User blog comment:B1mb0w/Omega Count/@comment-5529393-20160712114533

I notice that you like to equate different ordinals based on their fundamental sequences, and I don't think it's a good idea. For example, it's true that if you take $$\varepsilon_0$$ and keep taking the fundamental sequence at 2, you'll eventually get to $$ \omega + \omega$$,  but that doesn't mean that  $$ \omega + \omega$$ actually reaches  $$\varepsilon_0$$ in any sense, and I think making that association will only lead to errors.