User blog comment:Denis Maksudov/Nomenclature for the hyper operators/@comment-24920136-20161226181604/@comment-28606698-20161226224656

It's true. And also for example $$n\uparrow^{\omega^k}n=\lbrace \underbrace {n,n, \cdots,n}_{k+2 \quad n's}\rbrace \approx f_{\omega^k}(n)$$