On Friday, May 2, 2014 2:46:55 PM UTC-4, muec...@rz.fh-augsburg.de wrote: > 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. >
So, you don't have formal proof. Just more hand-waving. Thought so.
When it comes to foundational issues, everything must eventually be formally defined or proven.
So, get busy, WM! Start by fully understanding what a formal proof is. Imagine that a computer, without any knowledge of the outside world is checking your proof against a pre-determined list of rules and axioms. Every line must be justified by citing exactly one of them. My software may help you help you get into the right mindset.