All About Ordinal Numbers

It has come to my attention that an unusual mystery is afoot. The news is full of world events and tremendous calamities. We are devoting far too much attention to international tensions and domestic excitements and not enough to arithmetic, particularly to the importance of ordinal numbers. This qualifies as an enigma, but not an insuperable one. Here is an excellent and incomprehensible chart --from Wikipedia-- that will reward our scrutiny:

In the chart above, each turn of the spiral represents one power of ω --or a 3 that has fallen asleep on its back-- and represents ordinal numbers up to ω^ω , or a 3 that is both asleep and dreaming that it is asleep.

In set theory, an ordinal number, or just ordinal --if you are on a first name buddy-buddy basis with it-- is a type of a well-ordered set. It is most often identified with hereditarily transitive sets --born that way. Ordinals are an extension of natural numbers (numbers captured wild, then trained and sometimes even civilized) different from integers (Latin, interdigitus --numbers you can count on your fingers) and cardinals (numbers who dress like hand puppets and can vote for new Popes).

Like other numbers, ordinals can be added, multiplied or exponentiated. Exponentiatiaton, being the most expensive of the three, is an arithmetical status reserved for royalty. Thus did the child of Henry the Eighth (ordinal number) and his third wife (exponent 3), Jane Seymour, produce an heir to the throne (8 cubed) known as King Edward The Five Hundred And Twelfth, who shortened his name to Edward VI (his cube root minus 2 parents) so he could get a fake I.D. and buy beer.

Ordinals were introduced by mathematician, Georg Cantor, in 1883 to accommodate infinite sequences and classify certain orderly sets apart from sets that used foul language and started barroom brawls. He derived them by accident while working on a problem concerning trigonometric series when Sir Isaac Newton fell on his head. Although principal characters in this account were not contemporaries and lived centuries apart, such minor differences were set aside in view of the problem and its immense gravity. Would that the world do likewise.