The word pawn is derived from the Latin pignus, for pledge, and the items having been pawned to the broker are themselves called pledges or pawns, or simply the collateral.

Solutions like a security token give a formal proof answer by constantly shifting password.

For the first four years uncirculated coins came in cellophane with a blue plastic token in a blue envelope, while proof issues came in a proof set-like plastic case, contained in a brown " wood grain finish " slipcase box with a gold seal in the lower left corner on the front of the slipcase.

UniOTP 500 A water proof token device from SecuTech

UniOTP 500 A water proof token device from SecuTech

UniOTP 500 A water proof token device from SecuTech

ISAW claimed the State of Oklahoma could not or would not follow through on an earlier pledge of immediate donation in fee of 300 acres of land, and was instead offering only a 200-year lease of the land and / or was demanding proof that ISAW had the funding to build the museum prior to transfer of the land.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

The original proof is based on the Taylor series expansions of the exponential function e < sup > z </ sup > ( where z is a complex number ) and of sin x and cos x for real numbers x ( see below ).

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

Both proofs used methods from complex analysis, establishing as a main step of the proof that the Riemann zeta function ζ ( s ) is non-zero for all complex values of the variable s that have the form s = 1 + it with t > 0.

Also Cantor's proof that 2 < sup > n </ sup > > n breaks down unless n is finite.

In a proof by contradiction, we start by assuming the opposite, p: that there is a smallest rational number, say, r < sub > 0 </ sub >.

* Another proof that n < sup > th </ sup > roots of integers are irrational, except for perfect nth powers by Scott E. Brodie

An equivalent proof for R < sup > n </ sup > starts with the summation below.

In 1993, ILM visual effects specialist John Knoll created a proof of concept test of dogfighting X-wings and TIE fighters to demonstrate the feasibility of using commercially-available desktop computer software for simple animation work .< ref name = Homing145 >

Nash's proof of the C < sup > k </ sup >- case was later extrapolated into the h-principle and Nash – Moser implicit function theorem.

Cantor's original proof considers an infinite sequence S of the form ( s < sub > 1 </ sub >, s < sub > 2 </ sub >, s < sub > 3 </ sub >, ...) where each element s < sub > i </ sub > is an infinite sequence of 1s or 0s.

Whether you experienced the passion of desire I have, of course, no way of knowing, nor indeed have I wished with even the most fleeting fragment of a wish to know, for the fact that one constitutes by one's mere existence so to speak the proof of some sort of passion makes any speculation upon this part of one's parents' experience more immodest, more scandalizing, more deeply unwelcome than an obscenity from a stranger.

Both Alfred Harcourt and Donald Brace had written him enthusiastic praise of Elmer Gantry ( any changes could be made in proof, which was already coming from the printer ) and they had ordered 140,000 copies -- the largest first printing of any book in history.

It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

Among his major accomplishments were the 1940 proof, of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result ( from 1942 to 1946, most intensively ).

Paul Beekman Taylor used the Ynglingasaga as proof that the Beowulf poet was likewise working from Germanic tradition.

The burden of proof should be on the people who make these statements, to show where they got their information from, to see if their conclusions and interpretations are valid, and if they have left anything out.

In the course of the proof, he made use of a lemma that from any countable cover of the interval by smaller open intervals, it was possible to select a finite number of these that also covered it.

Eventually, complete proof came from chromosome maps in Morgan's own lab.

As an example of a conditional proof in symbolic logic, suppose we want to prove A → C ( if A, then C ) from the first two premises below:

More recently, both Elms and librarian Lee Weinstein have gathered circumstantial evidence to support the case for Linebarger's being " Allen ," but both concede there is no direct proof that Linebarger was ever a patient of Lindner's or that he suffered from a disorder similar to that of " Kirk Allen.

The rule makes it possible to eliminate a disjunction from a logical proof.

At the last moment, when his immense work was drawing to an end, he encountered a crowning mortification: he discovered that the bookseller, fearing the government's displeasure, had struck out from the proof sheets, after they had left Diderot's hands, all passages that he considered too dangerous.

In propositional logic, disjunction elimination ( sometimes named proof by cases or case analysis ), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

A proof from Euclid's elements that, given a line segment, an equilateral triangle exists that includes the segment as one of its sides.

* Axiomatic proof: Proofs are deductive derivations of propositions from primitive premises that are ‘ true ’ in some sense.

* Analytic proof: Proofs are non-deductive derivations of hypotheses from problems.

The imaginary company had produced a proof of the Riemann Hypothesis but then had great difficulties collecting royalties from mathematicians who had proved results assuming the Riemann Hypothesis.

* Fermat's Last Theorem Blog: Unique Factorization, A blog that covers the history of Fermat's Last Theorem from Diophantus of Alexandria to the proof by Andrew Wiles.

He asked Cantor to withdraw the paper from Acta while it was in proof, writing that it was "... about one hundred years too soon.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

Despite multiple parliamentary questions from as early as 2005, where it was stated that there was no proof that this was happening, Minister Ahern announced a ban on all handguns in November 2008.

The following lemma, which Gödel adapted from Skolem's proof of the Löwenheim-Skolem theorem, lets us sharply reduce the complexity of the generic formula for which we need to prove the theorem:

He tied this interest into his racist philosophy, looking for proof of Aryan and Nordic racial superiority from ancient times.