Yeah, I'm sure there are some holes (poor attempt at a pun), but you already know you can get arbitrarily close to whatever bound with rationals, much less computables, so it seems like someone better educated than me could shore that up.

Anyways, the computables have unfortunate properties too (not knowing if you'll eventually need to carry for addition, or when to stop testing for equality), so I'm left wondering if some genius in the future will come up with a new way to build the numbers which are more satisfying.

Thank you for the Reddit link.