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In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any , we have Additively indecomposable ordinals are also called gamma numbers or additive principal numbers. The additively indecomposable ordinals are precisely those ordinals of the form for some ordinal . From the continuity of addition in its right argument, we get that if and α is additively indecomposable, then The class of additively indecomposable numbers is closed and unbounded. Its enumerating function is normal, given by .