Traditionally, | v |=max(|v_i|). But in Julia we have:

julia> v=[1.0 2.0 -5.0]

1×3 Array{Float64,2}:

1.0 2.0 -5.0

julia> norm(v)

5.477225575051661

julia> norm(v,2)

5.477225575051661

julia> norm(v,Inf)

8.0

julia> norm(v,1)

5.0

In my opinion it is changed, that is, I guess that the correct way is norm(v,Inf)=5 and norm(v,1)=8. Am I wrong?