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Mathematicians (and those in related sciences) very frequently speak of whether a mathematical object — a number, a function, a set, a space of one sort or another — is "well-behaved" or not. While the term has no fixed formal definition, it can have fairly precise meaning within a given context. In pure mathematics, "well-behaved" objects are those that can be proved or analyzed by elegant means to have elegant properties. In both pure and applied mathematics, (optimization, numerical integration, or mathematical physics, for example,) well-behaved also means not violating any assumptions needed to successfully apply whatever analysis is being discussed. The opposite case is usually labelled pathological. It is not unusual to have situations in which most cases (in terms of cardinality) are pathological, but the pathological cases will not arise in practice unless constructed deliberately. Generally,
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