OrderedCompletion R¶

Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989

+: (%, %) -> % if R has AbelianMonoid

-: % -> % if R has AbelianGroup

<=: (%, %) -> Boolean if R has OrderedSet

from PartialOrder

<: (%, %) -> Boolean if R has OrderedSet

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean if R has OrderedSet

from PartialOrder

>: (%, %) -> Boolean if R has OrderedSet

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer
coerce: Integer -> % if R has RetractableTo Integer
coerce: R -> %

from CoercibleFrom R

convert: % -> InputForm if R has ConvertibleTo InputForm
finite?: % -> Boolean

`finite?(x)` tests if `x` is finite.

infinite?: % -> Boolean

`infinite?(x)` tests if `x` is +infinity or -infinity,

latex: % -> String

from SetCategory

max: (%, %) -> % if R has OrderedSet

from OrderedSet

min: (%, %) -> % if R has OrderedSet

from OrderedSet

minusInfinity: () -> %

`minusInfinity()` returns -infinity.

plusInfinity: () -> %

`plusInfinity()` returns +infinity.

rational?: % -> Boolean if R has IntegerNumberSystem

`rational?(x)` tests if `x` is a finite rational number.

rational: % -> Fraction Integer if R has IntegerNumberSystem

`rational(x)` returns `x` as a finite rational number. Error: if `x` cannot be so converted.

rationalIfCan: % -> Union(Fraction Integer, failed) if R has IntegerNumberSystem

`rationalIfCan(x)` returns `x` as a finite rational number if it is one and “failed” otherwise.

retract: % -> Fraction Integer if R has RetractableTo Fraction Integer
retract: % -> Integer if R has RetractableTo Integer
retract: % -> R

from RetractableTo R

retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer
retractIfCan: % -> Union(R, failed)

from RetractableTo R

smaller?: (%, %) -> Boolean if R has OrderedSet

from Comparable

whatInfinity: % -> SingleInteger

`whatInfinity(x)` returns 0 if `x` is finite, 1 if `x` is +infinity, and `-1` if `x` is -infinity.

BasicType

Comparable if R has OrderedSet

OrderedSet if R has OrderedSet

PartialOrder if R has OrderedSet

SetCategory