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One of the most important differences between a greatest element and a maximal element of a preordered set (,) has to do with what elements they are comparable to. Two elements x , y ∈ P {\displaystyle x,y\in P} are said to be comparable if x ≤ y {\displaystyle x\leq y} or y ≤ x {\displaystyle y\leq x} ; they are called incomparable if ...
In a directed set, every pair of elements (particularly pairs of incomparable elements) has a common upper bound within the set. If a directed set has a maximal element, it is also its greatest element, [proof 7] and hence its only maximal element. For a directed set without maximal or greatest elements, see examples 1 and 2 above.
Likewise, a greatest element of a partially ordered set (poset) is an upper bound of the set which is contained within the set, whereas the maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A), then m = b. Any least element or greatest element of a poset is unique, but a poset can have several minimal or ...
In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. [1] They are basic summary statistics , used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot .
Tidal range is the difference in height between high tide and low tide. Tides are the rise and fall of sea levels caused by gravitational forces exerted by the Moon and Sun, by Earth's rotation and by centrifugal force caused by Earth's progression around the Earth-Moon barycenter. Tidal range depends on time and location.
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b). [8]
Shire horses hold the title of the world's largest horse breed. When fully grown, these English draft horses can measure up to 19.2 hands high. One hand equals 4 inches, so that makes Shire horses ...
Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. [1] The supremum (abbreviated sup ; pl. : suprema ) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the least element in P {\displaystyle P} that is greater than or equal to each element of S , {\displaystyle S,} if such an ...