Comparing `ℵ₀` and `∞`

[putianyi889]

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

https://github.com/JuliaMath/Infinities.jl/blob/0972ead14abe0eee1218c6f5b2e244775bd9e4c8/test/test_cardinality.jl#L22 https://github.com/JuliaMath/Infinities.jl/blob/0972ead14abe0eee1218c6f5b2e244775bd9e4c8/test/test_cardinality.jl#L43 https://github.com/JuliaMath/Infinities.jl/blob/0972ead14abe0eee1218c6f5b2e244775bd9e4c8/test/test_cardinality.jl#L77-L78 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