ordinal arithmetic

Natural Ordinal Addition

Five different self-standing accounts of natural addition in the ordinals, reflecting five different philosophical perspectives on how we should best…

Mar 15 • Joel David Hamkins

Counting to Epsilon Naught

Let us aspire to count much higher in the ordinals. How high can you count?

Mar 4 • Joel David Hamkins

Cantor Normal Form

Cantor proved a remarkable fact about ordinals, providing an ordinal notation system in which every ordinal admits a unique canonical representation by…

Feb 12 • Joel David Hamkins

Indecomposable Ordinals

Which ordinals are closed under addition? Which are closed under multiplication? Let us try to identify them exactly.

Feb 1 • Joel David Hamkins

Ordinal arithmetic

Let's review the basics of ordinal arithmetic, addition, multiplication, and exponentiation, providing both the order-theoretic semantic definitions as…

Jan 22 • Joel David Hamkins

Shall we count together in the ordinals? Let us venture into that transfinite realm beyond infinity. Is infinity even or odd? Can we count to an…

Feb 22, 2023 • Joel David Hamkins

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