Where does domain collide?

The set of values on which a function is defined, that is, the collection of admissible inputs it accepts. In Rudin's Principles of Mathematical Analysis a function from a set A to a set B assigns to each element of A one element of B, and A is named the domain of the function. The referent is a set, fixed by the definition of the function itself, and the word carries no connotation of place, ownership, or structure. A change of domain changes the function: the same rule on a smaller set is a different mathematical object.[1]

Unit

The set on which a function is defined

Recovery means

Not applicable

Measured by

Stated as part of a function's definition; the set of admissible inputs, not an observed quantity

A compact region of a polypeptide chain that folds up on its own and often carries a distinct function, so that a single protein can be built from several such units. Wetlaufer, in Proceedings of the National Academy of Sciences, named these globular intrachain regions as sites where folding nucleates independently within the larger chain. The referent is a piece of physical structure, read off a protein's three-dimensional form, not a set and not a right. Two domains in one protein can fold, evolve, and act as separate parts while sharing a backbone.[2]

Unit

A compact, independently folding region of a polypeptide chain

Recovery means

Not applicable

Measured by

Identified from a protein's three-dimensional structure as a compact, separately folding region

The sovereign's power to take private property for public use, provided the owner is paid just compensation. The Fifth Amendment's Takings Clause bounds the power rather than granting it, and in Kelo v. City of New London the United States Supreme Court held that transfer to a private developer under an economic-development plan could count as a public use. The referent is a legal power held by the state over property, exercised through courts and statutes. Here the word keeps its old meaning of dominion, a realm one has authority over, which the other fields have shed.[3][4]

Unit

The sovereign's power to take private property for public use

Recovery means

Not applicable

Measured by

Established by constitutional text and case law, not measured