Meaning of generic property | Babel Free

Definitions

1. Used other than figuratively or idiomatically: see generic, property.
2. A property that is true almost everywhere in a given set (i.e., the set of points at which the property is not true is either of measure zero or a subset of a set of measure zero).
3. A property that is true in some dense open subset of a given set.

Examples

“To argue⟳ in that way, however, is not to compare⟳ like⟳ with like⟳; it is to contrast the generic property of extension with the more specific properties of hardness, smell⟳ and colour. It is not after all clear that it loses the generic properties of smell⟳, colour and perhaps solidity, as opposed to the more specific forms of those properties that the unmelted wax may have⟳.”

“1989, Thomas S. Parker, Leon O. Chua, Appendix C: Differential Topology, Practical Numerical Algorithms for Chaotic Systems, Springer, Softcover reprint, page 314, A property P that refers to members of a set⟳ Y is a generic property if the subset of Y whose members exhibit property P contains a dense open⟳ subset of Y. Remark⟳: If P₁ and P₂ are generic properties of a set⟳ Y, then so is the property "P₁ and P₂."”

“2001, Constantin I. Chueshov (translator), Igor Chueshov, Introduction to the Theory of Infinite-dimensional Dissipative Systems, [1999, Russian edition] Acta Scientific Publishing House, page 117, It should be noted that if a property of a dynamical system holds for the parameters from an open⟳ and dense set⟳ in the corresponding space, then it is frequently said that this property is a generic property. However, it should be kept in mind⟳ that the generic property is not the one that holds almost always. […] Therefore, it should be remembered that generic properties are quite frequently encountered and stay⟳ stable during small perturbations of the properties of a system.”

“We now formulate the first generic property concerning the singularities of a Hamiltonian function.”

CEFR level