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# Infinities.jl
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A Julia package for representing infinity in all its forms
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[![Build Status](https://github.com/JuliaMath/Infinities.jl/workflows/CI/badge.svg)](https://github.com/JuliaMath/Infinities.jl/actions)
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This Julia package is used to represent infinities, including:
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1. `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.
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2. `` to represent the positive real infinity.
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3. `RealInfinity` to represent `±∞`.
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4. `ComplexInfinity` to represent an oriented infinity `exp(im*θ)∞`
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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`.
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## Similar packages
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This package is meant to eventually replace [Infinity.jl](https://github.com/cjdoris/Infinity.jl) and the definitions of `` in [InfiniteArrays.jl](https://github.com/JuliaArrays/InfiniteArrays.jl). We do not yet support Infinity.jl's notions of `InfExtendedReal` but we hope to add this soon.

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