Godel's theorem applies to systems that model the natural numbers (specifically, Robinson arithmetic), not real numbers. The first-order theory of the real num

Godel's theorem applies to systems that model the natural numbers (specifically, Robinson arithmetic), not real numbers. The first-order theory of the real numbers is decidable. (The second-order theory is not, since you can define the natural numbers in that, and then Godel's theorem applies.) Your general point, of course, that Godel's theorem means a specific thing, and people should stop abusing it as if it means "everything has loopholes!", remains correct.