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# floor fn (FloorFn)

(FloorFn number) returns the largest Integer less than or equal to the RealNumber number.

## Ontology

SUMO / NUMERIC-FUNCTIONS

## Class(es)

 class

inheritable relation

unary function

floor fn

## Coordinate term(s)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  complement fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  initial node fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  minimal cut set fn  nano fn  numerator fn  organization fn  past fn  path weight fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Type restrictions

integer FloorFn(real number)

## Related WordNet synsets

See more related synsets on a separate page.

## Axioms (3)

If "the largest integer less than or equal to number" is equal to int, then there doesn't exist integer otherint so that otherint is less than or equal to number and otherint is greater than int.
```(=>
(equal
(FloorFn ?NUMBER)
?INT)
(not
(exists
(?OTHERINT)
(and
(instance ?OTHERINT Integer)
(lessThanOrEqualTo ?OTHERINT ?NUMBER)
(greaterThan ?OTHERINT ?INT)))))```

"number1 mod number2" is equal to number if and only if "(""the largest integer less than or equal to "number1/number2""*number2"+number)" is equal to number1.
```(<=>
(equal
(RemainderFn ?NUMBER1 ?NUMBER2)
?NUMBER)
(equal
(MultiplicationFn
(FloorFn
(DivisionFn ?NUMBER1 ?NUMBER2))
?NUMBER2)
?NUMBER)
?NUMBER1))```

• if "number1 rounded" is equal to number2,
• then
• if "(number1-"the largest integer less than or equal to number1")" is less than , then number2 is equal to "the largest integer less than or equal to number1"
• or
• if "(number1-"the largest integer less than or equal to number1")" is greater than or equal to , then number2 is equal to "the ceiling of number1"
• .
```(=>
(equal
(RoundFn ?NUMBER1)
?NUMBER2)
(or
(=>
(lessThan
(SubtractionFn
?NUMBER1
(FloorFn ?NUMBER1))
0.5)
(equal
?NUMBER2
(FloorFn ?NUMBER1)))
(=>
(greaterThanOrEqualTo
(SubtractionFn
?NUMBER1
(FloorFn ?NUMBER1))
0.5)
(equal
?NUMBER2
(CeilingFn ?NUMBER1)))))```