greatest element and it can have at most one least element. Whenever a greatest element of S {\displaystyle S} exists and is unique then this element...

other element in S {\displaystyle S} . The notions of maximal and minimal elements are weaker than those of greatest element and least element which are...

P} is the greatest element in P {\displaystyle P} that is less than or equal to each element of S , {\displaystyle S,} if such an element exists. If...

mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied...

first to use the term "element (στοιχεῖον, stoicheîon)" in reference to air, fire, earth, and water. The ancient Greek word for element, stoicheion (from stoicheo...

several notions of "greatest" and "least" element in a poset P , {\displaystyle P,} notably: Greatest element and least element: An element g ∈ P {\displaystyle...

inclusion, is a lattice. The greatest element of Sub(A) is the set A itself. For any S, T in Sub(A), the greatest lower bound of S and T is the set theoretic...

triangles and contains the least volume with the greatest surface area. This also makes fire the element with the smallest number of sides, and Plato regarded...

orders play an important role in PCF theory. Greatest element and least element Infimum and supremum Maximal and minimal elements Schaefer, Helmut H.; Wolff...

An Alu element is a short stretch of DNA originally characterized by the action of the Arthrobacter luteus (Alu) restriction endonuclease. Alu elements...

Mercury is a chemical element; it has symbol Hg and atomic number 80. It is also known as quicksilver and was formerly named hydrargyrum (/haɪˈdrɑːrdʒərəm/...

In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically...

chemical element; it has symbol Sg and atomic number 106. It is named after the American nuclear chemist Glenn T. Seaborg. As a synthetic element, it can...

meet and joins exist. Bounded lattice: a lattice with a greatest element and least element. Distributive lattice: a lattice in which each of meet and join...

well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater...

m} (the position of the middle element) to the floor of L + R 2 {\displaystyle {\frac {L+R}{2}}} , which is the greatest integer less than or equal to...

the greatest magnetic penetration depth of any element. In addition, it is one of the three elemental Type II superconductors, along with vanadium and technetium...

Radon is a chemical element; it has symbol Rn and atomic number 86. It is a radioactive noble gas and is colorless and odorless. Of the three naturally...

numbers. If S has exactly one element, then its only element is a least upper bound. So consider S with more than one element, and suppose that S has an upper...

a greatest element (also called maximum, or top element, and denoted by 1 , {\displaystyle 1,} or by ⊤ {\displaystyle \top } ) and a least element (also...

Iodine is a chemical element; it has symbol I and atomic number 53. The heaviest of the stable halogens, it exists at standard conditions as a semi-lustrous...

mathematics: the greatest element and least element of a partially ordered set This disambiguation page lists articles associated with the title Top and bottom...

Phosphorus is a chemical element; it has symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but...

distributive lattice with least element 0 and greatest element 1, in which every element x has a complement ¬x, such that x ∧ ¬x = 0 and x ∨ ¬x = 1. Bounded...

tennessine, and oganesson" accessed 27 August 2016. Iyengar G. V. 1998, "Reevaluation of the trace element content in Reference Man", Radiation Physics and Chemistry...

set of elements has a least upper bound (their "join") and a greatest lower bound (their "meet"), so that it forms a lattice, and more specifically (for...

numbers into two sets A and B, such that each element of A is less than every element of B, and A contains no greatest element. The set B may or may not...

and have the property that every set of ordinals has a least or "smallest" element (this is needed for giving a meaning to "the least unused element")...

Iridium is a chemical element; it has symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is...

a top are called unital or topped. An order that has both a least and a greatest element is bounded. However, this should not be confused with the notion...