User blog:Rgetar/Help to name function

Please, help me to name function of ordinal α such as if Ωβ ≤ α < Ωβ + 1, then value of this function is Ωβ. How to name it?

I was thinking about "cardinality", but I am confused that its output is ordinal, not cardinal. Or, maybe, Ωβ is an ordinal and also a cardinal? Explain, please.