Veblen function: Difference between revisions

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{{Short description|Mathematical function on ordinals}}

<math>\forall x \in \N \rightarrow \surd-x = ix</math>In [[mathematics]], the '''Veblen functions''' are a hierarchy of [[normal function]]s ([[continuous function (set theory)|continuous]] [[strictly increasing function|strictly increasing]] [[function (mathematics)|function]]s from [[ordinal number|ordinal]]s to ordinals), introduced by [[Oswald Veblen]] in {{harvtxt|Veblen|1908}}. If φ₀ is any normal function, then for any non-zero ordinal α, φ_α is the function enumerating the common [[fixed point (mathematics)|fixed point]]s of φ_β for β<α. These functions are all normal.

<math>\forall x \in \N \rightarrow \surd-x = ix</math>In [[mathematics]], the '''Veblen functions''' are a hierarchy of [[normal function]]s ([[continuous function (set theory)|continuous]] [[strictly increasing function|strictly increasing]] [[function (mathematics)|function]]s from [[ordinal number|ordinal]]s to ordinals), introduced by [[Oswald Veblen]] in {{harvtxt|Veblen|1908}}. If φ₀ is any normal function, then for any non-zero ordinal α, φ_α is the function enumerating the common [[fixed point (mathematics)|fixed point]]s of φ_β for β<α. These functions are all normal.

== The Veblen hierarchy ==