5 ms·
> Here are some more irrational numbers expressed in this way Rather, rational numbers awfully close (in ordinary human terms) to specific, well known irration
by dllthomas 3y ago
> Here are some more irrational numbers expressed in this way
Rather, rational numbers awfully close (in ordinary human terms) to specific, well known irrational numbers. There are, I think, just as many irrational numbers comparably close to any rational number.
- tashi 3y agoIf 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 rational numbers close to an irrational number. But in both cases, it's definitely a bunch.
- 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.