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...

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...

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...

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...

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

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

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

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

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...

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...

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...

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...

is a chemical element; it has symbol Pu and atomic number 94. It is a silvery-gray actinide metal that tarnishes when exposed to air, and forms a dull...

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...

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...

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...

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...

element; it has symbol Pb (from Latin plumbum) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable...

numbers ordered by divisibility. Its least element is 1, which divides all natural numbers, while its greatest element is 0, which is divisible by all natural...

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...

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...

sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist...