Definition:Ordinal Addition

Definition
Let $x$ and $y$ be ordinals. We shall define $x+y$ using transfinite recursion:


 * $\displaystyle x + \varnothing = x$
 * $\displaystyle x + y^+ = (x+y)^+$
 * For limit ordinals $y$, $\displaystyle x+y = \bigcup_{z \in y} (x+z)$