Schauder basisIn mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This makes Schauder bases more suitable for the analysis of infinite-dimensional topological vector spaces including Banach spaces. Schauder bases were described by Juliusz Schauder in 1927, although such bases were discussed earlier.
Infinite setIn set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite. It is the only set that is directly required by the axioms to be infinite. The existence of any other infinite set can be proved in Zermelo–Fraenkel set theory (ZFC), but only by showing that it follows from the existence of the natural numbers.
Letter caseLetter case is the distinction between the letters that are in larger uppercase or capitals (or more formally majuscule) and smaller lowercase (or more formally minuscule) in the written representation of certain languages. The writing systems that distinguish between the upper- and lowercase have two parallel sets of letters: each in the majuscule set has a counterpart in the minuscule set. Some counterpart letters have the same shape, and differ only in size (e.g. {C,c} or {S,s}), but for others the shapes are different (e.
Camel caseCamel case (sometimes stylized as camelCase or CamelCase, also known as camel caps or more formally as medial capitals) is the practice of writing phrases without spaces or punctuation and with capitalized words. The format indicates the first word starting with either case, then the following words having an initial uppercase letter. Common examples include "YouTube", "iPhone" and "eBay". Camel case is often used as a naming convention in computer programming.
Dedekind-infinite setIn mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists). Proposed by Dedekind in 1888, Dedekind-infiniteness was the first definition of "infinite" that did not rely on the definition of the natural numbers.
Social equalitySocial equality is a state of affairs in which all individuals within a specific society have equal rights, liberties, and status, possibly including civil rights, freedom of expression, autonomy, and equal access to certain public goods and social services. Social equality requires the absence of legally enforced social class or caste boundaries and the absence of discrimination motivated by an inalienable part of an individual's identity.
Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
Künneth theoremIn mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of two objects to the homology of their product. The classical statement of the Künneth theorem relates the singular homology of two topological spaces X and Y and their product space . In the simplest possible case the relationship is that of a tensor product, but for applications it is very often necessary to apply certain tools of homological algebra to express the answer.
Minkowski–Bouligand dimensionIn fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand. To calculate this dimension for a fractal , imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set.
ContinuationIn computer science, a continuation is an abstract representation of the control state of a computer program. A continuation implements (reifies) the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process's execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment. Continuations are useful for encoding other control mechanisms in programming languages such as exceptions, generators, coroutines, and so on.
Equality before the lawEquality before the law, also known as equality under the law, equality in the eyes of the law, legal equality, or legal egalitarianism, is the principle that all people must be equally protected by the law. The principle requires a systematic rule of law that observes due process to provide equal justice, and requires equal protection ensuring that no individual nor group of individuals be privileged over others by the law. Sometimes called the principle of isonomy, it arises from various philosophical questions concerning equality, fairness and justice.
Spectral sequenceIn homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra. Motivated by problems in algebraic topology, Jean Leray introduced the notion of a sheaf and found himself faced with the problem of computing sheaf cohomology.
