ReciprocalFn Comparison Table

Entity > Abstract > Class > Relation > BinaryRelation > UnaryFunction > ReciprocalFn

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ReciprocalFn comparison table

Subject have domain1 be first domain of have range be second domain of documentation have axiom is a kind of is an instance of

RelationExtendedToQuantities valence subrelation A RelationExtendedToQuantities is a Relation that, when it is true on a sequence of arguments that are RealNumbers, it is also true on a sequence of ConstantQuantites with those magnitudes in some unit of measure. For example, the lessThan relation is extended to quantities. This means that for all pairs of quantities ?QUANTITY1 and ?QUANTITY2, (lessThan ?QUANTITY1 ?QUANTITY2) if and only if, for some ?NUMBER1, ?NUMBER2, and ?UNIT, ?QUANTITY1 = (MeasureFn ?NUMBER1 ?UNIT), ?QUANTITY2 = (MeasureFn ?NUMBER2 ?UNIT), and (lessThan ?NUMBER1 ?NUMBER2), for all units ?UNIT on which ?QUANTITY1 and ?QUANTITY2 can be measured. Note that, when a RelationExtendedToQuantities is extended from RealNumbers to ConstantQuantities, the ConstantQuantities must be measured along the same physical dimension
(=>
(and
(instance ?REL RelationExtendedToQuantities)
(instance ?REL BinaryRelation)
(instance ?NUMBER1 RealNumber)
(instance ?NUMBER2 RealNumber)
(holds ?REL ?NUMBER1 ?NUMBER2))
(forall (?UNIT)
(=>
(instance ?UNIT UnitOfMeasure)
(holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))
Relation

UnaryFunction rangeSubclass inverse The Class of Functions that require a single argument
(=>
(instance ?FUNCTION UnaryFunction)
(valence ?FUNCTION 1))
Function

ReciprocalFn Quantity rangeSubclass Quantity inverse (ReciprocalFn ?NUMBER) is the reciprocal element of ?NUMBER with respect to the multiplication operator (MultiplicationFn), i.e. 1/?NUMBER. Not all numbers have a reciprocal element. For example the number 0 does not. If a number ?NUMBER has a reciprocal ?RECIP, then the product of ?NUMBER and ?RECIP will be 1, e.g. 3*1/3 = 1. The reciprocal of an element is equal to applying the ExponentiationFn function to the element to the power -1
(equal 1 (MultiplicationFn ?NUMBER (ReciprocalFn ?NUMBER)))
UnaryFunction

Subject	have domain1	be first domain of	have range	be second domain of	documentation	have axiom	is a kind of	is an instance of
RelationExtendedToQuantities		valence		subrelation	A RelationExtendedToQuantities is a Relation that, when it is true on a sequence of arguments that are RealNumbers, it is also true on a sequence of ConstantQuantites with those magnitudes in some unit of measure. For example, the lessThan relation is extended to quantities. This means that for all pairs of quantities ?QUANTITY1 and ?QUANTITY2, (lessThan ?QUANTITY1 ?QUANTITY2) if and only if, for some ?NUMBER1, ?NUMBER2, and ?UNIT, ?QUANTITY1 = (MeasureFn ?NUMBER1 ?UNIT), ?QUANTITY2 = (MeasureFn ?NUMBER2 ?UNIT), and (lessThan ?NUMBER1 ?NUMBER2), for all units ?UNIT on which ?QUANTITY1 and ?QUANTITY2 can be measured. Note that, when a RelationExtendedToQuantities is extended from RealNumbers to ConstantQuantities, the ConstantQuantities must be measured along the same physical dimension	(=> (and (instance ?REL RelationExtendedToQuantities) (instance ?REL BinaryRelation) (instance ?NUMBER1 RealNumber) (instance ?NUMBER2 RealNumber) (holds ?REL ?NUMBER1 ?NUMBER2)) (forall (?UNIT) (=> (instance ?UNIT UnitOfMeasure) (holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))	Relation
UnaryFunction		rangeSubclass		inverse	The Class of Functions that require a single argument	(=> (instance ?FUNCTION UnaryFunction) (valence ?FUNCTION 1))	Function
ReciprocalFn	Quantity	rangeSubclass	Quantity	inverse	(ReciprocalFn ?NUMBER) is the reciprocal element of ?NUMBER with respect to the multiplication operator (MultiplicationFn), i.e. 1/?NUMBER. Not all numbers have a reciprocal element. For example the number 0 does not. If a number ?NUMBER has a reciprocal ?RECIP, then the product of ?NUMBER and ?RECIP will be 1, e.g. 31/3 = 1. The reciprocal of an element* is equal to applying the ExponentiationFn function to the element to the power -1	(equal 1 (MultiplicationFn ?NUMBER (ReciprocalFn ?NUMBER)))		UnaryFunction

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