Comparing ℵ₀ and ∞

[putianyi889]

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

Infinities.jl/test/test_cardinality.jl

Line 22 in 0972ead

@test ℵ₀ == ∞ && ∞ == ℵ₀

Infinities.jl/test/test_cardinality.jl

Line 43 in 0972ead

@test !(∞ < ℵ₀) && ∞ ≤ ℵ₀

Infinities.jl/test/test_cardinality.jl

Lines 77 to 78 in 0972ead

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

https://github.com/JuliaLang/julia/blob/43d7f881f8e26eb4bb7ef3d6f84b378d28125325/base/promotion.jl#L532-L533

[dlfivefifty]

Where do you get "strictly greater than"?

[dlfivefifty]

It actually says "not strictly greater than"

[putianyi889]

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.

[dlfivefifty]

Not always:

julia> min(1.0, 1)
1.0

julia> min(1, 1.0)
1.0

[putianyi889]

It's because of promotion

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