# OnePointCompletion R¶

- R: SetCategory

Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989

- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer
- from RetractableTo Fraction Integer
- coerce: Integer -> % if R has RetractableTo Integer
- from RetractableTo Integer
- coerce: R -> %
- from RetractableTo R

- finite?: % -> Boolean
`finite?(x)`

tests if`x`

is finite.- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory

- infinite?: % -> Boolean
`infinite?(x)`

tests if`x`

is infinite.

- infinity: () -> %
`infinity()`

returns infinity.- latex: % -> String
- from SetCategory

- rational: % -> Fraction Integer if R has IntegerNumberSystem
`rational(x)`

returns`x`

as a finite rational number. Error: if`x`

is not a rational number.

- rational?: % -> Boolean if R has IntegerNumberSystem
`rational?(x)`

tests if`x`

is a finite rational number.

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

returns`x`

as a finite rational number if it is one, “failed” otherwise.- retract: % -> Fraction Integer if R has RetractableTo Fraction Integer
- from RetractableTo Fraction Integer
- retract: % -> Integer if R has RetractableTo Integer
- from RetractableTo Integer
- retract: % -> R
- from RetractableTo R
- retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer
- from RetractableTo Fraction Integer
- retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer
- from RetractableTo Integer
- retractIfCan: % -> Union(R, failed)
- from RetractableTo R

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer