the interval (1/2, 3/2), because there are arbitrarily large n for which the value of the sequence is in the interval. formal, formally Qualifies anything that is sufficiently precise to be translated straightforwardly in a formal system. For example. a formal proof, a formal definition. generic This term has similar connotations as almost all but is used particularly for concepts outside the purview of measure theory. A property holds "generically" on a set if the set satisfies some (context-dependent) notion of density, or perhaps if its complement satisfies some (context-dependent) notion of smallness. For example, a property which holds on a dense Gδ (intersection of countably many open sets) is said to hold generically. In algebraic geometry, one says that a property of points on an algebraic variety that holds on a dense Zariski open set is true generically; however, it is usually not said that a property which holds merely on a dense set (which is not Zariski open) is generic in this situation. in general In a descriptive context, this phrase introduces a simple characterization of a broad class of objects, with an eye towards identifying a unifying principle. This term introduces an "elegant" description which holds for "arbitrary" objects. Exceptions to this description may be mentioned explicitly, as "pathological" cases. left-hand side, right-hand side (LHS, RHS) Most often, these refer simply to the left-hand or the right-hand side of an equation; for example, has on the LHS and on the RHS. Occasionally, these are used in the sense of lvalue and rvalue: an RHS is primitive, and an LHS is derivative. nice A mathematical object is colloquially called nice or sufficiently nice if it satisfies hypotheses or properties, sometimes unspecified or even unknown, that are especially desirable in a given context. It is an informal antonym for pathological. For example, one might conjecture that a differential operator ought to satisfy a certain boundedness condition "for nice test functions," or one might state that some interesting topological invariant should be computable "for nice spaces X." onto A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English.