6 ms·
He's associating to each x in [0,1) an infinite sequence of natural numbers (just like decimal representations do), and there's uncountably many such sequences
by ginnungagap 4y ago
He's associating to each x in [0,1) an infinite sequence of natural numbers (just like decimal representations do), and there's uncountably many such sequences
- yarg 4y agoBut he's defining the numbers with a property that makes them countably infinite? prefix = '0.'; queue = new Queue(prefix); for(;;){ s = queue.poll(); for(c:['0'...'9']){ queue.add(s + c); } } When the constraint is "run forever" I don't think that the generator he defined produces results any different from the snippet above.
- yarg 4y agoI may have misread that one, but I still think the reverse mapping only gets as far as within arbitrary bounds.
- yarg 4y agoThe part that seems problematic is "each real number" the reals exist across bounds, I'm not sure there can be an "each". I think his iterator is generating infinitesimals of rational and not continuous nature.