On Tuesday, 11 June 2013 18:50:54 UTC+2, Zeit Geist wrote: > However, in set theory, if we have an axiom of infinity then we can define a function ( with finite number of symbols ) to do the task. This works very well enumerating the set of rationals, or to find the diagonal of a countably infinite list of real numbers.
Why should it work less well for the aleph_0 steps of well-ordering the rations by magnitude?
Every step is well-defined such that we, you and me, when starting with the same enumaration of |Q, will up to step n (for every n) get the same result including as many rationals as we like. And if we apply the axiom we get that for all steps.
Mathematics is an ideal theory that doesn't not necessarily correspond directly with reality.
Matheology is in direct contradiction with reality, science, and sanity.
> Despite the lack of correspondence, Science finds Mathematics useful in its endeavors.
Yes, but never matheology which is even less scientific as astrology.
> Even the Infinite! Supertasks are not physically possible. You can't increase the efficiency of a machine, or operation, an infinite number of times ( in reality ). Supertasks are a nice heuristic theory used to explain the Infinite to people who lack the Mathematical intuition of the Infinite.
Every application of the axiom of infinity generates a super task. Enumerating all rationals is but one example that is so simple that most people do not realize its character as a super task.