User blog comment:Deedlit11/The slow-growing hierarchy and other hierarchies/@comment-5150073-20130315163450/@comment-1605058-20180208115944

For \(\alpha=\varepsilon_0\) we have \(f_{\varepsilon_0}(n)=f_{\omega\uparrow\uparrow n}(n)=H_{\omega\uparrow\uparrow(n+1)}(n)\neq H_{\omega\uparrow\uparrow n}(n)=H_{\varepsilon_0}(n)\).