In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) iff it is continuous and strictly mononotically increasing. That is, a function is normal iff the following two conditions hold:
- For every limit ordinal γ, f(γ) = {f(ν) : ν < γ}.
- For all ordinals α < β, f(α) < f(β).