About: Hyper-E notation   Sponge Permalink

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E# is not primitive recursive, and specifically the function E(n) = En##n eventually dominates all primitive recursive functions. In fact, in the fast-growing hierarchy, \(n \mapsto E100\#\#n\) dominates \(f_n\) for all \(n < \omega\) and is itself dominated by \(f_\omega\). E# and xE# form part of a larger notation, the Extensible-E System, that also encompasses Cascading-E Notation. Nathan Ho and Wojowu proved termination for the rules of Hyper-E Notation.

AttributesValues
rdfs:label
  • Hyper-E notation
rdfs:comment
  • E# is not primitive recursive, and specifically the function E(n) = En##n eventually dominates all primitive recursive functions. In fact, in the fast-growing hierarchy, \(n \mapsto E100\#\#n\) dominates \(f_n\) for all \(n < \omega\) and is itself dominated by \(f_\omega\). E# and xE# form part of a larger notation, the Extensible-E System, that also encompasses Cascading-E Notation. Nathan Ho and Wojowu proved termination for the rules of Hyper-E Notation.
dcterms:subject
dbkwik:googology/p...iPageUsesTemplate
Name
  • Extended Hyper-E notation
fgh
  • \omega
  • \omega^{\omega}
Base
abstract
  • E# is not primitive recursive, and specifically the function E(n) = En##n eventually dominates all primitive recursive functions. In fact, in the fast-growing hierarchy, \(n \mapsto E100\#\#n\) dominates \(f_n\) for all \(n < \omega\) and is itself dominated by \(f_\omega\). E# and xE# form part of a larger notation, the Extensible-E System, that also encompasses Cascading-E Notation. Nathan Ho and Wojowu proved termination for the rules of Hyper-E Notation.
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