Euclid frequently used the method of proof by contradiction, and therefore the traditional presentation of Euclidean geometry assumes classical logic, in which every proposition is either true or false, i. e., for any proposition P, the proposition " P or not P " is automatically true.

The most commonly used of these provisions are the first and second, prohibiting the presentation of false claims to the government and making false records to get a false claim paid.

After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations.

This presentation may be accurate or not — that is, it can give either a true or a false account of the subject in question — however, it is generally assumed that authors of such accounts believe them to be truthful at the time of their composition or, at least, pose them to their audience as historically or empirically true.

In the 2005 season the fans were again making a difference in games and were recognized with the presentation of a special game ball for their efforts in a game against the New York Giants, a game in which the Giants committed 11 false start penalties in large part because of the crowd noise.

* January 25 Jeffrey Skilling makes false presentation to investors.

Official media coverage of the Zhanfan's presentation focused on his call to avoid " fake news and false reports ( 失实报道 )" but also incorporated the " mouthpiece " comment.

Although much of his work has been proven to be insufficient and some even as false, the presentation of localized regions of function within the brain presented a new idea that the brain was more complex than previously imagined.

These segments, though carefully disclaimed after concerns were brought up about the original program model of Daytime, are designed to give a business a detailed presentation of their service that might not be possible in a traditional thirty-second or one minute ad, or a declining form of advertising where a special sale for a certain time period with a sales pitch is offered within the false setting of a phone bank or telethon.

Species of fraudulence begin with the ascription of the various biographies to different invented ' authors ', and continue with the dedicatory epistles to Diocletian and Constantine, the quotation of fabricated documents, the citation of non-existent authorities, the invention of persons ( extending even to the subjects of some of the minor biographies ), presentation of contradictory information to confuse an issue while making a show of objectivity, deliberately false statements, and the inclusion of material which can be shown to relate to events or personages of the late 4th century rather than the period supposedly being written about.

* Omission: The presentation of some facts but not all the facts may lead to false and biased conclusions.

" if it contains false information and is therefore untruthful ... or if it or its overall presentation in any way deceives or is likely to deceive the average consumer ... even if the information is factually correct "

The presentation, titled Unusual Car Navigation Tricks, raised the point that RDS-TMC is a wireless cleartext protocol and showed how to build a receiver and transmitter with cheap electronics, capable of injecting false and potentially dangerous messages.

Many American television shows ( most notably South Park and The Daily Show with Jon Stewart ) have parodied this campaign as laughably hyperbolic, unnecessarily violent, and its ironic presentation of a false choice.

* Also citizens involved in the false presentation of slavery for benefit could become slaves.

Byng had not been Meighan's first choice for presentation to the King, since he preferred someone with more civilian credentials.

Consumers have a broad choice whether they receive a general feed of the most " important " information of the day or a highly customized presentation of a single type of content.

) Henkin's 1949 proof is much easier to survey than Gödel's and has thus become the standard choice of completeness proof for presentation in introductory classes and texts.

* Specifying the architecture at a finer level including the choice of presentation layer technology, business logic layer technology, persistence technology and persistence mapping technology ( e. g. object-relational mapper ).

Although The Raft of the Medusa retains elements of the traditions of history painting, in both its choice of subject matter and its dramatic presentation, it represents a break from the calm and order of the then-prevailing Neoclassical school.

If the number of generators, r, is less than or equal to the number of relations, s, then we consider the ideal generated by all r by r minors of the matrix ; this is the zero ' th Fitting ideal or Alexander ideal and does not depend on choice of presentation matrix.

One may forget the cell complex structure and look only at the underlying topological space ( the manifold ) – as different cell complexes give the same underlying manifold, one may ask if the function is independent of choice of presentation, in which case it is an intrinsically defined invariant.

This is the case for the Euler characteristic, and a general method for defining and computing invariants is to define them for a given presentation and then show that they are independent of the choice of presentation.

Applications consist of three parts: an interview with four to five members of the Society, a presentation on a topic of the applicant's choice to a General Meeting of the Society, and a submission of creative or critical value.

Upon his presentation in 1977, he said: " Playing for Real Madrid is like touching the sky, Real Madrid has always been my first choice as a team and Madrid has always been my favorite as a city ".

GameSpot, in electing FreeSpace 2 as one of the " Greatest Games of All Time ", pointed out that while most of the game's features could be found in its predecessor or peers, its " sheer quality of presentation and gameplay " was the key reason for their choice.

The choice of imaging depends on the clinical presentation ( history, symptoms and examination findings ).

TOK requires 100 hours of instruction, the completion of an externally assessed essay of 1, 200 – 1, 600 words ( from a choice of ten titles prescribed by the IB ), and an internally assessed presentation on the candidate's chosen topic.

The choice of symbols and aspects of their presentation, such as size and background, depend on an individual's preferences as well as their linguistic, visual, and cognitive skills.

Aerial acrobatics are common in a presentation roda, while not seen as often in a more serious one.

It has become generally accepted that certain sayings in John are as old or older than their synoptic counterparts, that John's knowledge of things around Jerusalem is often superior to the synoptics, and that his presentation of Jesus ' agony in the garden and the prior meeting held by the Jewish authorities are possibly more historically accurate than their synoptic parallels.

From scientific journals to news reporting, the presentation of opinion and facts is often improved with graphics and thoughtful compositions of visual information-known as information design.

In software engineering, multi-tier architecture ( often referred to as n-tier architecture ) is a client – server architecture in which presentation, application processing, and data management functions are logically separated.

" Other remarkable differences between the presentation of adult optic neuritis as compared to pediatric cases include more often unilateral optic neuritis in adults, while children much predominantly present with bilateral involvement.

In RA, the joints are often affected in a fairly symmetrical fashion, although this is not specific, and the initial presentation may be asymmetrical.

Film speed is often a vexed issue among scholars and film buffs in the presentation of silents today, especially when it comes to DVD releases of restored films ; the 2002 restoration of Metropolis ( Germany, 1927 ) may be the most fiercely debated example.

As an adult he was fond of science fiction movies, but often lamented their mediocrity ( not just in their presentation of science, but in their storytelling as well ).

Signs and symptoms of temporomandibular joint disorder vary in their presentation and can be very complex, but are often simple.

Other ceremonies sometimes associated with the Westminster system include an annual Speech from the Throne ( or equivalent ) in which the Head of State gives a special address ( written by the government ) to parliament about what kind of policies to expect in the coming year, and lengthy State Opening of Parliament ceremonies that often involve the presentation of a large ceremonial mace.

Its popularity is often attributed to its ease of cultivation — the grapes have thick skins and the vines are hardy and resistant to rot and frost — and to its consistent presentation of structure and flavours which express the typical character (" typicity ") of the variety.

The specific presentation of content on these sites is unique, but is merely an amalgamation of content taken from other sources, often without permission.

Regardless of presentation, tonkatsu is most commonly eaten with a type of thick Japanese Worcestershire sauce that uses pureed apples as a principal ingredient and is called tonkatsu sauce ( tonkatsu sōsu ) () or simply sōsu ( sauce ), and often with a bit of spicy yellow karashi ( Japanese mustard ) and perhaps a slice of lemon.

While traditional public relations may also rely on creative presentation of the facts, " spin " often, though not always, implies disingenuous, deceptive and / or highly manipulative tactics.

Always a poet, and usually gay, fresh, and delicate, in his presentation of idylls exquisitely dainty and characteristically Gallic, illustrating the more " charming " side of love, often pure and sometimes extremely materialistic.

The inception of the term in the 1960s referred to a strict and focused practice of idea-based art that often defied traditional visual criteria associated with the visual arts in its presentation as text.

Lectures, on the other hand, are often geared more towards factual presentation than connective learning.

Thus although polymyositis is more or less tissue specific in presentation, it may be included in this group because the autoantigens are often ubiquitous t-RNA synthetases.

The clinical underpinnings of two of the most common spasticity conditions, spastic diplegia and multiple sclerosis, can be described as follows: in spastic diplegia, the upper motor neuron lesion arises often as a result of neonatal asphyxia, while in conditions like multiple sclerosis, spasticity is thought by some to be as a result of the autoimmune destruction of the myelin sheaths around nerve endings — which in turn can mimic the gamma amino butyric acid deficiencies present in the damaged nerves of spastic diplegics, leading to roughly the same presentation of spasticity, but which clinically is fundamentally different from the latter.

Every group has a presentation, and in fact many different presentations ; a presentation is often the most compact way of describing the structure of the group.

" Similarly the Encyclopædia Britannica Online, while agreeing that these terms are " often used interchangeably ," suggests, that " while an interior monologue may mirror all the half thoughts, impressions, and associations that impinge upon the character ’ s consciousness, it may also be restricted to an organized presentation of that character ’ s rational thoughts ".< ref >" interior monologue.

The parties often include a 15-30 minute presentation on fire safety.

The core premise of the show allowed for tremendous variety in presentation, but unlike Monty Python, which often would cut from one sketch to another without any resolution, the SCTV format required television style bridges.