Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

Titanfall

Titanfall is a multiplayer first-person shooter video game developed by Respawn Entertainment and published by Electronic Arts. It was released for Microsoft Windows and Xbox One on March 11, 2014; an Xbox 360 version ported by Bluepoint Games was released April 8, 2014. The game was highly anticipated as the debut title from developers formerly behind the successful Call of Duty franchise.

In Titanfall, players control "pilots" and their mech-style Titans, and fight in six-on-six matches set in war-torn outer space colonies. The game is optimized for fast-paced, continual action, aided by wall-running abilities and populations of computer-controlled soldiers. Up to 50 characters can be active in a single game, and non-player activity is offloaded to Microsoft's cloud computing services to optimize local graphical performance. The game's development team began work on the title in 2011, and their Titan concept grew from a human-sized suit into a battle tank exoskeleton. The team sought to bring "scale, verticality, and story" to its multiplayer genre through elements traditionally reserved for single-player campaigns. The 65-person project took inspiration from Blade Runner, Star Wars, Abrams Battle Tank, and Masamune Shirow of Ghost in the Shell.

Watch Dogs

Watch Dogs (stylized as WATCH_DOGS) is an open world action-adventure third-person shooter stealth video game developed and published by Ubisoft. It was released worldwide on 27 May 2014 for Microsoft Windows, PlayStation 3, PlayStation 4, Xbox 360 and Xbox One, while a Wii U version was released in November 2014. Set within a fictionalized version of Chicago, Illinois, the single-player story follows a hacker and his efforts to seek revenge after the killing of his niece. The open world design lets players freely roam Chicago, which includes the urban city, open countryside, and the run-down neighborhoods that surround downtown.

The game is played from a third-person perspective and its world is navigated on-foot or by vehicle. Players control Aiden Pearce, a highly skilled grey hat hacker who can hack into the "ctOS", a centralized operating system which manages the hyper-connected city of Chicago, and formed after the Northeast blackout of 2003 was caused by a hacker. An online multiplayer mode is also provided in the game, allowing up to eight players to engage in both cooperative and competitive gameplay in a recreation of the single-player setting.

Single-player video game

A single-player video game is a video game where input from only one player is expected throughout the course of the gaming session. "Single-player game" usually refers to a game that can only be played by one person, while "single-player mode" usually refers to a particular game mode that is designed to be played by a single-player, though the game also contains modes that can be played by several players simultaneously.

The vast majority of modern console games and arcade games are designed so that they can be played by a single-player; although many of these games have modes that allow two or more players to play (not necessarily simultaneously), very few actually require more than one player for the game to be played. The Unreal Tournament series is one example of such.

History

The earliest video games, such as Tennis for Two (1958), Spacewar! (1962), and Pong (1972), were symmetrical games designed to be played by two players. Single-player games gained popularity only after this, with early titles such as Speed Race (1974) and Space Invaders (1978).