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 RelationExtendedToQuantities comparison table
 have domain2 have domain1 be first domain of be second domain of have range documentation have inverse have axiom have identityElement is an instance of Subject AdditionFn Quantity Quantity valence subrelation Quantity If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers `(<=> (equal (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER) (equal (AdditionFn (MultiplicationFn (FloorFn (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))` 0 RelationExtendedToQuantities DivisionFn Quantity Quantity valence subrelation Quantity If ?NUMBER1 and ?NUMBER2 are Numbers, then (DivisionFn ?NUMBER1 ?NUMBER2) is the result of dividing ?NUMBER1 by ?NUMBER2. An exception occurs when ?NUMBER1 = 1, in which case (DivisionFn ?NUMBER1 ?NUMBER2) is the reciprocal of ?NUMBER2 `(equal (MeasureFn ?NUMBER AngularDegree) (MeasureFn (MultiplicationFn ?NUMBER (DivisionFn Pi 180)) Radian))` 1 RelationExtendedToQuantities equal Entity Entity valence subrelation (equal ?ENTITY1 ?ENTITY2) is true just in case ?ENTITY1 is identical with ?ENTITY2 `(=> (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)))))` RelationExtendedToQuantities ExponentiationFn Integer Quantity identityElement distributes Quantity (ExponentiationFn ?NUMBER ?INT) returns the RealNumber ?NUMBER raised to the power of the Integer ?INT `(equal (ReciprocalFn ?NUMBER) (ExponentiationFn ?NUMBER -1))` RelationExtendedToQuantities greaterThan Quantity Quantity valence subrelation (greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2 lessThan `(=> (larger ?OBJ1 ?OBJ2) (forall (?QUANT1 ?QUANT2) (=> (and (measure ?OBJ1 (MeasureFn ?QUANT1 LengthMeasure)) (measure ?OBJ2 (MeasureFn ?QUANT2 LengthMeasure))) (greaterThan ?QUANT1 ?QUANT2))))` TransitiveRelation greaterThanOrEqualTo Quantity Quantity valence subrelation (greaterThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2 lessThanOrEqualTo `(=> (instance ?NUMBER NonnegativeRealNumber) (greaterThanOrEqualTo ?NUMBER 0))` RelationExtendedToQuantities lessThan Quantity Quantity valence subrelation (lessThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than the Quantity ?NUMBER2 `(=> (instance ?NUMBER NegativeRealNumber) (lessThan ?NUMBER 0))` TransitiveRelation lessThanOrEqualTo Quantity Quantity valence subrelation (lessThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than or equal to the Quantity ?NUMBER2 `(=> (instance (MonthFn ?NUMBER ?YEAR) Month) (lessThanOrEqualTo ?NUMBER 12))` RelationExtendedToQuantities MaxFn Quantity Quantity valence subrelation Quantity (MaxFn ?NUMBER1 ?NUMBER2) is the largest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MaxFn returns one of its arguments `(=> (equal (MaxFn ?NUMBER1 ?NUMBER2) ?NUMBER) (or (and (equal ?NUMBER ?NUMBER1) (greaterThan ?NUMBER1 ?NUMBER2)) (and (equal ?NUMBER ?NUMBER2) (greaterThan ?NUMBER2 ?NUMBER1)) (and (equal ?NUMBER ?NUMBER1) (equal ?NUMBER ?NUMBER2))))` RelationExtendedToQuantities MinFn Quantity Quantity valence subrelation Quantity (MinFn ?NUMBER1 ?NUMBER2) is the smallest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MinFn returns one of its arguments `(=> (equal (MinFn ?NUMBER1 ?NUMBER2) ?NUMBER) (or (and (equal ?NUMBER ?NUMBER1) (lessThan ?NUMBER1 ?NUMBER2)) (and (equal ?NUMBER ?NUMBER2) (lessThan ?NUMBER2 ?NUMBER1)) (and (equal ?NUMBER ?NUMBER1) (equal ?NUMBER ?NUMBER2))))` RelationExtendedToQuantities MultiplicationFn Quantity Quantity valence subrelation Quantity If ?NUMBER1 and ?NUMBER2 are Numbers, then (MultiplicationFn ?NUMBER1 ?NUMBER2) is the arithmetical product of these numbers `(equal (MeasureFn ?NUMBER YearDuration) (MeasureFn (MultiplicationFn ?NUMBER 365) DayDuration))` 1 RelationExtendedToQuantities ReciprocalFn Quantity rangeSubclass inverse Quantity (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 RemainderFn Quantity Quantity identityElement distributes Quantity (RemainderFn ?NUMBER ?DIVISOR) is the remainder of the number ?NUMBER divided by the number ?DIVISOR. The result has the same sign as ?DIVISOR `(=> (instance ?NUMBER OddInteger) (equal (RemainderFn ?NUMBER 2) 1))` RelationExtendedToQuantities RoundFn Quantity rangeSubclass inverse Quantity (RoundFn ?NUMBER) is the Integer closest to ?NUMBER on the number line. If ?NUMBER is halfway between two Integers (for example 3.5), it denotes the larger Integer `(=> (equal (RoundFn ?NUMBER1) ?NUMBER2) (or (=> (lessThan (SubtractionFn ?NUMBER1 (FloorFn ?NUMBER1)) .5) (equal ?NUMBER2 (FloorFn ?NUMBER1))) (=> (greaterThanOrEqualTo (SubtractionFn ?NUMBER1 (FloorFn ?NUMBER1)) .5) (equal ?NUMBER2 (CeilingFn ?NUMBER1)))))` UnaryFunction SubtractionFn Quantity Quantity valence subrelation Quantity If ?NUMBER1 and ?NUMBER2 are Numbers, then (SubtractionFn ?NUMBER1 ?NUMBER2) is the arithmetical difference between ?NUMBER1 and ?NUMBER2, i.e. ?NUMBER1 minus ?NUMBER2. An exception occurs when ?NUMBER1 is equal to 0, in which case (SubtractionFn ?NUMBER1 ?NUMBER2) is the negation of ?NUMBER2 `(equal (MeasureFn ?NUMBER Celsius) (MeasureFn (SubtractionFn ?NUMBER 273.15) Kelvin))` 0 RelationExtendedToQuantities

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