Hyper-E Notation (E# for short) is a notation for large numbers devised by Sbiis Saibian. It was first introduced on his Web book One to Infinity: A Finite Journey on November 19, 2011, and was generalized to Extended Hyper-E Notation (xE# for short). Hyper-E Notation is a refined version of a notation Sbiis Saibian devised as a child. 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↦E100##n dominates fn for all n<ω and is itself dominated by fω. 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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