Bitcoins are generated through mining. There will be a total of 21,000,000 Bitcoins generated.
Bitcoins are mined at a pre-determined rate by powerful computers using a lot of resources to solve increasingly complicated mathematical problems. A Bitcoin is equivalent to 100,000,000 divisible elements called satoshis (named after the bitcoin inventor, Satoshi Nakamoto). This means it is possible to buy 0.0000001BTC. No one knows the future but it is likely that mining will continue, because transaction fees will make it worthwhile to do so. In the future Bitcoins may be further divisible if or when the need arises.
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