Do you know the definition of countable? A set S is countable if there is a one-to-one mapping from S to N where N is the natural numbers. Do you know that 0 is not a member of the natural numbers? We literally start counting at 1 by definition of countable.
> Equivalently, a set S is countable if there exists an injective function f : S → N from S to N; it simply means that every element in S corresponds to a different element in N.
Defining N is usually done via a successor set, on which case 0 makes no sense to include.
Standard construction of ordinals is that each ordinal is the set of all its predecessors. (0 has no predecessors , hence 0 is the empty set.) (And so finite ordinals have the same ordinaliity as cardinality).
