Neither the reals nor the naturals “exist”. We produce them as we need them. Reals and naturals both have the same number of symbols: unknowable (“infinity”).

Neither the reals nor the naturals “exist”. We produce them as we need them. Reals and naturals both have the same number of symbols: unknowable (“infinity”). > Feel free to give me a generator function and I will give you a finite number that it cannot reach in finite steps. f(n)=n If you give n to that formula, it will generate n in 1 step. > On the other hand, try giving me a finite positive integer that I cannot reach in finite steps. Can’t come up with one. As long as is finite you can always just output the number itself. Anything finite is countable. Anything infinite is unknowable.