Zermelo set theoryZermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory (NBG). It bears certain differences from its descendants, which are not always understood, and are frequently misquoted. This article sets out the original axioms, with the original text (translated into English) and original numbering.
Graphical widgetA graphical widget (also graphical control element or control) in a graphical user interface is an element of interaction, such as a button or a scroll bar. Controls are software components that a computer user interacts with through direct manipulation to read or edit information about an application. User interface libraries such as Windows Presentation Foundation, Qt, GTK, and Cocoa, contain a collection of controls and the logic to render these.
Lorentz transformationIn physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.
Graphical user interfaceThe graphical user interface, or GUI (ˌdʒi:juːˈaɪ or ˈɡu:i ), is a form of user interface that allows users to interact with electronic devices through graphical icons and audio indicators such as primary notation, instead of text-based UIs, typed command labels or text navigation. GUIs were introduced in reaction to the perceived steep learning curve of command-line interfaces (CLIs), which require commands to be typed on a computer keyboard. The actions in a GUI are usually performed through direct manipulation of the graphical elements.
Galilean transformationIn physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Competitive equilibriumCompetitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium, introduced by Kenneth Arrow and Gérard Debreu in 1951, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Empty setIn mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
