Projectively extended real lineIn real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real numbers, , by a point denoted ∞. It is thus the set with the standard arithmetic operations extended where possible, and is sometimes denoted by or The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.
Real closed fieldIn mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers. A real closed field is a field F in which any of the following equivalent conditions is true: F is elementarily equivalent to the real numbers. In other words, it has the same first-order properties as the reals: any sentence in the first-order language of fields is true in F if and only if it is true in the reals.
Foundations of geometryFoundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view.
Algebraic numberAn algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x^2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number is algebraic because it is a root of x^4 + 4. All integers and rational numbers are algebraic, as are all roots of integers.
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.
Parental leaveParental leave, or family leave, is an employee benefit available in almost all countries. The term "parental leave" may include maternity, paternity, and adoption leave; or may be used distinctively from "maternity leave" and "paternity leave" to describe separate family leave available to either parent to care for small children. In some countries and jurisdictions, "family leave" also includes leave provided to care for ill family members. Often, the minimum benefits and eligibility requirements are stipulated by law.
End userIn product development, an end user (sometimes end-user) is a person who ultimately uses or is intended to ultimately use a product. The end user stands in contrast to users who support or maintain the product, such as sysops, system administrators, database administrators, Information technology (IT) experts, software professionals and computer technicians. End users typically do not possess the technical understanding or skill of the product designers, a fact easily overlooked and forgotten by designers: leading to features creating low customer satisfaction.
End-to-end principleThe end-to-end principle is a design framework in computer networking. In networks designed according to this principle, guaranteeing certain application-specific features, such as reliability and security, requires that they reside in the communicating end nodes of the network. Intermediary nodes, such as gateways and routers, that exist to establish the network, may implement these to improve efficiency but cannot guarantee end-to-end correctness.
End groupEnd groups are an important aspect of polymer synthesis and characterization. In polymer chemistry, they are functional groups that are at the very ends of a macromolecule or oligomer (IUPAC). In polymer synthesis, like condensation polymerization and free-radical types of polymerization, end-groups are commonly used and can be analyzed by nuclear magnetic resonance (NMR) to determine the average length of the polymer. Other methods for characterization of polymers where end-groups are used are mass spectrometry and vibrational spectrometry, like infrared and raman spectroscopy.
End-to-end encryptionEnd-to-end encryption (E2EE) is a private communication system in which only communicating users can participate. As such, no one, including the communication system provider, telecom providers, Internet providers or malicious actors, can access the cryptographic keys needed to converse. End-to-end encryption is intended to prevent data being read or secretly modified, other than by the true sender and recipient(s). The messages are encrypted by the sender but the third party does not have a means to decrypt them, and stores them encrypted.
