# Difference between revisions of "Indecomposable"

An indecomposable ordinal is an ordinal that can't be expressed as the sum of two smaller numbers.

## Form

An indecomposable ordinal is in the form $$\omega^n$$.

### Proof

Any ordinal that multiplies with a finite amount or added with anything can be expressed as the sum of two smaller ordinals. To avoid this, start with the smallest indecomposable ordinal and multiply it by $$\omega$$ every time. This is the best way of finding all indecomposable ordinals. Why? It is because $$\omega^n$$ is equal to $$\omega$$ sums of $$\omega^{n-1}$$.

    This article is a stub. Please help us to improve Cantor's Attic by adding information.