User talk:Wythagoras/Dollar function/Extended Bracket notation

In rule #4, we can remove "(in case you want to know, the subscripts are for the next part)"

You need a rule for when the active bracket is [0]_X where X is an array.

It depends on exactly what the rule is, but it certainly appears that if array X corresponds to ordinal \(\alpha\), then [0]_X corresponds approximately to ordinal \(\psi(\Omega_{\alpha})\). So since [0]_2 corresponds to the ordinal \(\varepsilon_0\), \([0]_{[0]_2}\) corresponds to the ordinal \(\psi(\Omega_{\varepsilon_0})\). \([0]_{[0]_{[0]_{\cdots}}}\) will correspond to \(\psi(\Omega_\Omega)\).

Can you explain why you believe \([0]_{[0]_2}\) corresponds to the ordinal \(\psi(\Omega_\Omega)\)? Deedlit11 (talk) 14:01, March 5, 2014 (UTC)