On Friday, 2 May 2014 20:35:19 UTC+2, Dan Christensen wrote:
> > 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. > > > How do "we" know this? Is it too much to ask for a formal proof?
Yes, such things usually are learned before formalism are used to veil mathematical facts. Every person discussing here should know it.
> > > Nothing that can appear in this discourse, which *is* mathematics, can be uncountable.
> Makes no sense.
What? That only things that can appear in discourse can belong to mathematics? Otherwise you would have to believe in things that cannot be mentioned. That does not make sense, in particular since every result of every uncountability "proof" can be mentioned.
> > > Some matheologians have argued that "definition" cannot be definied, therefore we could not talk about the countable set of definable numbers. >
> Makes perfect sense to me.
We need not count numbers only. We can count everything that can be mentioned. Numbers are a subset of this set of all things that can be mentioned. >
> > 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". >