The well ordering theorem is proved by "negation" (assume there was not, then you prove that any real number can be either equal, larger or smaller than itself, contradiction, QED) no need for the axiom of choice, but when you got into set theory and deal with sets that contains themselves, you are frozen without the axiom of choice. (g). As for ordering dimples, there are different sets of dimples; lone dimples within a set of fully detached chads, single dimples in otherwise untouched ballots (why bother and vote?), and a "presidential" dimple, in association with an admixture of dimples and variously detached chads. The logic of ordering varies according to each set. No axiom of choice necessary, I would say that any logician would tell you discard set one and accept all "presidential dimples" on the rest.
As for the theory of numbers corollary, poor Cantor must be turning in his grave seeing people only treating "Alef 0" as a measure for all "possible" voting intents, he would have liked you to go to at least "Alef 1", and he would be happy to prove that there are at least "Alef 0" and no more than "Alef 0" of "Alef n"'s. (g), obeying the inductive rule "Alef n" < "Alef n+1".
Gee, it has been some time since I had to handle these concepts... I wonder how useful would Cantor's theory be in analyzing the market?
Zeev |
