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The maximum number of bitcoins that can exist is 21 million. New bitcoins are made by confirming that transactions happened. Every 4 years the amount of bitcoins people get when they solve a block is halved. When you keep on halving something you never get zero, so someone will always get paid some amount of bitcoins, but the max number of bitcoins that can exist is 21 million. So how is the total number of bitcoins not going to go over 21 million?
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This is more a math question, but basically, the sum is a geometric series:
https://en.wikipedia.org/wiki/Geometric_series
1/2 + 1/4 + 1/8 + 1/16 + ... = 1
That's basically what's happening here except with 21 million instead of 1.
This does serve to correct the misconception, but in fact there is a simpler reason: in the actual Bitcoin protocol, the halving does not continue indefinitely. Beyond a certain block, the reward is simply 0, so we are dealing with a finite sum, not an infinite series. – Nate Eldredge – 2015-11-07T07:22:33.040
Actually, each halving gives an upper limit on how many bitcoins may be created in the reward. At some point, a halving takes this below one satoshi, and thusly the reward cannot give out anything more than 0 satoshis. The halving continues though. – Murch – 2015-11-07T15:50:13.020
@NateEldredge if that is true what will make people want to confirm transactions? – Riley Potts – 2015-11-08T07:13:35.043
@Riley: Transaction fees, in theory. You can find this discussed in many questions on this site. – Nate Eldredge – 2015-11-08T08:04:20.637
@NateEldredge transaction fees halfed? Or what? – Riley Potts – 2015-11-08T08:23:51.017
@RileyPotts: The mining reward is composed of two parts: The transaction fees and the block reward. The block reward is halved as described above. The transaction fees are roughly proportional to the number of transaction in a block as most transactions should attach a fee. – Murch – 2015-11-11T15:24:45.960
possible duplicate of How many bitcoins will there eventually be?
– Murch – 2015-11-07T15:55:58.630Similar paradox: When traveling to any destination, you always have to halve the remaining distance before you get there. No matter how far away you are, there will always be a half way point between you and the destination. Therefore you can never reach the destination, since there is always a half way point to arrive at first. – Brad Thomas – 2015-11-07T16:16:03.457