GenerationA generation refers to all of the people born and living at about the same time, regarded collectively. It can also be described as, "the average period, generally considered to be about 20–30 years, during which children are born and grow up, become adults, and begin to have children." In kinship terminology, it is a structural term designating the parent-child relationship. It is known as biogenesis, reproduction, or procreation in the biological sciences.
Irrational numberIn mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
Greatest GenerationThe Greatest Generation, also known as the G.I. Generation and the World War II generation, is the Western demographic cohort following the Lost Generation and preceding the Silent Generation. The generation is generally defined as people born from 1901 to 1927. They were shaped by the Great Depression and were the primary generation composing the enlisted forces in World War II. Most people of the Greatest Generation are the parents of the Silent Generation and Baby Boomers, and, in turn, were the children of the Lost Generation.
Generation ZGeneration Z (often shortened to Gen Z), colloquially known as zoomers, is the demographic cohort succeeding Millennials and preceding Generation Alpha. Researchers and popular media use the mid-to-late 1990s as starting birth years and the early 2010s as ending birth years. Most members of Generation Z are children of Generation X or younger Baby Boomers. The older members may be the parents of the younger members of Generation Alpha.
Silent GenerationThe Silent Generation, also known as the Traditionalist Generation, is the Western demographic cohort following the Greatest Generation and preceding the baby boomers. The generation is generally defined as people born from 1928 to 1945. By this definition and U.S. Census data, there were 23 million Silents in the United States as of 2019. In the United States, the Great Depression of the 1930s and World War II in the early-to-mid 1940s caused people to have fewer children and as a result, the generation is comparatively small.
Scheme (mathematics)In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
Generation XGeneration X (often shortened to Gen X) is the demographic cohort following the baby boomers and preceding the millennials. Researchers and popular media use the mid-to-late 1960s as starting birth years and the late 1970s to early 1980s as ending birth years, with the generation being generally defined as people born from 1965 to 1980. By this definition and U.S. Census data, there are 65.2 million Gen Xers in the United States as of 2019.
Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
Singularity (mathematics)In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the function has a singularity at , where the value of the function is not defined, as involving a division by zero. The absolute value function also has a singularity at , since it is not differentiable there. The algebraic curve defined by in the coordinate system has a singularity (called a cusp) at .
Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Quadratic irrational numberIn mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their least common denominator, a quadratic irrational is an irrational root of some quadratic equation with integer coefficients.
Singularity theoryIn mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string.
Locally compact spaceIn topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; they are abbreviated as LCH spaces. Let X be a topological space. Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.
Fiber product of schemesIn mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The of schemes is a broad setting for algebraic geometry.
Proof that π is irrationalIn the 1760s, Johann Heinrich Lambert was the first to prove that the number pi is irrational, meaning it cannot be expressed as a fraction , where and are both integers. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. Many of these are proofs by contradiction.
Time zoneA time zone is an area which observes a uniform standard time for legal, commercial and social purposes. Time zones tend to follow the boundaries between countries and their subdivisions instead of strictly following longitude, because it is convenient for areas in frequent communication to keep the same time. All time zones are defined as offsets from Coordinated Universal Time (UTC), ranging from UTC−12:00 to UTC+14:00. The offsets are usually a whole number of hours, but a few zones are offset by an additional 30 or 45 minutes, such as in India, South Australia and Nepal.
Σ-compact spaceIn mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces. A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact. That terminology can be somewhat confusing as it does not fit the usual pattern of σ-(property) meaning a countable union of spaces satisfying (property); that's why such spaces are more commonly referred to explicitly as σ-compact (weakly) locally compact, which is also equivalent to being exhaustible by compact sets.
Morphism of schemesIn algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism in the category of schemes. A morphism of algebraic stacks generalizes a morphism of schemes. By definition, a morphism of schemes is just a morphism of locally ringed spaces. A scheme, by definition, has open affine charts and thus a morphism of schemes can also be described in terms of such charts (compare the definition of morphism of varieties).
