JuliaMath / Infinities.jl

Does these mean ℵ₀ is strictly greater than ∞ while they are also equal? What is the purpose behind it?

Line 22 in 0972ead

@test ℵ₀ == ∞ && ∞ == ℵ₀

Line 43 in 0972ead

@test !(∞ < ℵ₀) && ∞ ≤ ℵ₀

Lines 77 to 78 in 0972ead

    
           @test min(∞,ℵ₀) ≡ min(ℵ₀,∞) ≡ ∞ 
        
           @test max(∞,ℵ₀) ≡ max(ℵ₀,∞) ≡ ℵ₀

Where do you get "strictly greater than"?

It actually says "not strictly greater than"

because Julia base defines min and max as

min(x,y) = ifelse(y < x, y, x)
max(x,y) = ifelse(y < x, x, y)

so if min(x,y) == min(y,x) == x then x must be strictly less.

Not always:

julia> min(1.0, 1)
1.0

julia> min(1, 1.0)
1.0

It's because of promotion

min(x::Real, y::Real) = min(promote(x,y)...) # promotion.jl

	@test min(∞,ℵ₀) ≡ min(ℵ₀,∞) ≡ ∞
	@test max(∞,ℵ₀) ≡ max(ℵ₀,∞) ≡ ℵ₀

Comparing `ℵ₀` and `∞`