Data.ExtendedReal

Extension of real numbers with positive/negative infinities (±∞). It is useful for describing various limiting behaviors in mathematics.

Remarks:

∞ - ∞ is left undefined as usual, but we define 0 × ∞ = 0 × -∞ = 0 by following the convention of probability or measure theory.

References:

Wikipedia contributors, "Extended real number line," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Extended_real_number_line (accessed September 1, 2014).

1 type

3 values

datadata Extended r

Extended r is an extension of r with positive/negative infinity (±∞).

Instances11Functor, Bounded, Eq, Fractional, Data, Num, …

Functor ExtendedDefined in extended-reals-0.2.4.0 · Data.ExtendedReal
Bounded (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Eq r => Eq (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
(Fractional r, Ord r) => Fractional (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Note that Extended r is not a field, nor a ring.
Data r => Data (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
(Num r, Ord r) => Num (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Note that Extended r is not a field, nor a ring.
PosInf + NegInf is left undefined as usual, but we define 0 * PosInf = 0 * NegInf = 0 by following the convention of probability or measure theory.
Ord r => Ord (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Read r => Read (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Show r => Show (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
NFData r => NFData (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal
Hashable r => Hashable (Extended r)Defined in extended-reals-0.2.4.0 · Data.ExtendedReal