omega

omega

In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditary transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals. Like other kinds of numbers, ordinals can be added, multiplied, and exponentiated. Each turn of the spiral represents one power of ω.

This spiral represents all ordinal numbers less than ωω. The first round of the spiral represents the finite ordinals, i.e. 1, 2, 3, 4, etc. The second round is the ordinal of the form ω·m+n, therefore ω, ω+1, ω+2, etc., ω·2, ω·2+1, ω·2+2, etc., ω·3, ω·3+1, etc., ω·4, etc. etc. Then the third round is the ordinal of the form ω²·m+omega·n+p, and so on; each turn of the spiral represents a power of omega.