FiniteSet Comparison Table

Entity > Abstract > Class > Set > FiniteSet

Next Set: NullSet Up: Set

FiniteSet comparison table

Subject documentation is a kind of have axiom

Set A Class that satisfies extensionality as well as other conditions specified by some choice of set theory. Unlike Classes generally, Sets need not have an associated condition that determines their membership. Rather, they are thought of metaphorically as `built up' from some initial stock of objects by means of certain constructive operations (such as the pairing or power set operations). Note that extensionality alone is not sufficient for identifying Classes with Sets, since some Classes (e.g. Entity) cannot be assumed to be Sets without contradiction Class
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

FiniteSet A Set containing a finite number of elements Set
(=>
(instance ?SET FiniteSet)
(exists (?NUMBER)
(and
(instance ?NUMBER NonnegativeInteger)
(equal ?NUMBER (CardinalityFn ?SET)))))

Subject	documentation	is a kind of	have axiom
Set	A Class that satisfies extensionality as well as other conditions specified by some choice of set theory. Unlike Classes generally, Sets need not have an associated condition that determines their membership. Rather, they are thought of metaphorically as `built up' from some initial stock of objects by means of certain constructive operations (such as the pairing or power set operations). Note that extensionality alone is not sufficient for identifying Classes with Sets, since some Classes (e.g. Entity) cannot be assumed to be Sets without contradiction	Class	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
FiniteSet	A Set containing a finite number of elements	Set	(=> (instance ?SET FiniteSet) (exists (?NUMBER) (and (instance ?NUMBER NonnegativeInteger) (equal ?NUMBER (CardinalityFn ?SET)))))

Next Set: NullSet Up: Set