I understand that the supply of Bitcoins, by design, will not continue to grow to infinity, but is "capped" at 21,000,000. This amount is not in circulation, however, because there are coins that have yet to be mined. I also understand that the reward for a successful miner is 25 coins, but that the reward will be reduced by a factor of 0.5 at certain points. It seems like the supply of coins will always approach 21,000,000 but never actually get there - a limit. If this is all accurate (please correct me if it isn't), does this imply that the incentives for miners will also be reduced? As time goes on, following this logic, miners should stop working altogether, at which point, new transactions can no longer be added.
Assuming this all plays out, would people simply "roll" into a new blockchain at that time?