Ranking

A ranking is a relationship between a set of items, often recorded in a list, such that, for any two items, the first is either "ranked higher than", "ranked lower than", or "ranked equal to" the second.^[1] In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by

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