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Circulation and the Fast-Growing Hierarchy

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Circulation and the Fast-Growing Hierarchy
Catullus Offline
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Question  06/06/2022, 02:33 AM (This post was last modified: 07/08/2022, 10:03 AM by Catullus.)
(06/06/2022, 01:24 AM)JmsNxn Wrote: I don't see how that would relate to Fast Growing Hierarchies. Could you clarify your question, Catullus?
[Image: svg.image?f_\alpha(x)%3E]2[alpha+1]x. for alpha greater than 1. So [Image: svg.image?f_\omega(x)] would be greater than 2[omega+1]x. the super function of 2[omega]x or 2 omegated to the x. But on the Googology Wiki page for circulation (https://googology.fandom.com/wiki/Circulation) it says "Using only nonnegative integers, there are only four cases where circulation is defined:". Should not its super function at base two grow slower than [Image: svg.image?f_\omega(x)]? [Image: svg.image?F_\omega(x)] is defined using for lots of cases, using only positive integers.
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ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
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RE: Circulation and the Fast-Growing Hierarchy - by Catullus - 06/06/2022, 02:33 AM

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