Definition:Ordinal Subtraction

Definition
Let $x$ and $y$ be ordinals such that $x \le y$.

Then the operation of ordinal subtraction is defined as:


 * $\ds y - x = \bigcup \set {z: x + z = y}$

From Ordinal Subtraction when Possible is Unique, there's only one member in the set $\set{z: x+z=y}$, and we can define the subtraction by


 * $ z=y-x\iff x+z=y$

Also see

 * Ordinal Subtraction when Possible is Unique