state quarter design for the state of Utah ( though not: File: 2007 UT Proof Rev. png | the one that was eventually minted )

Proof of this must be supplied with one's application for naturalisation.

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

Note that the relationships above are only valid for the form of the Fourier transform shown in the Proof section below.

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

This informal analysis can be formalized to make a rigorous proof of the incompleteness theorem, as described in the section " Proof sketch for the first theorem " below.

* Proof ( truth ), sufficient evidence or argument for the truth of a proposition

* Proof coinage, coins once made as a test, but now specially struck for collectors

* Proof test, for a firearm

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.

In the shortest of them ( 43 pages as of 2009 ), which he titles " Apology for the Proof of the Riemann Hypothesis " ( using the word " apology " in the rarely used sense of apologia ), he claims to use his tools on the theory of Hilbert spaces of entire functions to prove the Riemann Hypothesis for Dirichlet L-functions ( thus proving GRH ) and a similar statement for the Euler zeta function, and even to be able to assert that zeros are simple.

TenNapel did the cover art for several of Five Iron Frenzy's albums, including a sculpture for their live album, Proof That the Youth Are Revolting.

* Proof of the existence of a bijection at cut-the-knot

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.

However, subsequent episodes such as season three's " Proof Positive " show that McGee's real intentions lie much deeper than this, and that his main motive is purely to understand this fascinating creature ( to whom his references as the Hulk are not shared by other characters ) for himself, for his amazement at the existence of such a remarkable creature has caused him to become totally obsessed with the Hulk to the extent that it has ruined his personal life ; the Hulk is permanently on his mind, and his annoyance over his lack of success in catching the Hulk is exacerbated by other people's refusal even to believe that the Hulk actually exists — not even his own colleagues at the National Register take the story seriously, and they view him as a laughing stock for believing that the Hulk is real.

Some of them made the existence of the DJ without the MC possible. This chapter also features the DJ Marz, DJ Eddie Def, DJ Cue, DJ Quest ( Bullet Proof Space Travelors ), Billy Jam, Dave Paul, DJ Relm, DJ Flare, DJ Shadow, Apollo, Rob Swift ( X-ecutioners ),

Proof of the verse's existence is preserved within tradition ( i. e through a hadith report ) as well as in the Fiqh.

As such, this was also a rejection of the Ontological Proof of God's existence and also Hegel's Absolute idealism, with its Absolute Spirit.

Becker's Postulate later played a role in the formalization given, by Charles Hartshorne, the American process theologian, of the Ontological Proof of God's existence, stimulated by conversations with the logical positivist and opponent of the alleged proof, Rudolf Carnap.

Proof of the existence of traveling wave solutions and analysis of their properties is often done by the phase space method.

: Proof of the existence of linear differential equations having a prescribed monodromic group

Proof for this comes from the writing, Mahapurana ( also known as Uttara Purana ), by Gunabhadra in which the author states " blissful for the world is the existence of Jinasenacharya, by bowing to whom Amoghavarsha Nrupathunga considered himself to be purified ".

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.

" The Accusation " states a common criticism of Israel, " The Accusers " lists several quotations from critics supporting the accusation, " The Reality " contains a short statement contradicting the accusation, and " The Proof " contains Dershowitz's explanation of his viewpoint.

Proof: Suppose the product of two primitive polynomials f ( x ) and g ( x ) is not primitive, so there exists a prime number p that is a common divisor of all the coefficients of the product.

Many famous or successful rappers were once featured, including The Notorious B. I. G., Eminem, DMX, 50 Cent, Immortal Technique, Common, Mobb Deep ( appearing as Poetical Prophets ), Bishop Lamont, Ya Boy, Joell Ortiz, Lil Flip, Streetz-n-Young Deuces, DJ Shadow, Percee-P, Rasco, Proof, German Shepard Shepherd, Pitbull, Jay-Z & D12, and Tef Poe.

" Oakley blamed this on lazy writing, and added that " Proof of this comes when, on more than once occasion, the scripts include get-out clauses for the ridiculous storylines being churned out.

* Genealogical Proof Standard, also known as Cluster genealogy

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

In 1917 Proof Garden for Technical Plantation () was established by Gerrit van Iterson, which today is known as Botanical Garden of TU Delft.

* David Auburn-Playwright and screenplay writer, best known for his award winning play ( and adapted screenplay ) for Proof.

In 1899, Henry Gottlieb Eckstein developed the " waxed sealed package " for freshness, known then as the " Eckstein Triple Proof Package ," a dust, germ and moisture-proof paper package.

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.

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.

He is best known for his 2000 play Proof, which won the 2001 Tony Award for Best Play, as well as the 2001 Pulitzer Prize for Drama.

DeShaun Dupree Holton ( October 2, 1973 – April 11, 2006 ), better known by his stage name Proof, was an American rapper and actor from Detroit, Michigan.

Originally known as Maximum, under the moniker " Proof ", Holton first rose to national prominence as a part of the rap group D12, a hip-hop group he was instrumental in forming.

She is best known for her roles in Rent, Cold Case, The Devil Wears Prada, Death Proof, and the short-lived Fox television series Wonderfalls.

He is best known for his television roles as Detective Peter Baker on the soap opera Home and Away ( 2004 – 07 ) and as Peter Dunlop on the ABC medical drama Body of Proof ( 2011-2012 ).