Hmm, Ordinal Numbers...

In the last post, Why Ordinal Numbers, I had intuitively guessed that I would be left with a perfect set after enough application of derived sets on \({S}\). By the end, I gave an example of a set that had a nonempty “infinite” derived set, \({S^{(\infty)},}\) that was not ...


Why Ordinal Numbers?

It's about time I write on a non-Euler topic -- the birth of ordinals. I've been reading Georg Cantor's Contributions to the Founding of the Theory of Transfinite Numbers. In two papers published in 1895 and 1897, Cantor creates the theory of cardinals and ordinals from the ground ...