Actually, push! behaves strange even with Set{Int64}(), e.g.,

julia> s=Set{Int}() 
Set{Int64}()julia> push!(s, 1)
julia> push!(s, 2)
julia> push!(s, 3)
julia> push!(s, 4)
julia> push!(s, 5)
julia> push!(s, 6) 
         Set([4,2,3,5,6,1]) 

as compared to doing the same on a v = Int64[], which leads to the expected:

6-element Array{Int64,1}: 
1 
2 
3 
4 
5 
6

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