Relation CONTINUOUS-AT

• Defined in theory: Cml
• Source code: cml.lisp

Slots on this relation:

Documentation:

A function ?f is continuous at the point ?p. This definition needs work. It will be something like this

(forall (?x ?epsilon)
(=> (< (norm (value ?f ?p) (value ?f ?x)) ?epsilon)
(exists (?delta)
(< (norm (- ?x ?p) ?delta)))))

Instance-Of: Relation

Arity: 2

Domain: Function

Subrelation-Of: Holds

Other Related Axioms:

(=> (Continuous-At $X $Y) (Function $X))

(<=> (Continuous-Over ?F ?Beg ?End)
     (And (Unary-Scalar-Function-Quantity ?F)
          (Member ?Beg (Exact-Domain ?F))
          (Member ?End (Exact-Domain ?F))
          (Forall (?X)
                  (=> (And (< ?Beg ?X) (< ?X ?End))
                      (And (Defined (Value ?F ?X))
                           (Continuous-At ?F ?X))))))

Notes:

• THIS DEFINITION NEEDS WORK.