A higher arithmetic on the ordinals

Summary · qwen2.5:32b

The article introduces an infinite sequence of binary operations extending both standard ordinal arithmetic and natural number hyperoperations. This unification is significant for advancing understanding in transfinite arithmetic. The study offers a new framework that could potentially simplify complex ordinal computations by aligning them with more familiar hyperoperation structures.

Excerpt

arXiv:2508.13334v3 Announce Type: replace Abstract: We motivate and study an infinite sequence of binary operations on the ordinal numbers, providing a common extension of the standard arithmetic on the ordinals and the hyperoperations on the naturals.