DiscretizationIn applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.
Partition of a setIn mathematics, a partition of a set is a grouping of its elements into non-emptysubsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.
Categorical variableIn statistics, a categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types.
LogicStudy of correct reasoningLogic studies valid forms of inference like modus ponens.Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory.
Greek languageGreek (Modern Greek: ελληνικά, romanized: elliniká; Ancient Greek: ἑλληνική, romanized: hellēnikḗ) is an Indo-European language, constituting an independent Hellenic branch within the Indo-European language family. It is native to the territories that have had populations of Greeks since antiquity: Greece, Cyprus, Egypt, Turkey, Italy (in Calabria and Salento), southern Albania, and other regions of the Balkans, Caucasus, the Black Sea coast, and the .
Conceptual modelConceptual model is any model that is the direct output of a or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience.
Dual (category theory)In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite categoryC.
Discretization errorIn numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost.
Complement (set theory)In set theory, the complement of a setA, often denoted by Ac{\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the universe, i.e. all elements under consideration, are considered to be members of a given set U, the absolute complement of A is the set of elements in U that are not in A. The relative complement of A with respect to a set B, also termed the set difference of B and A, written B∖A,{\displaystyle B\setminus A,} is the set of elements in B that are not in A. Absolute complementDefinitionIf A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined).
Set theoryBranch of mathematics that studies setsA Venn diagram illustrating the intersection of two setsSet 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 objects that are relevant to mathematics as a whole.Binary dataBinary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics.PropositionPropositions are the meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, such as the English "Snow is white" and the German "Schnee ist weiß", can have identical meaning by expressing the same proposition. Similarly, they ground the fact that different people can share a belief by being directed at the same content. True propositions describe the world as it is, while false ones fail to do so.
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