Normal function

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In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions:

1. For every limit ordinal γ (i.e. γ is neither zero nor a successor), it is the case that f (γ) = sup{f (ν) : ν < γ}.
2. For all ordinals α < β, it is the case that f (α) < f (β).