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.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Empty setIn mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
Polyethylene terephthalatePolyethylene terephthalate (or poly(ethylene terephthalate), PET, PETE, or the obsolete PETP or PET-P), is the most common thermoplastic polymer resin of the polyester family and is used in fibres for clothing, containers for liquids and foods, and thermoforming for manufacturing, and in combination with glass fibre for engineering resins. In 2016, annual production of PET was 56 million tons. The biggest application is in fibres (in excess of 60%), with bottle production accounting for about 30% of global demand.
Aluminium recyclingAluminium recycling is the process by which scrap aluminium can be reused in products after its initial production. The process involves simply re-melting the metal, which is far less expensive and energy-intensive than creating new aluminium (Recycled Aluminum-Secondary Aluminium) through the electrolysis of aluminium oxide (), which must first be mined from bauxite ore and then refined into aluminium oxide using the Bayer process and then refined again into aluminium metal using the Hall–Héroult process.
ZabbaleenThe Zabbaleen (زبالين Zabbalīn, zæbbæˈliːn) is a word which literally means "garbage people" in Egyptian Arabic. The contemporary use of the word in Egyptian Arabic is to mean "garbage collectors". In cultural contexts, the word refers to teenagers and adults who have served as Cairo's informal garbage collectors since approximately the 1940s. The Zabbaleen (singular: زبال Zabbāl, zæbˈbæːl) are also known as Zarraba (singular: Zarrab), which means "pig-pen operators.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Value chainA value chain is a progression of activities that a firm operating in a specific industry performs in order to deliver a valuable product (i.e., good and/or service) to the end customer. The concept comes through business management and was first described by Michael Porter in his 1985 best-seller, Competitive Advantage: Creating and Sustaining Superior Performance. The idea of the value chain is based on the process view of organizations, the idea of seeing a manufacturing (or service) organization as a system, made up of subsystems each with inputs, transformation processes and outputs.
EgyptEgypt (مصر ALA mɑsʕr), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and the Sinai Peninsula in the southwest corner of Asia. It is bordered by the Mediterranean Sea to the north, the Gaza Strip of Palestine and Israel to the northeast, the Red Sea to the east, Sudan to the south, and Libya to the west. The Gulf of Aqaba in the northeast separates Egypt from Jordan and Saudi Arabia.
