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A state controls the money supply by granting itself a monopoly on money production (i.e. it outlaws the production of "counterfeit" money). Bitcoin uses a different strategy — while anyone is allowed to make bitcoins, the increasing production costs ensure there will only be a limited supply. At leasts that's my understanding of how bitcoin works. At any rate, none of this has anything to do with being fiat money. Fiat money means that the money is backed by "trust", i.e. people accept it as currency because they trust that others will also accept it.

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