On Friday, 2 May 2014 16:54:15 UTC+2, Dan Christensen wrote:
> > After over a century of intensive scrutiny,
Wrong. Most mathematicians have simply accepted what their leaders said. Some have really found contradictions but they have been silenced, i.e., their papers have rarely been mentioned by the leading matheologians.
> no one has been able to demonstrate any inconsistency arising from that the Peano's Axioms for the infinite set of natural numbers.
There is no inconsistency if |N is interpreted as a potentially infinite set.
But we know that every expression that can appear in eternity in the whole, possibly infinite, universe belongs to a countable set. Therefore also every expression that can appear in the mathematical discourse belongs to a countable set.
Nothing that can appear in this discourse, which *is* mathematics, can be uncountable.
Some matheologians have argued that "definition" cannot be definied, therefore we could not talk about the countable set of definable numbers. But they who have argued so and they who have accepted it must be fools or, if intelligent, swindlers. We do *n* need any definition of "definition". It is enough to prove that every expression belongs to a countable set and every real number must be used in mathematics by a finite expression each time it appears in mathematics. >