Equivalence relationY indicates that the column's property is always true for the row's term (at the very left), while ✗ indicates that the property is not guaranteedin general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric,is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively.
Transitive relationIn mathematics, a binary relationR on a setX is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive.
Binary relationY indicates that the column's property is always true for the row's term (at the very left), while ✗ indicates that the property is not guaranteedin general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric,is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
Equality (mathematics)Basic notion of sameness in mathematicsThe equals sign, used to represent equality symbolically in an equationIn mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. Equality between A and B is denoted with an equals sign as A = B, and read "A equals B". A written expression of equality is called an equation or identity depending on the context.Symmetric relationA symmetric relation is a type of binary relation. A homogeneous relation R {\displaystyle R} on a set X {\displaystyle X} is symmetric if: for all a {\displaystyle a} and b {\displaystyle b} in X {\displaystyle X} , a R b {\displaystyle aRb} if and only if b R a {\displaystyle bRa} , where the notation a R b {\displaystyle aRb} means that the ordered pair ( a , b ) {\displaystyle (a,b)} is in the relation R {\displaystyle R} .
Set (mathematics)In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.
ReflexIn biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a stimulus. Reflexes are found with varying levels of complexity in organisms with a nervous system. A reflex occurs via neural pathways in the nervous system called reflex arcs. A stimulus initiates a neural signal, which is carried to a synapse. The signal is then transferred across the synapse to a motor neuron, which evokes a target response.
Classical LatinClassical Latin is the form of Latin recognized as a literarystandard by writers of the late Roman Republic and early Roman Empire. It developed around 75 BC from Old Latin, and developed by the 3rd century AD into Late Latin. In some later periods, the former was regarded as good or proper Latin, while the latter was seen as debased, degenerate, or corrupted.
Medieval LatinMedieval Latin was the form of Literary Latin used in Roman CatholicWestern Europe during the Middle Ages. It was also the administrative language in the former Roman Provinces of Mauretania, Numidia and Africa Proconsularis under the Vandals, the Byzantines and the Romano-Berber Kingdoms, until it declined after the Arab Conquest.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
Early Modern EnglishEarly Modern English (sometimes abbreviated EModE or EMnE), also known as Early New English (ENE), and colloquially Shakespeare's English, Shakespearean English, or King James' English, is the stage of the English language from the beginning of the Tudor period to the English Interregnum and Restoration, or from the transition from Middle English, in the late 15th century, to the transition to Modern English, in the mid-to-late 17th century.*As an Amazon Associate I earn from qualifying purchases.