3 ms·

If we want to open the floodgates on being too pedantic, I think there are uncountably more irrational numbers close to any rational number than there are ratio

• dllthomas 3y ago
  > If we want to open the floodgates on being too pedantic It's math. There's no such thing as "too pedantic", as long as you're being interesting and not mean about it. > I think there are uncountably more irrational numbers close to any rational number than there are rational numbers close to an irrational number. I think that's right. Irrationals near a rational are almost certainly uncountable, as otherwise I think we can force all the irrationals to be countable by bucketing them. I think that concern is countered if any bucket has to be uncountable, but if it's not all that makes some rationals special in a way they probably aren't. Rationals near an irrational is definitely countable, as all the rationals is countable.