On 18 Mrz., 07:26, fom <fomJ...@nyms.net> wrote: > > You turn to an outdated strategy directed to > a situation that no longer exists rather > than do the hard work of grounding your > claims. You do this to say that just > because you do not believe a particular > axiom,
Wrong. I prove that the axiom is nonsense liek the axiom that a triangle with four edges exists.
Of course I presume that in mathematics facts can be proven. A simple statement of faith in the Cartesian product cannot be overcome. So be satisfied, nobody will ever cause you to change your belief, if it is only fimr enough. You may even include the belief that you are doing mathematics or logic.
> Yet, there is an > established criterion for demonstrating > that the axiom you do not believe > is, in fact, in error.
If the inhabitants of a mad house establish a criterion I am not obliged to accept it.
> You say that > you do not need to respect this > criterion. Nor, do you elucidate > an alternate criterion that others > might consider.
Hahaha. Every axiom, beginning with Euclid, established or formalized a triviality. AC formalizes a counterfactuality.
To choose a number means to name it. There are not enough names to name uncountably many numbers. This proves for everybody except those who are or should be in mad houses that the axiom of choice is wrong.