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Strict weak orders are very closely related to total preorders or (non-strict) weak orders, and the same mathematical concepts that can be modeled with strict weak orderings can be modeled equally well with total preorders. A total preorder or weak order is a preorder in which any two elements are comparable. [7]
Total orders, orderings that specify, for every two distinct elements, which one is less than the other; Weak orders, generalizations of total orders allowing ties (represented either as equivalences or, in strict weak orders, as transitive incomparabilities) Well-orders, total orders in which every non-empty subset has a least element
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Using reduced words one may define three partial orders on the Coxeter group, the (right) weak order, the absolute order and the Bruhat order (named for François Bruhat). An element v exceeds an element u in the Bruhat order if some (or equivalently, any) reduced word for v contains a reduced word for u as a substring, where some letters (in ...
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Zinc is with 65 parts per million (ppm) the most abundant in the group while cadmium with 0.1 ppm and mercury with 0.08 ppm are orders of magnitude less abundant. [63] Copernicium, as a synthetic element with a half-life of a few minutes, may only be present in the laboratories where it was produced. Sphalerite (ZnS), an important zinc ore
A chemical element, often simply called an element, is a type of atom which has a specific number of protons in its atomic nucleus (i.e., a specific atomic number, or Z). [ 1 ] The definitive visualisation of all 118 elements is the periodic table of the elements , whose history along the principles of the periodic law was one of the founding ...
In mathematics, specifically in order theory and functional analysis, an element of a vector lattice is called a weak order unit in if and also for all , {, | |} = = [1] Examples [ edit ]