KLEENE'S 𝒪
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ε₁
ε₁
Limit
Notation: 3·5^e₈
The next epsilon number after ε₀ — the next fixed point of α ↦ ω^α.
CONSTRUCTION
Enumerate ε₀+1, ω^(ε₀+1), ω^(ω^(ε₀+1)), ...
SIGNIFICANCE
The epsilon numbers form their own sequence: ε₀, ε₁, ε₂, ... each a fixed point of exponentiation.
Recursive ordinals · ω₁ᶜᶾ boundary · rotates daily