Relation CONTINUOUS-OVER

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

Slots on this relation:

Documentation:

A function ?f is continous over the interval ?beg ?end if it is defined and continuous-at every point between ?beg and ?end exclusive.

Arity: 3

Axioms:

(Nth-Domain Continuous-Over 1 Unary-Scalar-Function-Quantity)

(<=> (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))))))