> > if you pick a real number uniformly at random between 0 and 1, there is literally zero chance that you will pick a rational number. > Unfortunately, beca

> > if you pick a real number uniformly at random between 0 and 1, there is literally zero chance that you will pick a rational number. > Unfortunately, because the computable numbers are countable, the set of irrational numbers that you will almost surely see in your setup will almost surely be uncomputable. That only applies if you assume some continous distribution. The world may for all we know be discrete and finitary, and so it may be that any real number which pops up is computable. And surely there is nothing preventing a measuring instrument to produce irrational numbers. It is just that it will still be an approximation, and thus there are rational numbers which are just as close to the real value.