In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any
From the continuity of addition in its right argument, we get that if
Obviously 1 is additively indecomposable, since
The class of additively indecomposable numbers is closed and unbounded. Its enumerating function is normal, given by
The derivative of
Multiplicatively indecomposable
A similar notion can be defined for multiplication. If α is greater than the multiplicative identity, 1, and β < α and γ < α imply β·γ < α, then α is multiplicatively indecomposable. 2 is multiplicatively indecomposable since 1·1 = 1 < 2. Besides 2, the multiplicatively indecomposable ordinals (also called delta numbers) are those of the form