2 ms·

For (any subset of)rational numbers there exist many simple algorithms to form an ordering. eg. Take the number is reduced for `(+/-)a/b`. A number is smaller i

For (any subset of)rational numbers there exist many simple algorithms to form an ordering. eg. Take the number is reduced for `(+/-)a/b`. A number is smaller if its `a+b` is smaller. In case of tie number is smaller if its `a` is smaller. Even in case of tie positive number is smaller. I don't know the proof but there could be no algorithm like that for real numbers.

wizzwizz4 5y ago
$<$ gives an ordering over the reals. It's an ordering with a first element that's the tricky bit.