📂Julia

Using Infinity in Julia

Overview

Infinities.jl is a package that aids in using infinity symbols in Julia¹. Surprisingly, infinity is quite useful in scientific computing coding.

Code

julia> 8 < Inf
true

The reason it’s mentioned that it helps in using infinity symbols, not just infinity, in the introduction is that you can actually use them without the package.

julia> using Infinities

julia> 8 < ∞
true

julia> -∞ < 8
true

julia> max(∞, 10, 11)
∞

julia> sin(∞)
ERROR: MethodError: no method matching AbstractFloat(::Infinities.Infinity)

As you can see, it possesses all the expected properties of infinity.

julia> ℵ₀ < ℵ₁
true

julia> ℵ₀ > ℵ₁
false

julia> ∞ == ℵ₁
false

julia> ∞ == ℵ₀
true

julia> ∞ === ℵ₀
false

Moreover, it allows the use of the cardinality of infinite sets with $\aleph_{0}$ and $\aleph_{1}$, which makes it possible to have the same infinity in terms of computation but still give them an order for sorting or comparison.

Environment

• OS: Windows
• julia: v1.6.2