Well-behaved
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 being 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 of the assumptions needed for the analysis to work properly.
The opposite case is usually labelled pathological.
Generally,
- continuous functions are better-behaved than discontinuous ones;
- differentiable functions better-behaved than others;
- smooth functions are better-behaved than others.
- rational numbers are better behaved than irrational numbers;
- attractive fixed pointss are better-behaved than repulsive fixed points
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further examples should be listed here