This is why transaction fees will increasingly be important as BTC matures, after all 21 Million are gone the only reward for "mining" will be the award of all transaction fees paid for transactions in that block, so much like the old west, mining is gradually replaced with banking/processing :-)
The reward for mining a block just halved; it'll continue to halve as the supply increases, so that 21 million is not the endpoint so much as it is an asymptote.
It will continue to halve, exactly one more time to 12.5, and then the next time after that, it will stop. Once the 12.5 reward is gone, the network will be supported entirely by transaction fees, and no new bitcoins will be created.
So, yes, asymptote, but the rest of your comment seems misleading. It will halve once more, that's not exactly "continue to halve."
I was also wondering how to reconcile this (seemingly very) early first halving with my concept of a 21 year bitcoin generation span. Thanks for clearing that up!
*edit: Turns out I was misinformed about the 21 year thing too. These projections have the halving terminating estimated at 2140. Don't suppose either of us will be around to see it.
And, actually, it may continue well beyond 2140. The only reason it would stop there is because the smallest value bitcoin can currently represent is 0.00000001 BTC (1e-8). Many people believe that the rising value of bitcoin will bring about a need to increase the number of decimal places that bitcoin supports. If this change is made to the protocol before 2140, the the mining reward will probably keep on halving to values even less than 1e-8 BTC.
I like it. Produce the proof that your rig solved the latest block, and you get your name in the book. Sounds much better than "no further rewards will be issued from this date."
[1] - https://en.bitcoin.it/wiki/Controlled_Currency_Supply#Projec...