Recurrence and Recursion

In contemporary Mathematical Logic. 'Recursion' usually connotes a repetition of relations, often by which a progressive series of elements is generated, e. g. 'is succeeded by' is recursive, since every new successor itself has a successor.  Hence, despite the etymological equivalence, Recursion is not to be confused with 'Recurrence' as Nietzsche uses it, i. e. with a mere repetition of elements.  Thus, the attribution of 'Eternal Recurrence' to the Self-Overcoming dynamic of the Will to Power is mistaken, since the latter is, more precisely, 'recursive', not 'recurrent', i. e. in that dynamic, every new level is itself subject to further overcoming.  Perhaps interpretations that posit that attribution tend to ignore that in the work that first unveils the concept of Eternal Recurrence, the fundamental principle is still the Will to Live, not yet the Will to Power, i. e. in #1 of The Gay Science, "the preservation of the species" is cited as that principle.  Instead, it is upon being affirmed that Eternal Recurrence is transformed into Eternal Recursion, and, concomitantly, Will to Live into Will to Power, and Man into Overman.