 An ordinal α  is a successor ordinal if  α = β ∪ {β} for some (other) ordinal β. Ordinals which are neither 0 nor successor ordinals are called limit ordinals.   The smallest limit ordinal is  ω; it is  d(1) for the well-order we saw above, 0    &lt; 2   &lt;  4 &lt;  …  1  &lt;    3  &lt; 5 &lt;    … 