Question

Give a satisfying explanation for the real numbers being a much larger set than the natural numbers or the rational numbers.

Answer 1

i think there's a theorem for that ...

Answer 2

how about the fact that between any to natural numbers there is an infinite number of reals? it's at least intuitive

Answer 3

It's because real numbers is the MASTER-set(lol) and then the rational numbers is a subset. Natural numbers is then a subset of the rational numbers.

Answer 4

there are more real numbers in 0 and 1 than the set of natural numbers

Answer 5

Real numbers include the irrational numbers too.