20 feet is fine unless you want 4K 120 Hz and stuff like that. I'm which case 20 feet may also be fine with a passive cable, but a bit on the edge of where AOC starts to make sense.
As for 1080p and 4K30 I think 10 meters can work passively.
Edit: My in-head unit conversion was a bit off, 20 feet is probably a bit over what's sensible for 4K120. But it's probably fine for non-UHS HDMI.
No, because that "some point" will never happen. There is no last nine to round up, because if there were a last nine, they wouldn't be infinitely many.
There are many different proofs of this online, more or less rigorous.
Well, most of the time. There's this bastard: Ø.
That's a letter, not a zero. Second-to-last letter in the Danish and Norwegian alphabets. We Swedes use Ö instead.