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Limit ordinal
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== Indecomposable ordinals == {{main article|Indecomposable ordinal}} '''Additively indecomposable''' A limit ordinal α is called additively indecomposable if it cannot be expressed as the sum of β < α ordinals less than α. These numbers are any ordinal of the form <math>\omega^\beta</math> for β an ordinal. The smallest is written <math>\gamma_0</math>, the second is written <math>\gamma_1</math>, etc.<ref name=":0">{{Cite web|title=Limit ordinal - Cantor's Attic|url=http://cantorsattic.info/Limit_ordinal#Types_of_Limits|access-date=2021-08-10|website=cantorsattic.info}}</ref> '''Multiplicatively indecomposable''' A limit ordinal α is called multiplicatively indecomposable if it cannot be expressed as the product of β < α ordinals less than α. These numbers are any ordinal of the form <math>\omega^{\omega^\beta}</math> for β an ordinal. The smallest is written <math>\delta_0</math>, the second is written <math>\delta_1</math>, etc.<ref name=":0" /> '''Exponentially indecomposable and beyond''' The term "exponentially indecomposable" does not refer to ordinals not expressible as the exponential product ''(?)'' of β < α ordinals less than α, but rather the [[Epsilon numbers (mathematics)|epsilon numbers]], "tetrationally indecomposable" refers to the zeta numbers, "pentationally indecomposable" refers to the eta numbers, etc.<ref name=":0" />
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