Scalar-quantity IDENTITY-SCALAR

• Defined in theory: Scalar-quantities
• Source code: scalar-quantities.lisp

Slots on this scalar-quantity:

Documentation:

The 'one' element for scalar-quantites or the identity element with respect to multiplication. This element is unique and common to all scalar-quantities regardless of associated physical dimension. Therefore this element is equal to the number 1. The axioms tell us that the product of any scalar-quantity x and the identity-scalar is x.

Instance-Of: Scalar-quantity

Axioms:

(Identity-Element-For Identity-Scalar * Scalar-Quantity)

(= (Quantity.Dimension Identity-Scalar) Identity-Dimension)

Other Related Axioms:

(=> (And (Scalar-Quantity ?X) (Recip ?X ?Y))
    (And (Scalar-Quantity ?Y)
         (Forall (?Dim)
                 (=> (/= ?X (The-Zero-Scalar-For-Dimension ?Dim))
                     (= (* ?X ?Y) Identity-Scalar)))))