3 ms·
Well, first you would have to explain what you mean by your statement.
by auggierose 5y ago
Well, first you would have to explain what you mean by your statement.
- l33t2328 5y agoI mean that for any epsilon > 0, you can have a set of intervals of the form (a_i, b_i) where every rational number is in some interval and the sum over all i of b_i - a_i < epsilon. That is, you can cover the rationals with intervals of arbitrarily small total length.
- auggierose 5y agoI see. But is that not just a simple conclusion of the fact that the rationals are countable, and that there exists a converging series of positive numbers?
- l33t2328 5y agoRight but explaining why the reals are different is the tricky part