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...

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

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...

Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is the...

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

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...

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

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...

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

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

lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0. Complements...

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...

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...

non-empty finite meet semilattice has a least element and any non-empty finite join semilattice has a greatest element. (In neither case will the semilattice...

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...

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...

by showing that P has both a least element and a greatest element. Let D = {x | x ≤ f(x)} and x ∈ D (we know that at least 0L belongs to D). Then because...

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...

position of the middle element) to L {\displaystyle L} plus the floor of R − L 2 {\displaystyle {\frac {R-L}{2}}} , which is the greatest integer less than...

Phosphorus is a chemical element; it has symbol P and atomic number 15. All elemental forms of phosphorus are highly reactive and are therefore never found...

chemical element; it has symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is...

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...

ACCP is a UFD if and only if every irreducible element is prime. Any two elements of a UFD have a greatest common divisor and a least common multiple....

since passing to the opposite order relation turns the least values into the greatest, and vice versa. While priority queues are often implemented using...

mathematical field of order theory, an element a of a partially ordered set with least element 0 is an atom if 0 < a and there is no x such that 0 < x < a...

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