@Cerberus I'm pretty sure you're happy with the explanations that people gave about 'non-real' numbers, but of course I can't stop poking the bear.
Most people think that all the numbers there are are in the continuum (informally distances that can be subdivided as much as you like).
But, in trying to formalize what a 'distance' might be, you could try to reduce it (explain it) in terms of things that are much easier t ounderstand,
I'll take it for granted that integers are 'accessible' (easily understood) and that ratios of integers are too then. We'll call the latter fractions or 'the …