On Mar 14, 10:07 am, Tonico <Tonic...@yahoo.com> wrote: > On Mar 14, 5:23 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com> > wrote: > > > On Usenet, 1+1=2 is controversial. > > No, that's a fact. > Yes...exactly as |N| = Aleph_o and |N| < |R| are facts within ZFC and > the current definitions...exactly the very same.
I've stated before that I definitely do _not_ consider "1+1=2" and "card(N)<card(R)" to be "exactly the very same." In particular, I consider those who refute the former to be indefensible, but not those who refute the latter.
Why? Surely "1+1=2" solves many more real-world problems than "card(N)<card(R)" does. And if one's going to dig deep to find problems not solved by "1+1=2" (pianos, rabbits, etc.), but then "card(N)<card(R)" doesn't help us with pianos or rabbits either. I don't draw the line of defensibility at what ZFC proves or refutes.
So to me, "1+1=2" is noncontroversial, but "card(N)<card(R)" is a controversial statement.
