User blog comment:Edwin Shade/Negatively Indexed Epsilon Numbers/@comment-1605058-20171224230129

"it is quite plain to see that \(\varepsilon_{-1}\) must equal \(\omega\)" Actually, any ordinal \(\omega\leq\gamma<\varepsilon_0\) satisfies \(\gamma\uparrow\uparrow\omega=\varepsilon_0\).