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For me, some ordinals are too big to understand. So I came up with this notation:

If the ordinal \beta whose g_\beta(x) is the closest to f_\alpha(x) of all ordinals (I can't define proper definition for that, but it's just intuitive thing for me),

f_\alpha(\omega)=\beta

This definition is from the nature of SGH.

Here's some examples:

Since f_1(x)=2x , f_1(\omega)= \omega 2.

Since f_\omega(x)\simeq x\uparrow^x x , f_\omega(\omega)\simeq \omega\uparrow ^{\omega}\omega \simeq \varphi(\omega,0).

Also, SVO would be f_{\omega^{\omega}}(\omega).


But I think it works under \vartheta(\Omega_{\omega}) because at that point, FGH becomes equal to SGH.

(note: if this were defined properly, it would be a great discovery in googology.)

(Being written)

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