# Infinities.jl

A Julia package for representing infinity in all its forms

This Julia package is used to represent infinities, including:

`InfiniteCardinal{k}`

, for the cardinality of an infinite set, e.g.,`ℵ₀`

for the cardinality of the integers and`ℵ₁`

for the cardinality of the reals.`∞`

to represent the positive real infinity.`RealInfinity`

to represent`±∞`

.`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.