Select language: english | cesky | deutsch | italiano | simplified chinese | traditional chinese | hindi Concept: English word: Home

# 緇计ㄧ计 (RemainderFn)

(RemainderFn number divisor) is the remainder of the number number divided by the number divisor. The result has the same sign as divisor.

## Ontology

SUMO / NUMERIC-FUNCTIONS

 贺摸

膥┯闽玒

じㄧ计
 贺摸

膥┯闽玒

籔秖闽玒

緇计ㄧ计

## Coordinate term(s)

猭ㄧ计  らㄧ计  盞ㄧ计  埃猭ㄧ计  ゅセセㄧ计  计ㄧ计  瓜隔畖ㄧ计  ㄧ计  ユ栋ㄧ计  丁筳ㄧ计  贺摸磞瓃ㄧ计  挡ㄧ计  ㄧ计  癸计ㄧ计  程ㄧ计  程秖隔畖ㄧ计  代秖ㄧ计  场だ俱砰畉钵ㄧ计  场だ俱砰ユ栋ㄧ计  场だ俱砰羆ㄧ计  程ㄧ计  程秖隔畖ㄧ计  だ牧ㄧ计  るㄧ计  猭ㄧ计  戳戳ㄧ计  计ㄧ计  秅戳┦禯ㄧ计  闽玒が干ㄧ计  癸丁ㄧ计  俱计ㄧ计  牧ㄧ计  ╰ㄧ计  硉ㄧ计  搭猭ㄧ计  丁虫ㄧ计  丁菌祘ㄧ计  羛栋ㄧ计  竚ㄧ计  单    ┪单    ┪单

## Axioms (10)

```(=>
(equal
(GreatestCommonDivisorFn @ROW)
?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?ELEMENT ?NUMBER)
0))))```

```(=>
(equal
(GreatestCommonDivisorFn @ROW)
?NUMBER)
(not
(exists
(?GREATER)
(and
(greaterThan ?GREATER ?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?ELEMENT ?GREATER)
0)))))))```

```(=>
(equal
(LeastCommonMultipleFn @ROW)
?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?NUMBER ?ELEMENT)
0))))```

```(=>
(equal
(LeastCommonMultipleFn @ROW)
?NUMBER)
(not
(exists
(?LESS)
(and
(lessThan ?LESS ?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?LESS ?ELEMENT)
0)))))))```

"number1 緇计 number2" 单 number if and only if "(""程 俱计  ┪ 单 "number1/number2""*number2"+number)" 单 number1.
```(<=>
(equal
(RemainderFn ?NUMBER1 ?NUMBER2)
?NUMBER)
(equal
(MultiplicationFn
(FloorFn
(DivisionFn ?NUMBER1 ?NUMBER2))
?NUMBER2)
?NUMBER)
?NUMBER1))```

If "number1 緇计 number2" 单 number, then "number2タ璽腹" 单 "numberタ璽腹".
```(=>
(equal
(RemainderFn ?NUMBER1 ?NUMBER2)
?NUMBER)
(equal
(SignumFn ?NUMBER2)
(SignumFn ?NUMBER)))```

If number案俱计龟ㄒ, then "number 緇计 " 单 .
```(=>
(instance ?NUMBER EvenInteger)
(equal
(RemainderFn ?NUMBER 2)
0))```

If number俱计龟ㄒ, then "number 緇计 " 单 .
```(=>
(instance ?NUMBER OddInteger)
(equal
(RemainderFn ?NUMBER 2)
1))```

```(=>
(forall
(?NUMBER)
(=>
(equal
(RemainderFn ?PRIME ?NUMBER)
0)
(or
(equal ?NUMBER 1)
(equal ?NUMBER ?PRIME)))))```

If leap秥龟ㄒ and leap 单 "number (s)", then
```(=>
(and
(instance ?LEAP LeapYear)
(equal
?LEAP
(MeasureFn ?NUMBER Year)))
(or
(and
(equal
(RemainderFn ?NUMBER 4)
0)
(not
(equal
(RemainderFn ?NUMBER 100)
0)))
(equal
(RemainderFn ?NUMBER 400)
0)))```