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Mike Rosoft (talk | contribs) Follow-up |
Mike Rosoft (talk | contribs) Follow-up |
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:If you check the definition of ''C''(ζ<sub>0</sub>+1), you will see that you would have to show that ζ<sub>0</sub> belongs to it (for some other reason) in addition to ζ<sub>0</sub> < ζ<sub>0</sub>+1 before you can conclude that ζ<sub>0</sub> belongs to it on account of being ψ(ζ<sub>0</sub>). [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 11:01, 16 June 2013 (UTC)
:I was also initially confused about the values of ψ, but I understand it now. "ψ(α) is the smallest ordinal which cannot be expressed from 0, 1, ω and Ω using sums, products, exponentials, and the ψ function itself (to previously constructed ordinals less than α)." The key part is "previously constructed"; I need to be able to create the ordinal number in a finite number of steps from {0, 1, ω, Ω} before I can apply the ψ function to it. Since ζ<sub>0</sub> cannot be constructed in a finite number of steps from {0, 1, ω}, the only way it can be generated is as ψ(Ω); and by definition, ψ(Ω) is not a member of any constructed sets before C(Ω+1). - [[User:Mike Rosoft|Mike Rosoft]] ([[User talk:Mike Rosoft|talk]]) 05:
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