User blog comment:Rgetar/Proof that limit of epsilon numbers is epsilon number/@comment-35470197-20200103082818/@comment-32213734-20200103105224

I tried to understand why. Scott continuity article
 * α = sup{α[n]}, n < cof(α)
 * f(sup{α[n]}) = sup{f(α[n])}
 * f(α) = sup{f(α[n])}

Fixed points:
 * α[n] = f(α[n])
 * sup{α[n]} = sup{f(α[n])}
 * α = f(α)

So limits of fixed points are also fixed points