The separation of a collection of things, called elements objects, concepts, phenomena, etc. into sets, called categories, according to a set of rules such that: given any element, the set in which that element belongs can be determined from the rules; and given any set, the elements in that set can be found. The number of elements may be finite or infinite; the number of sets may be finite or infinite. The sets themselves may be collected into larger groupings which are sets of sets, and these again collected into larger grouping which are sets of sets of sets, etc. The different stages of collection are usually given distinctive names such as phylum, class, order, family, and so on, or may be numbered as 1st level, 2nd level, and so on. A complete classification assigns each element to one and only one set of a particular level; all the elements in one set have at least one common characteristic (which is given by the rules); two elements from different sets (of a particular level) differ in at least one characteristic (as specified by the rules). A partial classification assigns each element to one or more sets of a particular level, i.e., an element may belong to two or more sets at the same level at the same time.