Quote from: AgeraS on February 22, 2014, 07:09:42 PM

As bitcoin approaches 2140, when "the last satoshi is created," how does the protocol handle this operation? Additionally, when people say, "there will never be more than 21 million bitcoins created," does that mean that technically there will not be more than 21 million bitcoins but that there can be slightly more than 21 million and it will never hit 22 million? In other words, is there an asymptote at 21 million, or 22 million, or neither because when the last satoshi is created is the exact same time it technically hits 21 million and the protocol checks and stops coinbase rewards?

Since the block reward started at 50 BTC, and halves every 4 years, then the total amount of btc produces is a geeometric series, which has a finite sum, of 21 million.

If there was infinite precision to the coins, then it would exactly hit 21 million. However, the coins cannot be subdivided more that the 8th decimal place. At one point, the halving of the reward will get lossy, and the coins actually rewarded will always be the "perfect" value rounded down to the nearest satoshi.

At one point the coins rewarded will be rounded to 0, and no more bitoins will be created. But since along the way, the rounding was always down, a little less that the "perfect" amount will have been created.

That being said, it is very possible that some times in the future, the protocol gets updated to allow a greather subdivision of the coins. (21 million bitcoins gives about 1000 satoshis per human being. It is not a lot of precision.) If it happens, then maybe the lossyness of the halving will start later, and the total amount of btc will be nearer to the "perfect" value.

ALSO, as it has been said earlier in the thread, some coins that were mined early on have been permently destroyed. So the total coins in circulation will be even lower than that.