ceiling fn (CeilingFn)

(CeilingFn number) returns the smallest Integer greater than or equal to the RealNumber number.

Ontology

SUMO / NUMERIC-FUNCTIONS

Class(es)

class

inheritable relation

unary function

ceiling 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 complement fn cosine fn cut set fn denominator fn end fn end node fn extension fn floor 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 CeilingFn(real number)

Axioms (2)

If "the ceiling of number" is equal to int, then there doesn't exist integer otherint so that otherint is greater than or equal to number and otherint is less than int.

(=>
      (equal
            (CeilingFn ?NUMBER)
            ?INT)
      (not
            (exists
                  (?OTHERINT)
                  (and
                        (instance ?OTHERINT Integer)
                        (greaterThanOrEqualTo ?OTHERINT ?NUMBER)
                        (lessThan ?OTHERINT ?INT)))))

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"
- 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)))))