A standardized choice of fundamental sequence for all " ? " d " " ? " 0 is described in the article on the fast-growing hierarchy.
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But more important, there is a deep arithmetic root common to both kinds of numbers, which can be expressed through a more fundamental sequence of numbers, also closely tied to.
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The "'Wainer hierarchy "'is the particular fast-growing hierarchy of functions " f " ? ( ? d " ? 0 ) obtained by defining the fundamental sequences as follows [ Gallier 1991 ] [ Pr?mel, et al ., 1991 ]:
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