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Infinite Mathematics in ODTOE: Infinity as the Depth of the Observer's Self-Observation — Overview
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ODTOE reads infinity as a verb: the depth of self-observation via the loop Ψ* = Φ(Ψ*). Potential infinity is the in-progress iterate Φn(Ψ); actual infinity is t
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ODTOE reads infinity as a verb: the depth of self-observation via the loop Ψ* = Φ(Ψ*). Potential infinity is the in-progress iterate Φn(Ψ); actual infinity is the completed fixed point, the unreachable ceiling S = 1 approached by a Banach contraction at rate q = φ−1. The mechanism lifts the depth-index from Z to the ordinals Ord, reading ε0 = fix(α ↦ ω^α) as the depth at which the depth-counter observes itself, tied to the Knaster–Tarski least fixed point and the identity 0 ≡ ∞.