Infinities.jl

A Julia package for representing infinity in all its forms

This Julia package is used to represent infinities, including:

1. InfiniteCardinal{k}, for the cardinality of an infinite set, e.g., ℵ₀ for the cardinality of the integers and ℵ₁ for the first uncountable cardinal. The statement that ℵ₁ is the cardinality of the reals is the continuum hypothesis, not an unconditional equality.
2. ∞ to represent the positive real infinity.
3. RealInfinity to represent ±∞.
4. ComplexInfinity to represent an oriented infinity exp(im*θ)∞

Note that we subtype based on interfaces, rather than strict mathematical definitions. For example, ℵ₀ isa Integer as Integer is often used to represent the size of a set or vector. Similarly, ∞ isa Real.

Similar packages

This package is meant to eventually replace Infinity.jl and the definitions of ∞ in InfiniteArrays.jl. We do not yet support Infinity.jl's notions of InfExtendedReal but we hope to add this soon.