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# ke3 huan4 han2 shu4 (CommutativeFunction)

A BinaryFunction is commutative if the ordering of the arguments of the function has no effect on the value returned by the function. More precisely, a function function is commutative just in case (function inst1 inst2) is equal to (function inst2 inst1), for all inst1 and inst2.

## Ontology

SUMO / BASE-ONTOLOGY

## Superclass(es)

 shi2 ti3

chou1 xiang4 de5

guan1 xi4

dan1 zhi2 guan1 xi4

han2 shu4
 shi2 ti3

chou1 xiang4 de5

guan1 xi4

san1 yuan2 guan1 xi4

er4 yuan2 han2 shu4

ke3 huan4 han2 shu4

## Instance(s)

cheng2 fa3 han2 shu4  jia1 fa3 han2 shu4  zui4 da4 zhi2 han2 shu4  zui4 xiao3 zhi2 han2 shu4

## Coordinate term(s)

guan1 lian2 han2 shu4

## Related WordNet synsets

commutative
(mathematics) of a binary operation; independent of order; as in e.g. "a x b = b x a"

## Axioms (1)

• if function shi4 ke3 huan4 han2 shu4 de5 shi2 li4,
• then for all inst1,inst2 holds: if function de5 lun4 yuan2 shi4 class de5 shi2 li4 and inst1 shi4 class de5 shi2 li4 and inst2 shi4 class de5 shi2 li4, then "function(inst1,inst2)" deng3 yu1 "function(inst2,inst1)"
• .
```(=>
(instance ?FUNCTION CommutativeFunction)
(forall
(?INST1 ?INST2)
(=>
(and
(domain ?FUNCTION 1 ?CLASS)
(instance ?INST1 ?CLASS)
(instance ?INST2 ?CLASS))
(equal
(AssignmentFn ?FUNCTION ?INST1 ?INST2)
(AssignmentFn ?FUNCTION ?INST2 ?INST1)))))```