That doesn't actually follow- even though the reals are uncountable, they're what's called "separable", which means that there is a countable set which is "arbi

That doesn't actually follow- even though the reals are uncountable, they're what's called "separable", which means that there is a countable set which is "arbitrarily good at approximating them", basically- the rationals! So even though there are uncountable reals, for any real number, you can find rational numbers that get arbitrarily close. You can actually see this pretty easily if you think of reals in decimal notation- sqrt(2) is irrational, but 1.4, 1.41, 1.414, 1.4142, 1.41421, 1.414123, ... etc are all rational numbers that get closer and closer to sqrt(2). So you should think of real numbers as uncountable, but nonetheless surrounded by rationals no matter how close you zoom in.