Von Neumann Ordinals as Java HashSets

VonNeumannOrdinal.java

import java.util.HashSet;
import java.util.Set;
import java.util.stream.Collectors;

public class VonNeumannOrdinal extends HashSet<Set> {
    private int toInt() { return size(); }
    @Override public String toString() {
        return "{" + (isEmpty() ? "" : stream().map(Object::toString)
                .collect(Collectors.joining(","))) + "}";
    }

    private VonNeumannOrdinal increment() {
        var next = new VonNeumannOrdinal();
        next.addAll(this);
        next.add(this);
        return next;
    }

    public static void main(final String... args) {
        var ordinal = new VonNeumannOrdinal();
        while (ordinal.toInt() < 16) {
            System.out.println(ordinal.toInt() + ": " + ordinal);
            ordinal = ordinal.increment();
        }
    }
}