Category:Ordinal Addition

This category contains results about Ordinal Addition.

Let $x$ and $y$ be ordinals.

The operation of ordinal addition $x + y$ is defined using the Second Principle of Transfinite Recursion on $y$, as follows.

Base Case

When $y = \O$, define:

$x + \O := x$

Inductive Case

For a successor ordinal $y^+$, define:

$x + y^+ := \paren {x + y}^+$

Limit Case

Let $y$ be a limit ordinal. Then:

$\ds x + y := \bigcup_{z \mathop \in y} \paren {x + z}$