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.
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 rational numbers close to an irrational number. But in both cases, it's definitely a bunch.
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.
Comments
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.
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 rational numbers close to an irrational number. But in both cases, it's definitely a bunch.
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 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.