Zeev,
Mathematical proof of existence is much weaker than the construction of the mapping fcn and the ordering itself. Now, for our purposes, if the subsets of scale factors for dimpled ballots have to be ordered, it is not sufficient to say that a well-ordering exists, such a well-ordering has to be constructed.
It is also clear that various states of dimpleness can exist, and if eg. the max-distance of the deepest point of a molecule on the surface of the dimple from the surface of the ballot was taken to be a the mapping function (normalized to (0,1) ) = delta then there can always be a smaller dimple that has scale=delta/2. If these ballots were counted in broward county, it would mean that the set that your logician would have us discard might turn out to have cardinality of 0. (vbg). After all, where magnifying glasses stop, there are always microscopes and electron microscopes. (vbg)
(vbg) Why does the well-ordering have to be constructed? If not constructed, there is no standard. In one universe, a dimple will have a different scale from the same dimple in a second universe, and we know what happens when there is no standard. (vbg)
MORE tortured metaphors. It's gone past all that, and but wasn't it interesting after day30 with no president-elect, some great theoretical mathematicians might be wondering (vbg) if they could borrow (vbg) Meyer's application of Zorn's Lemma to prove the existence of God and use it to prove the existence of a president-elect (end of more tortured metaphors) (vbg)
...boy! This is more fun than a baby's rattle on a rubber snake.
SbH |
