Where does proper collide?

In set theory a proper subset of a set is a subset that is strictly contained in it, that is, every element belongs to the larger set but at least one element of the larger set is left out, so the two sets are not equal. Halmos's Naive Set Theory draws this distinction between inclusion and proper inclusion. The referent is a formal containment relation that excludes equality, a quantitative statement about sets, and has nothing to do with a category of name or the drift of a star beyond the general meaning of strictness or belonging.[1]

Unit

A subset relation that holds while the sets remain unequal

Recovery means

Not applicable

Measured by

Verified by showing every element of the subset is in the set and that the set has an element the subset lacks

In grammar a proper noun is the name of a specific unique entity, such as a person, place, or organisation, conventionally capitalised and typically resisting the article and plural that common nouns take. Quirk, Greenbaum, Leech, and Svartvik's A Comprehensive Grammar of the English Language sets proper nouns against common nouns on these grounds. The referent is a lexical and syntactic class of words that pick out individuals, a feature of language unrelated to a set relation or a stellar motion apart from the shared word.[2]

Unit

A noun denoting a single, uniquely identified entity

Recovery means

Not applicable

Measured by

Identified by reference to a unique entity, capitalisation, and restricted use of determiners and number

In astronomy the proper motion of a star is its apparent angular movement across the sky per year, measured perpendicular to the line of sight, after the effects of parallax and the Sun's own motion are accounted for, reflecting the star's true transverse velocity through space. Carroll and Ostlie's An Introduction to Modern Astrophysics defines proper motion and relates it to transverse velocity and distance. The referent is a measured rate of angular displacement on the celestial sphere, a kinematic quantity with no connection to a subset relation or a class of noun beyond the Latin meaning of belonging to the object itself.[3]

Unit

Angular displacement across the sky per unit time (e.g., arcseconds per year)

Recovery means

Not applicable

Measured by

Measured from the change in a star's sky position between epochs by astrometry