Nota: La traducción de esta entrada está actualmente en revisión de calidad, por lo que parte del contenido se muestra temporalmente solo en inglés.
Esta entrada aún no se ha traducido a tu idioma, así que se muestra el original a continuación.
integrability
This term is a specialized technical descriptor used almost exclusively within the realms of calculus, differential equations, and theoretical physics. It describes a binary state of possibility: either a system or function possesses the mathematical property required for integration, or it does not. It carries a connotation of solvability and order, suggesting that a complex system can be reduced to a manageable, closed-form expression.
As an abstract property of mathematical systems, the word is treated as an uncountable mass noun. It does not refer to individual instances of integration but rather to the inherent quality of being integrable. Consequently, it is never pluralized and cannot be counted with numbers; one does not refer to multiple integrabilities, but rather to the presence or absence of integrability within a specific framework.
Meanings
The property of a mathematical function or system being capable of being integrated.
Examples
The professor explained the conditions required for the integrability of the function.
I wonder if this complex system possesses complete integrability.
We must first prove the integrability of the expression before proceeding with the calculation.
We must first prove the integrability of the expression before proceeding with the calculation.
The integrability of the Hamiltonian system allows for an exact solution.
Does this specific vector field satisfy the criteria for integrability?
The researcher focused on the integrability of the nonlinear wave equation.
If we can establish integrability, the entire problem becomes trivial.
The lack of integrability in this model leads to chaotic behavior.